What is the side-angle-side (SAS) congruence criterion.

Prove the corresponding parts of congruent triangles

Quadrilaterals Solutions for Class 9th Maths.

9th Maths EXERCISE 8.1,Page No:147, Questions No:12, Session 2023-2024.

Share

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

In AECD,

AE ∥ DC [∵ Given]

AD ∥ CE [∵ By construction]

Hence, AECD is a parallelogram.

AD = CE …(1) [∵ Opposite sides of a parallelogram are equal]

AD = BC …(2) [∵ Given]

Hence, CE = BC [∵ From the equation (1) and (2)]

Therefore, in ΔBCE,

∠3 = ∠4 …(3) [∵ In a triangle, the angles opposite to equal sides are equal]

Here, ∠2 + ∠3 = 180° …(4) [∵ Linear Pair]

∠1 + ∠4 = 180° …(5) [∵ Co-interior angles]

Therefore, ∠2 + ∠3 = ∠1 + ∠4 [∵ From the equation (4) and (5)]

⇒ ∠2 = ∠1 ⇒ ∠B = ∠A [∵ ∠3 = ∠4]

(ii) ABCD ia a trapezium in which AB ∥ DC, hence,

∠1 + ∠D = 180° …(6) [∵ Co-interior angles]

∠2 + ∠C = 180° …(7) [∵ Co-interior angles]

Therefore, ∠1 + ∠D = ∠2 + C [∵ From the equation (6) and (7)]

⇒ ∠D = ∠C [∵ ∠2 = ∠1]

(iii) In ΔABC and ΔBAD,

BC = AD [∵ Given]

∠ABC = ∠BAD [∵ Prove above]

AB = AB [∵ Common]

Hence, ΔABC ≅ ΔBAD [∵ SAS Congruency rule]

(iv) ΔABC ≅ ΔBAD [∵ Prove above]

Diagonal AC = diagonal BD [∵ CPCT]