Ncert exemplar solutions mathematics class 9 Solutions for Chapter 8 quadrilaterals

Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is

(A) 90º

(B) 95º

(C) 105º

(D) 120º

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is

(A) 55º

(B) 50º

(C) 40º

(D) 25º

ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is

(A) 40º

(B) 45º

(C) 50º

(D) 60º

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

(A) PQRS is a rectangle

(B) PQRS is a parallelogram

(C) diagonals of PQRS are perpendicular

(D) diagonals of PQRS are equal.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if

(A) PQRS is a rhombus

(B) PQRS is a parallelogram

(C) diagonals of PQRS are perpendicular

(D) diagonals of PQRS are equal.

If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a

(A) rhombus

(B) parallelogram

(C) trapezium

(D) kite

If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a

(A) rectangle

(B) rhombus

(C) parallelogram

(D) quadrilateral whose opposite angles are supplementary

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?

In quadrilateral ABCD, ∠A + ∠D = 180º. What special name can be given to this quadrilateral?

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.

ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle.

P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that ∠A = ∠B and ∠C = ∠D.

In Fig. , AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.