Olympiad – Class IX – Mathematics - Quadrilaterals

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Question - 1

In the parallelogram ABCD, AP and BP are bisectors of ∠A and ∠B which meet at P.

What is 2 ∠APB equivalent to?

  • A ∠A+∠B
  • B ∠A+∠C
  • C ∠B+∠D
  • D ∠A-∠D

Question - 2

In the given figure, AO and DO are the bisectors of ∠A and ∠D of the quadrilateral ABCD. Find ∠AOD.

  • A 67.5o
  • B 77.5o
  • C 87.5o
  • D 99.75o

Question - 3

In a parallelogram find the sum of the bisected angles of two adjacent angles

  • A 30o
  • B 45o
  • C 60o
  • D 90o

Question - 4

The diameter of the circumcircle is the diagonal of a rectangle which is 10 cm and breadth of the rectangle is 6 cm. Find its length.

  • A 6 cm
  • B 5 cm
  • C 8 cm
  • D 7 cm

Question - 5

In the parallelogram ABCD, what are the measures of the angles x and y?

  • A 60o,30o
  • B 30o,60o
  • C 45o,45o
  • D 90o,90o

Question - 6

In parallelogram PQRS, what are the values of ∠QSPand ∠SPQ?

  • A 45o,60o
  • B 60o,45o
  • C 70o,35o
  • D 35o ,70o

Question - 7

In the given figure, ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm and the distance between AB and DC is 4 cm.What is the value of x?

  • A 13 cm
  • B 16 cm
  • C 19 cm
  • D 12 cm

Question - 8

In a square ABCD, the diagonals bisect at O.What type of a triangle is \(\triangle \)AOB?

  • A An equilateral triangle
  • B An isosceles but not a right angled triangle.
  • C A right angled but not an isosceles triangle.
  • D An isosceles right angled triangle

Question - 9

ABCD is a quadrilateral. If ACA square and BD bisect each other, what is ABCD?

  • A A square
  • B A rectangle
  • C A parallelogram
  • D A rhombus

Question - 10

In a parallelogram ABCD, ∠D = 60o. Find the measure of ∠A.

  • A 120o
  • B 65o
  • C 90o
  • D 75o