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.
(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.