Prove the angle-angle-side congruence criterion.

What is implies rhombus.

Quadrilaterals Solutions for Class 9th Maths.

9th Maths EXERCISE 8.1,Page No:146, Questions No:6, Session 2023-2024.

Class 9th, NCERT Books for Session 2023-2024, based on CBSE Board.

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(i) ∠DAC = ∠BAC …(1) [∵ Given]

∠DAC = ∠BCA …(2) [∵ Alternate angle]

∠BAC = ∠ACD …(3) [∵Alternate angles]

From the equations (1), (2) and (3), we have

∠ACD = ∠BCA …(4)

Hence, Diagonal AC bisects angle C also.

(ii) From the equation (2) and (4), we have

∠ACD = ∠DAC

In ΔADC,

∠ACD = ∠DAC [∵ Prove above]

AD = DC [∵ In a triangle, the sides opposite to equal angle are equal]

A parallelogram whose adjacent sides are equal, is a rhombus. Hence, ABCD is a rhombus.