Q17 of 40 Page 8

ABCD is a rhombus. Show that diagonals AC bisect ∠A as well as ∠C, and diagonal BD bisects ∠B as well as ∠D.

To Prove: Diagonals AC bisects ∠A as well as ∠C and diagonal bisects ∠B as well as ∠D

Given: ABCD is a rhombus


Concept Used:


SSS Congruence theorem: If all the three angles of a triangle are equal to angles of another triangle, triangles are congruent.


All sides of a rhombus are equal.


Diagram:



Proof:


In Δ ABC and ΔADC, we have,


AB = AD [Since, ABCD is a rhombus]


BC = CD [Since, ABCD is a rhombus]


And, AC = CA [Common Side]


So, by SSS congruence theorem,


ΔABC and ΔADC are congruent.


Therefore,


∠BAC = ∠DAC and ∠ACB = ∠ACD


Thus, AC bisects ∠A and ∠C.


And similarly, we can prove that BD bisects ∠B and ∠D.


Hence, Proved.


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