Question

ABCD is a rhombus. explain why ABC is congruent to CDA

Answer 1

Solution:

Given: ABCD is a Rhombus

To Prove: ΔABC≅ΔCDA

Construction: Join AC as diagonal.

Proof: ABCD is Rhombus whose sides are equal and diagonal are perpendicular bisectors. Please see attach figure.

In ΔABC and ΔCDA

AB=CD           (Side of same Rhombus)

BC=DA           (Side of same Rhombus)

AC=CA           (Common Side of both triangle)

Therefore, ΔABC≅ΔCDA  by SSS property of congruence.

Hence Proved, ΔABC≅ΔCDA

Answer 2

Well, all sides in a rhombus have equal length (definition of a rhombus).
Therefore 3 sides ABC would be equal to three other sides CDA.