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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In a given rectangle ABCD, diagonals AC and BD intersect at O. If COD = 120, find angle OBA |
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| 2. |
The diagonals AC and BD of rectangle ABCDintersect each other in point P. If AP = 8 cm, findAC and BP |
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| 3. |
(2) The diagonals AC and BD of rectangle ABCDintersect each other in point P. If AP 8 cm, findAC and BP |
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| 4. |
Q5. If the diagonals AC and BD of a quadrilateral ABCD bisect each other then ABCD is aa) Parallelogramb) Rectanglec) Rhombus d) none of the |
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| 5. |
In an isosceles triangle ABC with AB-AC, BD is perpendicular from B to theside AC. Prove that13.BD2 - CD 2CD. AD |
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Answer» Proof: In triangle ABD., AB² = AD² + BD²But BC = ACAC² = AD² + BD²(AD+DC)² =AD² + BD²AB² + DC² + 2AD.DC = AD² + BC²2AD. DC = BD² - DC²BD² - DC² = 2AD.CDhence proved |
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| 6. |
AABC is an isosceles triangle in which AB-AC.Side BA is produced to D such that AD AB(see Fig. 7.34). Show that Z BCD'is a right angle. |
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| 7. |
aI13. In an isosceles triangle ABC with AB-AC, BD is perpendicular from B to theside AC. Prove thatBy-CD-=2CD . AD.res |
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Answer» UsingPythagoras theorem: AD² + BD² = AC² (= AB²) --- (1) CD² + BD² = BC² ------- (2) (2)- 2 * (1) =>=> CD² - BD² = BC² - 2AC² + 2 AD²=> = BC² - 2(AD +CD)² + 2 AD²=> = BC² - 2 CD² - 4 AD * CD=> = BD² + CD² - 2 CD² -4 AD * CD=> = BD² - CD² - 4 AD * CDSimplify to get BD² - CD² = 2 AD * CD |
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| 8. |
2 नाक olजज 4: 2 पारी o Sa oe"R dice i dosed e 3 o धन डे |
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| 9. |
) are the mid points on the sides CA and CAvight triangle, right anglesd at C. f p is the lengsh of the perpendiestiar fomaning, then prove thatO in the interior of a rectangle ABCD is joined widi eaco of sesntices ABCangled APOR, AP-90, l1 M is the mid poind of PO proveth srilateral ABCD, B-90 and ADABBC? CD, Peove that ZACDangled triangle, if a perpendicular is drawn from the right angle to the bygetenuse square of the perpendicular is equal to the area of the rectasnle formed by tieid point of the side AD of a parallelogram ABCD.Straight line BP inteserts fieD (produced) at O Prove that OR-2RBeles triangle ABC, with AB- AC, BD is perpendieular frons 8 to the side AC PasBD?-CD 2CD AD, AD BC, Prove that AB, CD AC, DB2de, AD is drawn perpendicular to BC. Prove that ABBDACCDangled triangle, the square of the hypotenuse is equal to the sumof thaesr two sides, Proveabove theorem, determine the length of AD in terms of b and cicht triangle, night-angled at C. Ir p ls the lenth of the perpendicular frams Cuaun the uual meaning, then prove that |
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Answer» Please specify the question you wanted to be answered! |
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| 10. |
The ratio of sides of a triangle is 1 :then it is1) Scalene2) Isosceles3) Right angled triangle4) 19.3 : 2 |
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Answer» If angles are in ratio 1:2:3 then angles are 30;60;90. Then ratio of their sides are sin30:sin60:sin90=1:√3:2 |
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| 11. |
19. In a right triangle ABC, right-angled at B,D is a point on hypotenuse such thatBD 1 AC. If DP 1 AB and DQ 1 BC thenprove that(a) DQ2 = DPQC (b) DP2 = DQ : AP. |
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Answer» We know that if a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then the triangles on the both sides of the perpendicular are similar to the whole triangle and also to each other.(a) Now using the same property in In △BDC, we get △CQD ∼ △DQBCQDQ=DQQB⇒DQ2=QB.CQ Now. since all the angles in quadrilateral BQDP are right angles.Hence, BQDP is a rectangle.So, QB = DP and DQ = PB∴DQ2=DP.CQ (b) Similarly, △APD ∼ △DPBAPDP=PDPB⇒DP2=AP.PB⇒DP2=AP.DQ[∵DQ=PB] |
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| 12. |
04: A polygon of n sides has t 3 diagonals. If a polygon has 9 diagonals, find the number of sidesof the polygon |
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| 13. |
A polygonhas 27 diagonals. How many sides does it have? |
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| 14. |
0-71) In the given figure, if AD=BD=CD. Prove that BAC is right angle, |
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| 15. |
g In the givenBD-LAC, Iffind CD.figure, ZABC 90 andBD-8cm, AD = 4cm,st2o |
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| 16. |
29,if AABC is an isosceles triangle such that AB -AC. Side BA is produced to D such thatAD -AB. Show that angle BCD is a right angle.ID |
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Answer» thankyou |
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| 17. |
29. If AABC is an isosceles triangle such that AB -AC. Side BA is produced to D such thatAD-AB. Show that angle BCD is a right angle. |
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Answer» Please like the solution 👍 ✔️👍 |
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| 18. |
2ABCD is a rhornbus whose diagonal AC makes an angle ι with AB. If cos aand OB¡3 cm,findthe length of its diagonals AC and BD |
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| 19. |
ABC is an isosceles triangle in which AB = ACSide BA is produced to D such that AD AB(see Fig. 7.34). Show that BCD is a right angle |
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| 20. |
In the given figure, ABCD is a rectangle whose diagonals AC and BD intersect each other at O. Iffind ZOBC.. |
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Answer» The angle obc=90-28=62as the sum of the angles are complementary. |
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| 21. |
Show that the bisectors of angles of a parallelogram form a rectangle. |
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Answer» figure is wrong |
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| 22. |
ABCD is a rhombus whose diagonal AC makesan angle α with AB. If cos α and OB 3 cm,find the length of its diagonals AC and BD. |
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| 23. |
howthat the bisectors of angles of a parallelogram form a rectangs |
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| 24. |
Show that the bisectors of angles of a parallelogram form a rectangle |
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| 25. |
sShow that the bisectors of angles of a parallelogram form a rectangle. |
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Answer» Like my answer if you find it useful! |
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| 26. |
18. 1 the bseciors of the hase angles of aright angled19. ABC is a triangle. The bisectors of the exterior angle at B and the bisectorsar B and the bisectors of C intersect eadother at D Prove that D-1 |
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| 27. |
The points A(4,-2), E(7,2), C(O,9) and D-3,5) form a parallelogram. Find the length of the altitude ofthe parallelogram on the base AB |
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Answer» Note : I have taken distance from point C because distance of altitude will be same irrespective. |
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| 28. |
6, Δ ABC is an isosceles triangle in which AB-AC.Side BA is produced to D such that AD AB(see Fig. 7.34). Show that BCD is a right angle. |
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| 29. |
6. Δ/ABC is an isosceles triangle in which AB AC.Side BA is produced to D such that AD AB(see Fig. 7.34). Show that BCD is a right angle. |
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| 30. |
6. In an isosceles triangle ABC with AB AC, BD is a perpendicular from B to the side AC.Prove that BD CD 2CD AD. |
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Answer» UsingPythagoras theorem: AD² + BD² = AC² (= AB²) --- (1) CD² + BD² = BC² ------- (2) (2)- 2 * (1) =>=> CD² - BD² = BC² - 2AC² + 2 AD²=> = BC² - 2(AD +CD)² + 2 AD²=> = BC² - 2 CD² - 4 AD * CD=> = BD² + CD² - 2 CD² -4 AD * CD=> = BD² - CD² - 4 AD * CDSimplify to get BD² - CD² = 2 AD * CD l |
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| 31. |
6. Construct a Δ ABC in which BC : 6.6 cm, AB-5.2 cm and AC-4.5 cm. Also draw aperpendicular bisector of the side BC. |
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Answer» figure do de do |
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| 32. |
140 EIn the given figure, ABCD is a rectangle whose diagonalsintersect at O. Diagonal AC is produced to E and ZECD140°, Find the angles of ΔΟΑΒ. |
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| 33. |
AABC is an isosceles triangle in which AB ACSide BA is produced to D such that AD AB(see Fig. 7.34). Show that L BCD is a right angle.6. |
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| 34. |
6. Construct aA ABC in which BC 6.6 cm, AB5.2 cm and AC- 4.5 cm. Also draw aperpendicular bisector of the side BC. |
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| 35. |
IPLE 2 In the adjoining figure, ABCD is a lIgmwhose diagonals AC and BD intersect atO. A line segment through O meets AB atP and DC at Q. Prove thatar(APQD) = ar(||gm ABCD)./2 |
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| 36. |
A straight line through a fixed point (2, 3)intersects the coordinate axes at distinctpoints P and Q. If O is the origin and therectangle OPRQ is completed, then thelocus of R is:(1) 3x +2y-6(2) 2x +3y ry(3) 3x +2y-xy(4) 3x +2y 6xy |
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| 37. |
BlAD and BC are equal anderpendiculars to a line segmentAB. Show that CD bisects AB. |
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| 38. |
in AABC, 4A is acute. BD and CE are perpendicular on AC and AB respectiveProve that AB × AE = AC x AD.14. |
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Answer» THANKS....BUT I KNOW THIS ANSWER....😃 I AM JUST TESTING SCHOLR |
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| 39. |
AD and BC are equal perpendiculars to a linesegment AB (sce Fig. 7.18) Show that CD bisectsAB |
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| 40. |
AD and BC are equal perpendiculars to a linesegment AB (see Fig. 7.18). Show that CD bisectsAB. |
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| 41. |
ABCD is a parallelogram. The angle bisectorsof ZA and D meet at O. The measure ofZAOD is |
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| 42. |
3.) AD and BC are equal perpendiculars to a linesegment AB (see Fig. 7.18). Show that CD bisectsAB. |
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| 43. |
1. Prove that, all the angle bisectors of aparallelogram form a rectangle. |
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| 44. |
Prove that the angle bisectors of aparallelogram form a rectangle. |
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| 45. |
AD and BC are equal perpendiculars to a linesegment AB (see Fig. 7.18). Show that CD bisectsAB.3. |
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Answer» thank u.... |
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| 46. |
Fig. 4.37Exercise 4.2The angles of a quadrilateralingles of a quadrilateral are in the ratio 2: 4:5:7. Find all the angles.rilateral ABCD, LA = 72ยบ and ZC is the supplementary of ZA. The other twoIn a quadrilateralangles are 2x-10 and x +4les are 2x-10 and x + 4. Find the value of x and the measure of all the angles.BCD is a rectangle whose diagonals AC and BD intersect at 0. If LOAB =46",find ZOBCThe lengths of the diagonals of a Rhombus are 12 cm and 16 cm. Find the side of therhombus.Show that the bisectors of angles of a parallelogram form a rectangle.6IfaIl a triangle and a parallelogram lie on the same base and between the same parallels.then nrou that th e of the triangle is equal to half of the area of parallelogram. |
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Answer» which question are you asking |
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| 47. |
6If two zeroes of the polynomial x - 4x - 3x + 12 are v3 and -V3, then find its third zero.[CBSE 2009, 1 |
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| 48. |
Find a quadratic polynomial whose zeroes are2V3and/3 |
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| 49. |
3. AD and BC are equal perpendiculars to a linesegment AB (see Fig. 7.18). Show that CD bisectsAB |
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| 50. |
0.5:The nh term of an A.P. is 1 + (-2)"/n-1, Find the6 ind ac side of a rhombus whose diagonals are 24 cm and 10 cm.fifthandsixthtermofA. |
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Answer» nth term is 1+(-2)^n /n - 1so 5th term is 1+(-2)^5 /5 -1=1-32/5-1=-32/5so 6th term is 1+(-2)^6 /6 -1=1+64/6-1=32/3 |
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