143 + Interview Questions in CONSTRUCTIONS IN GENERAL AWARENESS Page 2 InterviewSolution

51.	A line segment connecting two opposite vertices is called(a) side(b) diagonal(c) hypotenuse(d) base
Answer» A line segment connecting two opposite vertices is called hypotenuse.

Discussion

52.	Given below are the steps of construction of a pair of tangents to a circle of radius 6 cm from a point on the concentric circle of radius 8 cm. Find which of the following steps is INCORRECT? Steps of Construction Step I : Take a point O on the plane paper and draw a circle of radius OA = 6 cm. Also, draw a concentric circle of radius OB = 8 cm. Step II : Find the mid-point A of OB and draw a circle of radius BA = AO. Suppose this circle intersects the circle of radius 6 cm at P and Q. Step III : Join BP and BQ to get the desired tangents. (A) Step I(B) Step II(C) Step I and Step II(D) Step II and Step III
Answer» Step II of construction of a pair of tangents to a circle of radius 6 cm from a point on the concentric circle of radius 8 cm.

Discussion

53.	Which of the following steps of construction is INCORRECT while dividing a line segment of length 3.2 cm in the ratio of 3 : 5 internally.Steps of ConstructionStep I : Draw AB = 3.2 cmStep II : Construct an acute ∠BAX.Step III : On AX make 3 + 5 + 1 i.e. 9 equal parts and mark them as A1, A2, A3, A4, ..... A9Step IV : Join B to A8. From A3 draw A3C parallel to A8B. Point C divides AB internally in the ratio 3 : 5.Thus, AC : CB = 3:5.(A) Step II (B) Step III(C) Step IV (D) None of these
Answer» The correct option is: (B) Step III Explanation: Step III is incorrect as on X make 3 + 5 = 8 equal parts and mark them as A₁, A₂, A₃, A₄, ..... A₈ .

53.

Which of the following steps of construction is INCORRECT while dividing a line segment of length 3.2 cm in the ratio of 3 : 5 internally.Steps of ConstructionStep I : Draw AB = 3.2 cmStep II : Construct an acute ∠BAX.Step III : On AX make 3 + 5 + 1 i.e. 9 equal parts and mark them as A1, A2, A3, A4, ..... A9Step IV : Join B to A8. From A3 draw A3C parallel to A8B. Point C divides AB internally in the ratio 3 : 5.Thus, AC : CB = 3:5.(A) Step II (B) Step III(C) Step IV (D) None of these

Answer»

The correct option is: (B) Step III

Explanation:

Step III is incorrect as on X make 3 + 5 = 8 equal parts and mark them as A₁, A₂, A₃, A₄, ..... A₈ .

Discussion

54.	Can you draw a rhombus ZEAL where ZE = 3.5 cm, diagonal EL = 5 cm? Why?
Answer» Yes, the rhombus ZEAL with the given data can be drawn as it can be divided into two triangles ZEL and LEA.

Discussion

55.	A `DeltaABC` can be constructed in which `angleB = 60^(@), angleC = 45^(@) and AB + BC + CA = 12 cm`.
Answer» Correct Answer - 1 we know that sum of angles of a triangle is `180^(@)` `:. angleA + angleB+ angleC = 180^(@)` Here, `angleB + angleC = 60^(@) + 45^(@) = 105^(@) lt 180^(@)`, Thus, `DeltaABC` with given conditions can be constructed.

Discussion

56.	A `DeltaABC` can be constructed in which `angleB = 105^(@), angleC = 90^(@) and AB + BC + CA = 10 cm`.
Answer» Here, `angleB = 105^(@), angleC = 90^(@)` and `AB + BC + CA = 10cm` we know that , sum of angles of a triangle is `180^(@)`. `:. angleA + angleB + angleC = 180^(@)` Here, `angleB + angleC = 105^(@) + 90^(@)` = `195^(@) gt 180^(@)`, which is not true. Thes, `DeltaABC` with given conditions cannot be constructed.

Discussion

57.	The constuction of a `Delta` ABC, given that BC = 3cm, `angleC = 60^(@)` is possible when difference of AB and AC is equal toA. `3.2`cmB. `3.1`cmC. 3cmD. `2.8` cm
Answer» Correct Answer - D Given, BC = 3cm and `angleC = 60^(@)` We know that , the construction of a triangle is possible, if sum of two sides is greater than the third side of the triangle i.e., `AB + BC gt AC` `rArr BC gt AC - AB` `rArr 3 gt AC - AB` So, if AC - AB = `2.8`cm, then construction of `DeltaABC` with given conditions is possible.

Discussion

58.	`DeltaABC` can be constructed in which `BC = 6cm, angleC = 30^(@) and AC - AB = 4 cm`.
Answer» Correct Answer - 1 we know that, a triangle can be constructed if sum of its two sides is greater then third side. i.e., in `DeltaABC, AB + BC gt AC` `rArr BC gt AC - AB` `rArr 6 gt 4`, which is true , so `DeltaABC` with given conditions can be constructed.

Discussion

59.	An angle of `52.5^(@)` can be constructed.
Answer» Correct Answer - 1 To construct an angle of `52.5^(@)` firstly construct an angle of `90^(@)` , then construct an angle of `120^(@)` and then plot an angle bisector of `120^(@) and 90^(@)` to get an angle `105^(@) (90^(@)+15^(@))` Now, bisect this angle to get an angle of `52.5^(@)` .

Discussion

60.	Write True or False and give reasons for your answer.An angle of 67.5° can be constructed.
Answer» True. As 67.5° = 135/2 = 1/2 (90 + 45).

60.

Write True or False and give reasons for your answer.An angle of 67.5° can be constructed.

Answer»

True.

As 67.5°

= 135/2

= 1/2 (90 + 45).

Discussion

61.	Write whether True or False and justify your answer.An angle of 52.5° can be constructed.
Answer» True To construct an angle of 52.5° firstly construct an angle of 90°, then construct an angle of 120° and then plot an angle bisector of 120° and 90° to get an angle 105° (90° + 15°). Now, bisect this angle to get an angle of 52.5°.

61.

Write whether True or False and justify your answer.An angle of 52.5° can be constructed.

Answer»

True

To construct an angle of 52.5° firstly construct an angle of 90°, then construct an angle of 120° and then plot an angle bisector of 120° and 90° to get an angle 105° (90° + 15°). Now, bisect this angle to get an angle of 52.5°.

Discussion

62.	A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
Answer» Correct Answer - False Since, the radius of the circle is 3.5 cm i.e., r=3.5 cm and a point P situated at a distance of 3 cm from the centre i.e, d=3 cm We see that, `r gt d` i.e.,a point P lies inside the circle. So, no tangent can be drawn to a circle from a point lying inside it.

Discussion

63.	By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3):(1)/(sqrt(3))`.
Answer» Correct Answer - True Given, ratio `= sqrt(3):(1)/(sqrt(3))` Required ratio = 3:1 [ multiply `sqrt(3)` in each term ] So, `sqrt(3):(1)/(sqrt(3))` can be simplified as 3:1 and 3 as well as 1 both are positive integer. Hence, the geometrical construction is possible to divide a line segment in the ratio 3:1

Discussion

64.	The diagonal AC is drawn in a square ABCD then Δ ABC is a …………………. A) EquilateralB) Isosceles C) Scalene D) None
Answer» B) Isosceles

Discussion

65.	Diagonals are equal in ………………….. A) Kite B) Trapezium C) Rhombus D) Square
Answer» Correct option is D) Square

Discussion

66.	The side of a Rhombus is 5 cm then its perimeter is ………………..cm. A) 16 B) 19 C) 1D) 20
Answer» Correct option is (D) 20 \(\because\) All sides are equal in a Rhombus. Given that side of a Rhombus is 5 cm. \(\therefore\) Perimeter of Rhombus = Sum of all 4 sides = 4 \(\times\) 5 = 20 cm Correct option is D) 20

66.

The side of a Rhombus is 5 cm then its perimeter is ………………..cm. A) 16 B) 19 C) 1D) 20

Answer»

Correct option is (D) 20

\(\because\) All sides are equal in a Rhombus.

Given that side of a Rhombus is 5 cm.

\(\therefore\) Perimeter of Rhombus = Sum of all 4 sides

= 4 \(\times\) 5 = 20 cm

Correct option is D) 20

Discussion

67.	If the diagonals of a Rhombus are equal then it is a ……………… A) Kite B) RhombusC) Square D) None
Answer» Correct option is C) Square

Discussion

68.	In order to make the given Quadrilateral as a parallelogram ……………. should happen.A) PQ = RS B) RQ = PS C) PQ \|\| SR D) All the above
Answer» Correct option is (D) All the above In parallelogram, opposite sides are equal and parallel. D) All the above

68.

In order to make the given Quadrilateral as a parallelogram ……………. should happen.A) PQ = RS B) RQ = PS C) PQ || SR D) All the above

Answer»

Correct option is (D) All the above

In parallelogram, opposite sides are equal and parallel.

D) All the above

Discussion

69.	Number of vertices in a Quadrilateral is ………………….. A) 2 B) 3 C) 4 D) 5
Answer» Correct option is C) 4

Discussion

70.	Number of diagonals in a Quadrilateral is ………………. A) 3 B) 6 C) 4 D) 2
Answer» Correct option is D) 2

Discussion

71.	In the square ABCD, ∠BAC = ……………..A) 70° B) 45° C) 80° D) 60°
Answer» Correct option is (B) 45° \(\because\) AB = BC (sides of square ABCD) \(\therefore\) \(\triangle ABC\) is an isosceles triangle. \(\therefore\) \(\angle BAC\) = \(\angle ACB\) ______(1) (Opposite angles of equal sides are equal) Now in \(\triangle ABC\), \(\angle ABC\) = \(90^\circ\) (angle in square) Also, \(\angle ABC+\angle BAC+\angle ACB\) \(=180^\circ\) (Sum of angles in a triangle) \(\Rightarrow\) \(90^\circ+\) \(2\angle BAC\) \(=180^\circ\) (From equation (1)) \(\Rightarrow\) \(2\angle BAC\) \(=180^\circ-90^\circ\) \(=90^\circ\) \(\Rightarrow\) \(\angle BAC\) \(=\frac{90^\circ}2\) = \(45^\circ\) Correct option is B) 45°

71.

In the square ABCD, ∠BAC = ……………..A) 70° B) 45° C) 80° D) 60°

Answer»

Correct option is (B) 45°

\(\because\) AB = BC (sides of square ABCD)

\(\therefore\) \(\triangle ABC\) is an isosceles triangle.

\(\therefore\) \(\angle BAC\) = \(\angle ACB\) ______(1) (Opposite angles of equal sides are equal)

Now in \(\triangle ABC\), \(\angle ABC\) = \(90^\circ\) (angle in square)

Also, \(\angle ABC+\angle BAC+\angle ACB\) \(=180^\circ\) (Sum of angles in a triangle)

\(\Rightarrow\) \(90^\circ+\) \(2\angle BAC\) \(=180^\circ\) (From equation (1))

\(\Rightarrow\) \(2\angle BAC\) \(=180^\circ-90^\circ\) \(=90^\circ\)

\(\Rightarrow\) \(\angle BAC\) \(=\frac{90^\circ}2\) = \(45^\circ\)

Correct option is B) 45°

Discussion

72.	To construct a rectangle we need …………… independent measurements. A) 1 B) 2 C) 6 D) 4
Answer» Correct option is B) 2

Discussion

73.	The sum of adjacent angles in a parallelogram is ……………………. A) 190° B) 180° C) 200° D) 300°
Answer» Correct option is B) 180°

Discussion

74.	Area of rectangle is ……………… A) l + b B) 2 (l + b) C) l2b2D) lb
Answer» Correct option is D) lb

Discussion

75.	Number of angles in a Quadrilateral is ………………… A) 2 B) 4 C) 6 D) 3
Answer» Correct option is B) 4

Discussion

76.	Identify the correct among the following. A) Each angle in a rectangle is 90° B) Rhombus will have 5 sidesC) A Quadrilateral has two diagonals D) Each angle in a square is 50°
Answer» Correct option is (A) Each angle in a rectangle is 90° (A) Each angle in a rectangle is \(90^\circ.\) This statement is a correct statement. (B) Rhombus will have 4 sides. Thus, given statement 'Rhombus will have 5 sides' is a wrong statement. (C) \(\because\) A Quadrilateral has two diagonals \(\therefore\) 'A Quadrilateral has three diagonals' is a wrong statement. (D) \(\because\) Each angle in a square is \(90^\circ.\) \(\therefore\) 'Each angle in a square is \(50^\circ\)' is a wrong statement. A) Each angle in a rectangle is 90°

76.

Identify the correct among the following. A) Each angle in a rectangle is 90° B) Rhombus will have 5 sidesC) A Quadrilateral has two diagonals D) Each angle in a square is 50°

Answer»

Correct option is (A) Each angle in a rectangle is 90°

(A) Each angle in a rectangle is \(90^\circ.\) This statement is a correct statement.

(B) Rhombus will have 4 sides. Thus, given statement 'Rhombus will have 5 sides' is a wrong statement.

(C) \(\because\) A Quadrilateral has two diagonals

\(\therefore\) 'A Quadrilateral has three diagonals' is a wrong statement.

(D) \(\because\) Each angle in a square is \(90^\circ.\)

\(\therefore\) 'Each angle in a square is \(50^\circ\)' is a wrong statement.

A) Each angle in a rectangle is 90°

Discussion

77.	Each angle in a square is …………………. A) 90° B) 70° C) 80° D) 100°
Answer» Correct option is A) 90°

Discussion

78.	Number of sides in a Quadrilateral is ………………… A) 4 B) 6 C) 3 D) 5
Answer» Correct option is A) 4

Discussion

79.	If each angle of 90° is to be bisected then the measure of each angle is A) 60° B) 70° C) 80° D) 45°
Answer» Correct option is (D) 45° If an angle of \(90^\circ\) is to be bisected. Then each obtained angles \(=\frac{90^\circ}2=45^\circ.\) Alternative :- Let angles x & y are angles which is obtained by bisecting an angle of \(90^\circ.\) \(\therefore\) x = y and x+y = \(90^\circ.\) \((\because\) Both angles obtained by bisecting an angle of \(90^\circ)\) \(\Rightarrow\) 2x = 2y = \(90^\circ\) \(\Rightarrow\) \(x=y=\) \(\frac{90^\circ}2=45^\circ\) Correct option is D) 45°

79.

If each angle of 90° is to be bisected then the measure of each angle is A) 60° B) 70° C) 80° D) 45°

Answer»

Correct option is (D) 45°

If an angle of \(90^\circ\) is to be bisected.

Then each obtained angles \(=\frac{90^\circ}2=45^\circ.\)

Alternative :- Let angles x & y are angles which is obtained by bisecting an angle of \(90^\circ.\)

\(\therefore\) x = y and x+y = \(90^\circ.\) \((\because\) Both angles obtained by bisecting an angle of \(90^\circ)\)

\(\Rightarrow\) 2x = 2y = \(90^\circ\)

\(\Rightarrow\) \(x=y=\) \(\frac{90^\circ}2=45^\circ\)

Correct option is D) 45°

Discussion

80.	Sum of 4 angles in a Quadrilateral is ……………….. A) 160° B) 300° C) 180° D) 360°
Answer» Correct option is D) 360°

Discussion

81.	Opposite angles of a parallelogram are …………………. A) Equal B) ParallelC) 100° D) None
Answer» Correct option is (A) Equal Opposite angles of a parallelogram are equal. Correct option is A) Equal

81.

Opposite angles of a parallelogram are …………………. A) Equal B) ParallelC) 100° D) None

Answer»

Correct option is (A) Equal

Opposite angles of a parallelogram are equal.

Correct option is A) Equal

Discussion

82.	The perimeter of the given Quadrilateral is ………………….A) a + b – c – d B) a + b + c + dC) a – b – c – d D) a – b +2c + d
Answer» Correct option is (B) a + b + c + d Perimeter of the given quadrilateral = Sum of all sides of given quadrilateral = a + b + c + d B) a + b + c + d

82.

The perimeter of the given Quadrilateral is ………………….A) a + b – c – d B) a + b + c + dC) a – b – c – d D) a – b +2c + d

Answer»

Correct option is (B) a + b + c + d

Perimeter of the given quadrilateral

= Sum of all sides of given quadrilateral

= a + b + c + d

B) a + b + c + d

Discussion

83.	In a parallelogram ………………. A) Opposite sides are parallel B) Diagonals are not equal C) Sum of adjacent angles is 180° D) All the above
Answer» D) All the above

Discussion

84.	In a Quadrilateral ABCD, ∠A + ∠B = 200° then ∠C + ∠D = ……………… A) 110° B) 180° C) 160° D) 300°
Answer» Correct option is (C) 160° \(\because\) Sum of all angles in a quadrilateral is \(360^\circ.\) \(\therefore\) In quadrilateral ABCD, \(\angle A+\angle B\) \(+\angle C+\angle D\) \(=360^\circ\) \(\Rightarrow\) \(200^\circ\) \(+\angle C+\angle D\) \(=360^\circ\) \((\because\angle A+\angle B=200^\circ)\) \(\Rightarrow\) \(\angle C+\angle D\) \(=360^\circ-200^\circ=160^\circ\) Correct option is C) 160°

84.

In a Quadrilateral ABCD, ∠A + ∠B = 200° then ∠C + ∠D = ……………… A) 110° B) 180° C) 160° D) 300°

Answer»

Correct option is (C) 160°

\(\because\) Sum of all angles in a quadrilateral is \(360^\circ.\)

\(\therefore\) In quadrilateral ABCD,

\(\angle A+\angle B\) \(+\angle C+\angle D\) \(=360^\circ\)

\(\Rightarrow\) \(200^\circ\) \(+\angle C+\angle D\) \(=360^\circ\) \((\because\angle A+\angle B=200^\circ)\)

\(\Rightarrow\) \(\angle C+\angle D\) \(=360^\circ-200^\circ=160^\circ\)

Correct option is C) 160°

Discussion

85.	The diagonals of a Rhombus will intersect at ……………….. A) 60° B) 90° C) 110° D) 80°
Answer» Correct option is (B) 90° Diagonals of a Rhombus bisect each other at right angle (i.e., \(90^\circ).\) Correct option is B) 90°

85.

The diagonals of a Rhombus will intersect at ……………….. A) 60° B) 90° C) 110° D) 80°

Answer»

Correct option is (B) 90°

Diagonals of a Rhombus bisect each other at right angle (i.e., \(90^\circ).\)

Correct option is B) 90°

Discussion

86.	How many pairs of sides are parallel in a Trapezium ? A) 2 B) 1 C) 6 D) 3
Answer» Correct option is B) 1

Discussion

87.	The diagonals of a Rhombus PQRS will intersect at ‘O’ then ∠SOR = ………………..A) 50° B) 60° C) 80° D) 90°
Answer» Correct option is (D) 90° \(\because\) Diagonals of a Rhombus bisect each other at right angle. \(\therefore\) \(\angle SOR\) = right angle = \(90^\circ\) Correct option is D) 90°

87.

The diagonals of a Rhombus PQRS will intersect at ‘O’ then ∠SOR = ………………..A) 50° B) 60° C) 80° D) 90°

Answer»

Correct option is (D) 90°

\(\because\) Diagonals of a Rhombus bisect each other at right angle.

\(\therefore\) \(\angle SOR\) = right angle = \(90^\circ\)

Correct option is D) 90°

Discussion

88.	The perimeter of a Rhombus is 40 cm then the length of its side is…………cm. A) 10 B) 16 C) 32 D) 70
Answer» Correct option is (A) 10 All 4 sides are equal in a Rhombus. Let one side is of length a unit in Rhombus. \(\therefore\) Perimeter of Rhombus = Sum of all 4 sides = 4a \(\Rightarrow\) 4a = 40 cm \((\because\) Perimeter = 40 cm (given)) \(\Rightarrow\) \(a=\frac{40}4\,cm\) = 10 cm Correct option is A) 10

88.

The perimeter of a Rhombus is 40 cm then the length of its side is…………cm. A) 10 B) 16 C) 32 D) 70

Answer»

Correct option is (A) 10

All 4 sides are equal in a Rhombus.

Let one side is of length a unit in Rhombus.

\(\therefore\) Perimeter of Rhombus = Sum of all 4 sides

= 4a

\(\Rightarrow\) 4a = 40 cm \((\because\) Perimeter = 40 cm (given))

\(\Rightarrow\) \(a=\frac{40}4\,cm\) = 10 cm

Correct option is A) 10

Discussion

89.	How do we do the justification in the questions of constructing similar triangles
Answer» I think you should follow the steps of similar triangles or by basic proportionality theorem for justification. This can help you understand the thing: https://www.sarthaks.com/31405/draw-triangle-abc-which-4cm-6cm-and-9cm-construct-triangle-similar-%CE%B4abc-with-scale-factor https://www.sarthaks.com/31398/construct-triangle-similar-given-triangle-with-sides-equal-corresponding-sides-triangle

89.

How do we do the justification in the questions of constructing similar triangles

Answer»

I think you should follow the steps of similar triangles or by basic proportionality theorem for justification.

This can help you understand the thing:

https://www.sarthaks.com/31405/draw-triangle-abc-which-4cm-6cm-and-9cm-construct-triangle-similar-%CE%B4abc-with-scale-factor

https://www.sarthaks.com/31398/construct-triangle-similar-given-triangle-with-sides-equal-corresponding-sides-triangle

Discussion

90.	When construction of a triangle similar to a given triangle in the scale factor 5/3 , then what is the nature of given triangle ?
Answer» Triangle is bigger than to original Δ.

Discussion

91.	Construction of triangles similar to a given triangle :
Answer» (a) Steps of constructions, when m < n: Step I. Construct the given triangle ABC by using the given data. Step II. Take any one of the three sides of the given triangle as base. Let AB be the base of the given triangle. step III. At one end, say A, of base AB. Construct an acute ∠BAX below the base AB. Step IV. Along AX mark off n points A₁,A₂,A₃,..............,An such that AA₁ = A₁A₂ = ........... = A_n-1A_n. Step V. Join AnB. Step VI. Draw A_mB' parallel to A_nB which meets, AB at B'. Step VII. From B' draw B'C' \|\| CB meeting AC at C'. Triangle AB'C' is the required triangle each of whose sides is (m/n)^thof the corresponding side of ΔABC. (b) Steps of construction when m > n: Step I. Construct the given triangle by using the given data. Step II. Take any one of the three sides of the given triangle and consider it as the base. Let AB be the base of the given triangle. Step III. At one end, say A, of base AB. Construct an acute angle ∠BAX below the base AB i.e., on the opposite side of the vertex C. Step IV. Along AX mark off m (larger of m and n) points A₁,A₂,A₃,............A_m such that AA₁ = A₁A₂ = ............. = A_m-1A_m. Step V. Join A_nB to B and draw a line through A. parallel to A_nB, intersecting the extended line segment AB at B'. Step VI. Draw a line through B' parallel to BC intersecting the extended line segment AC at C'. ΔAB'C' so obtained is the required triangle.

91.

Construction of triangles similar to a given triangle :

Answer»

(a) Steps of constructions, when m < n:

Step I. Construct the given triangle ABC by using the given data.

Step II. Take any one of the three sides of the given triangle as base. Let AB be the base of the given triangle.

step III. At one end, say A, of base AB. Construct an acute ∠BAX below the base AB.

Step IV. Along AX mark off n points A₁,A₂,A₃,..............,An such that AA₁ = A₁A₂ = ........... = A_n-1A_n.

Step V. Join AnB.

Step VI. Draw A_mB' parallel to A_nB which meets, AB at B'.

Step VII. From B' draw B'C' || CB meeting AC at C'.

Triangle AB'C' is the required triangle each of whose sides is (m/n)^thof the corresponding side of ΔABC.

(b) Steps of construction when m > n:

Step I. Construct the given triangle by using the given data.

Step II. Take any one of the three sides of the given triangle and consider it as the base. Let AB be the base of the given triangle.

Step III. At one end, say A, of base AB. Construct an acute angle ∠BAX below the base AB i.e., on the opposite side of the vertex C.

Step IV. Along AX mark off m (larger of m and n) points A₁,A₂,A₃,............A_m such that AA₁ = A₁A₂ = ............. = A_m-1A_m.

Step V. Join A_nB to B and draw a line through A. parallel to A_nB, intersecting the extended line segment AB at B'.

Step VI. Draw a line through B' parallel to BC intersecting the extended line segment AC at C'.

ΔAB'C' so obtained is the required triangle.

Discussion

92.	In a ∆ABC, AB = 3 cm, BC = 2 cm and CA = 10 cm. Is it possible to construct a triangle on the basis of given measures ? If not, why ?
Answer» In ∆ABC AB = 3 cm, BC = 2 cm and CA = 10 cm ∵ 3 + 2 ⊁ 10, ⇒ AB + BC ⊁ AC ∴ ∆ is not possible because sum of any two side of a triangle is less than third side.

92.

In a ∆ABC, AB = 3 cm, BC = 2 cm and CA = 10 cm. Is it possible to construct a triangle on the basis of given measures ? If not, why ?

Answer»

In ∆ABC

AB = 3 cm, BC = 2 cm and CA = 10 cm

∵ 3 + 2 ⊁ 10, ⇒ AB + BC ⊁ AC

∴ ∆ is not possible because sum of any two side of a triangle is less than third side.

Discussion

93.	The sides of an equilateral triangle are:(A) equal(B) unequal(C) different(D) smaller – greater
Answer» The sides of an equilateral triangle are equal.

Discussion

94.	State whether True or False:(i) Triangle has four sides.(ii) A triangle has three altitudes.(iii) The difference of any two sides of a triangle is smaller than the third side.(iv) Three sides are equal in an isosceles triangle.
Answer» (i) False (ii) True (iii) True (iv) False

94.

State whether True or False:(i) Triangle has four sides.(ii) A triangle has three altitudes.(iii) The difference of any two sides of a triangle is smaller than the third side.(iv) Three sides are equal in an isosceles triangle.

Answer»

(i) False

(ii) True

(iii) True

(iv) False

Discussion

95.	The sides of a right angle triangle are 3 cm and 4 cm. Then the measure of third side will be :(A) 8(B) 10(C) 6(D) 5
Answer» The correct option is (D) 5.

Discussion

96.	In a right angled triangle base = 8 cm, perpendicular = 6 cm, then find the value of hypotenuse.
Answer» In a right angled triangle Base = 8 cm, perpendicular = 6 cm By Pythagorous theorem ∵ (Hypotenuse)² = (Perp)² + (Base)² (Hypotenuse)² = 6² + 8² ⇒ (Hypotenuse)² =36 + 64 ⇒ (Hypotenuse)² = 100, ∴ Hypotenuse = \(\sqrt{100}\) = 10 cm.

96.

In a right angled triangle base = 8 cm, perpendicular = 6 cm, then find the value of hypotenuse.

Answer»

In a right angled triangle Base = 8 cm,

perpendicular = 6 cm

By Pythagorous theorem

∵ (Hypotenuse)² = (Perp)² + (Base)²

(Hypotenuse)² = 6² + 8²

⇒ (Hypotenuse)² =36 + 64

⇒ (Hypotenuse)² = 100,

∴ Hypotenuse = \(\sqrt{100}\) = 10 cm.

Discussion

97.	(Hypotenuse)2 = (Perpendicular)2 + (Base)2 is the theorem of :(A) Pythagorous(B) Euclid(C) Newton(D) Dekart
Answer» (A) Pythagorous

Discussion

98.	The construction of a triangle ABC, given that BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to: (A) 6.9 cm (B) 5.2 cm (C) 5.0 cm (D) 4.0 cm
Answer» (A) 6.9 cm Given, BC = 6 cm and ∠B= 45° We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle. i.e., AB + BC < AC => BC < AC – AB => 6 < AC-AB So, if AC – AB= 6.9 cm, then construction of ΔABC with given conditions is not possible.

98.

The construction of a triangle ABC, given that BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to: (A) 6.9 cm (B) 5.2 cm (C) 5.0 cm (D) 4.0 cm

Answer»

(A) 6.9 cm

Given, BC = 6 cm and ∠B= 45°

We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.

i.e., AB + BC < AC

=> BC < AC – AB

=> 6 < AC-AB

So, if AC – AB= 6.9 cm, then construction of ΔABC with given conditions is not possible.

Discussion

99.	The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to : (A) 3.2 cm (B) 3.1 cm (C) 3 cm (D) 2.8 cm
Answer» (D) 2.8 cm Given, BC = 3 cm and ∠C=60° We know that, the construction of a triangle is possible, if sum of two sides is greater than the third side of the triangle i.e., AB+ BC > AC => BC > AC – AB => 3 > AC – AB So, if AC – AB = 2.8 cm, then construction of ΔABC with given conditions is possible.

99.

The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to : (A) 3.2 cm (B) 3.1 cm (C) 3 cm (D) 2.8 cm

Answer»

(D) 2.8 cm

Given, BC = 3 cm and ∠C=60°

We know that, the construction of a triangle is possible, if sum of two sides is greater than the third side of the triangle i.e.,

AB+ BC > AC

=> BC > AC – AB

=> 3 > AC – AB

So, if AC – AB = 2.8 cm, then construction of ΔABC with given conditions is possible.

Discussion

100.	Give three sides such that construction of a triangle is possible.
Answer» To construct a triangle sum of two sides of a triangle must be greater than largest side. Let the sides are 2.5 cm, 4.5 cm and 6.5 cm.

100.

Give three sides such that construction of a triangle is possible.

Answer»

To construct a triangle sum of two sides of a triangle must be greater than largest side.

Let the sides are 2.5 cm, 4.5 cm and 6.5 cm.

Discussion

Explore topic-wise InterviewSolutions in .

A line segment connecting two opposite vertices is called(a) side(b) diagonal(c) hypotenuse(d) base

Can you draw a rhombus ZEAL where ZE = 3.5 cm, diagonal EL = 5 cm? Why?

A `DeltaABC` can be constructed in which `angleB = 60^(@), angleC = 45^(@) and AB + BC + CA = 12 cm`.

A `DeltaABC` can be constructed in which `angleB = 105^(@), angleC = 90^(@) and AB + BC + CA = 10 cm`.

The constuction of a `Delta` ABC, given that BC = 3cm, `angleC = 60^(@)` is possible when difference of AB and AC is equal toA. `3.2`cmB. `3.1`cmC. 3cmD. `2.8` cm

`DeltaABC` can be constructed in which `BC = 6cm, angleC = 30^(@) and AC - AB = 4 cm`.

An angle of `52.5^(@)` can be constructed.

Write True or False and give reasons for your answer.An angle of 67.5° can be constructed.

Write whether True or False and justify your answer.An angle of 52.5° can be constructed.

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3):(1)/(sqrt(3))`.

The diagonal AC is drawn in a square ABCD then Δ ABC is a …………………. A) EquilateralB) Isosceles C) Scalene D) None

Diagonals are equal in ………………….. A) Kite B) Trapezium C) Rhombus D) Square

The side of a Rhombus is 5 cm then its perimeter is ………………..cm. A) 16 B) 19 C) 1D) 20

If the diagonals of a Rhombus are equal then it is a ……………… A) Kite B) RhombusC) Square D) None

In order to make the given Quadrilateral as a parallelogram ……………. should happen.A) PQ = RS B) RQ = PS C) PQ || SR D) All the above

Number of vertices in a Quadrilateral is ………………….. A) 2 B) 3 C) 4 D) 5

Number of diagonals in a Quadrilateral is ………………. A) 3 B) 6 C) 4 D) 2

In the square ABCD, ∠BAC = ……………..A) 70° B) 45° C) 80° D) 60°

To construct a rectangle we need …………… independent measurements. A) 1 B) 2 C) 6 D) 4

The sum of adjacent angles in a parallelogram is ……………………. A) 190° B) 180° C) 200° D) 300°

Area of rectangle is ……………… A) l + b B) 2 (l + b) C) l2b2D) lb

Number of angles in a Quadrilateral is ………………… A) 2 B) 4 C) 6 D) 3

Identify the correct among the following. A) Each angle in a rectangle is 90° B) Rhombus will have 5 sidesC) A Quadrilateral has two diagonals D) Each angle in a square is 50°

Each angle in a square is …………………. A) 90° B) 70° C) 80° D) 100°

Number of sides in a Quadrilateral is ………………… A) 4 B) 6 C) 3 D) 5

If each angle of 90° is to be bisected then the measure of each angle is A) 60° B) 70° C) 80° D) 45°

Sum of 4 angles in a Quadrilateral is ……………….. A) 160° B) 300° C) 180° D) 360°

Opposite angles of a parallelogram are …………………. A) Equal B) ParallelC) 100° D) None

The perimeter of the given Quadrilateral is ………………….A) a + b – c – d B) a + b + c + dC) a – b – c – d D) a – b +2c + d

In a parallelogram ………………. A) Opposite sides are parallel B) Diagonals are not equal C) Sum of adjacent angles is 180° D) All the above

In a Quadrilateral ABCD, ∠A + ∠B = 200° then ∠C + ∠D = ……………… A) 110° B) 180° C) 160° D) 300°

The diagonals of a Rhombus will intersect at ……………….. A) 60° B) 90° C) 110° D) 80°

How many pairs of sides are parallel in a Trapezium ? A) 2 B) 1 C) 6 D) 3

The diagonals of a Rhombus PQRS will intersect at ‘O’ then ∠SOR = ………………..A) 50° B) 60° C) 80° D) 90°

The perimeter of a Rhombus is 40 cm then the length of its side is…………cm. A) 10 B) 16 C) 32 D) 70

How do we do the justification in the questions of constructing similar triangles

When construction of a triangle similar to a given triangle in the scale factor 5/3 , then what is the nature of given triangle ?

Construction of triangles similar to a given triangle :

In a ∆ABC, AB = 3 cm, BC = 2 cm and CA = 10 cm. Is it possible to construct a triangle on the basis of given measures ? If not, why ?

The sides of an equilateral triangle are:(A) equal(B) unequal(C) different(D) smaller – greater

State whether True or False:(i) Triangle has four sides.(ii) A triangle has three altitudes.(iii) The difference of any two sides of a triangle is smaller than the third side.(iv) Three sides are equal in an isosceles triangle.

The sides of a right angle triangle are 3 cm and 4 cm. Then the measure of third side will be :(A) 8(B) 10(C) 6(D) 5

In a right angled triangle base = 8 cm, perpendicular = 6 cm, then find the value of hypotenuse.

(Hypotenuse)2 = (Perpendicular)2 + (Base)2 is the theorem of :(A) Pythagorous(B) Euclid(C) Newton(D) Dekart

The construction of a triangle ABC, given that BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to: (A) 6.9 cm (B) 5.2 cm (C) 5.0 cm (D) 4.0 cm

The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to : (A) 3.2 cm (B) 3.1 cm (C) 3 cm (D) 2.8 cm

Give three sides such that construction of a triangle is possible.