## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 13 Understanding Quadrilaterals Ex 13.2

Question 1.

In the given figure, ABCD is a parallelogram. Complete each statement along with the definition or property used.

(i) AD = ………..

(ii) DC = ………..

(iii) ∠DCB = ………..

(iv) ∠ADC = ………..

(v) ∠DAB = ………..

(vi) OC = ………..

(vii) OB = ………..

(viii) m∠DAB + m∠CDA = ………..

Solution:

Question 2.

Consider the following parallelograms. Find the values of x, y, z in each.

Solution:

Question 3.

Two adjacent sides of a parallelogram are in the ratio 5 : 7. If the perimeter of a parallelogram is 72 cm, find the length of its sides.

Solution:

Question 4.

The measure of two adjacent angles of a parallelogram is in the ratio 4 : 5. Find the measure of each angle of the parallelogram.

Solution:

Question 5.

Can a quadrilateral ABCD be a parallelogram, give reasons in support of your answer.

(i) ∠A + ∠C= 180°?

(ii) AD = BC = 6 cm, AB = 5 cm, DC = 4.5 cm?

(iii) ∠B = 80°, ∠D = 70°?

(iv) ∠B + ∠C= 180°?

Solution:

Question 6.

In the following figures, HOPE and ROPE are parallelograms. Find the measures of angles x, y and z. State the properties you use to find them.

Solution:

Question 7.

In the given figure TURN and BURN are parallelograms. Find the measures of x and y (lengths are in cm).

Solution:

Question 8.

In the following figure, both ABCD and PQRS are parallelograms. Find the value of x.

Solution:

Question 9.

In the given figure, ABCD, is a parallelogram and diagonals intersect at O. Find :

(i) ∠CAD

(ii) ∠ACD

(iii) ∠ADC

Solution:

Question 10.

In the given figure, ABCD is a parallelogram. Perpendiculars DN and BP are drawn on diagonal AC. Prove that:

(i) ∆DCN ≅ ∆BAP

(ii) AN = CP

Solution:

Question 11.

In the given figure, ABC is a triangle. Through A, B and C lines are drawn parallel to BC, CA and AB respectively, which forms a ∆PQR. Show that 2(AB + BC + CA) = PQ + QR + RP.

Solution:

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