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1.

If one of the angles of a quadrilateral is not right angle but all the sides are equal, it is called a square.(a) True(b) FalseI got this question in semester exam.The question is from Types of Quadrilaterals topic in chapter Quadrilaterals of Mathematics – Class 9

Answer» RIGHT answer is (b) False

To elaborate: For a quadrilateral to be a square, following conditions has to be satisfied.

All the sides should be EQUAL, each PAIR of the sides should be PARALLEL and one ANGLE has to be right angle.
Discussion
2.

If one pair of opposite sides are parallel in a quadrilateral, it is called __________(a) trapezium(b) rhombus(c) square(d) parallelogramThe question was asked in my homework.The question is from Types of Quadrilaterals topic in chapter Quadrilaterals of Mathematics – Class 9

Answer»

Right choice is (a) trapezium

To EXPLAIN: In a trapezium, one PAIR of sides are PARALLEL as SHOWN in the diagram.
Discussion
3.

If the ratio of four angles of a quadrilateral is ∠A : ∠B : ∠C : ∠D = 1 : 2 : 3 : 4, what is the value of ∠C?(a) 90°(b) 108°(c) 180°(d) 72°I had been asked this question in unit test.The doubt is from Another Condition for a Quadrilateral to be a Parallelogram in division Quadrilaterals of Mathematics – Class 9

Answer» CORRECT answer is (b) 108°

To elaborate: LET ∠A = x, then ∠B = 2x, ∠C = 3X and ∠D = 4x

We know that sum of the four angles of a quadrilateral is 360°.

Therefore, ∠A + ∠B + ∠C + ∠D = 360°

x+ 2x + 3x+ 4x= 360°

10x= 360°.

x= 36°.

Now, ∠C = 3x = 3(36°) = 108°.
Discussion
4.

What is the quadrilateral formed by the angle bisectors of a parallelogram?(a) Square(b) Rectangle(c) Circle(d) RhombusI got this question in semester exam.This intriguing question comes from Properties of a Parallelogram in section Quadrilaterals of Mathematics – Class 9

Answer»

Correct CHOICE is (b) Rectangle

For explanation I would say: PQ || RS ⇒ ∠P + ∠S = 180°(Interior ANGLES on the same side of transversal)

⇒ ½ ∠P + ½ ∠S = ½ x 180°

⇒ ∠APS + ∠PSA = 90°——————-(i)

In ΔASP, ∠APS + ∠PSA + ∠SAP = 180°(Angle sum property of triangle)

⇒ 90° + ∠SAP = 180°(from equation i)

⇒ ∠SAP = 90°

⇒ ∠DAB = 90° (Vertically OPPOSITE angle)

Similarly, ∠ADB = 90°, ∠ABC = 90°, ∠DCB = 90°.

Hence, ABCD is a rectangle.
Discussion
5.

A rectangle is a parallelogram.(a) True(b) FalseThe question was posed to me during an interview.This intriguing question comes from Quadrilaterals Basics topic in portion Quadrilaterals of Mathematics – Class 9

Answer»

Right option is (a) True

Best explanation: A quadrilateral is said to be parallelogram if the opposite SIDES of it are parallel as SHOWN in below DIAGRAM.

In rectangle, opposite sides are parallel and FOUR ANGLES are right angles as shown in below diagram. Hence, a rectangle has all the properties of a parallelogram.
Discussion
6.

At which angle do diagonals of a rhombus bisects each other?(a) 180°(b) 360°(c) 270°(d) 90°This question was addressed to me in homework.Question is from Types of Quadrilaterals in chapter Quadrilaterals of Mathematics – Class 9

Answer»

Right option is (d) 90°

The best explanation: A rhombus is SHOWN in the diagram below.

For ∆AOB and ∆AOD,

AB = AD (sides of the same rhombus)

OB = OD (diagonals of a parallelogram bisect each other)

OA = OA (same side)

Hence, ACCORDING to SSS rule, ∆AOB and ∆AOD are CONGRUENT to each other.

Therefore,

∠AOB = ∠AOD

∠AOB + ∠AOD = 180° (linear PAIR of ANGLES)

2∠AOD = 180°

Therefore, ∠AOD = 90°
Discussion
7.

If three out of four points are collinear, we get __________(a) line(b) square(c) triangle(d) rectangleI got this question during an interview.I need to ask this question from Quadrilaterals Basics topic in chapter Quadrilaterals of Mathematics – Class 9

Answer»

Correct answer is (c) triangle

Explanation: As shown in FIGURE, out of FOUR points A, B, C and D, THREE points A, B and C are collinear and we GET a triangle.
Discussion
8.

From the diagram, if BD and AC are diagonals of a parallelogram ABCD then what is true for them?(a) BO = AO(b) BO = OC(c) BO = OD(d) AO = ODThis question was posed to me in an interview.I'm obligated to ask this question of Properties of a Parallelogram in chapter Quadrilaterals of Mathematics – Class 9

Answer» CORRECT option is (C) BO = OD

Easiest explanation: According to theorem 8.6, diagonal of a PARALLELOGRAM bisect each other.

It means that BO = OD and AO = OC.
Discussion
9.

Quadrilateral has __________ sides.(a) one(b) two(c) three(d) fourThe question was asked during an interview for a job.My enquiry is from Quadrilaterals Basics in division Quadrilaterals of Mathematics – Class 9

Answer»

Correct option is (d) four

Best EXPLANATION: A figure formed by joining four points is called quadrilateral as shown in the diagram. It ALSO has four SIDES (AB, BC, CD and AD) and four angles (∠A, ∠B,∠C and ∠D).
Discussion
10.

The sum of four angles of quadrilateral is equal to __________(a) 90°(b) 360°(c) 180°(d) 270°This question was posed to me in exam.I want to ask this question from Quadrilaterals Basics in division Quadrilaterals of Mathematics – Class 9

Answer»

Correct OPTION is (b) 360°

For EXPLANATION I would say: Let’s TAKE a quadrilateral as shown in figure. By dividing it diagonally, we can see that it breaks into two triangles.

We know that sum of three ANGLES of any TRIANGLE is equal to 180°.

Hence, ∠QPR + ∠Q + ∠QRP = 180° and ∠SPR + ∠S + ∠PRS = 180°.

Now to get the sum of four angles of quadrilateral,

∠P + ∠Q + ∠R + ∠S = (∠QPR + ∠SPR) + ∠Q + (∠QRP + ∠PRS) + ∠S

= (∠QPR + ∠Q + ∠QRP) + (∠SPR + ∠S + ∠PRS)

= 180° + 180°

= 360°
Discussion