Pls abcd is a rhombus. explain why abc is congruent to cda

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Answer from: blacee01

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 from: dondre54

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.

Therefore 3 sides ABC would be equal to three other sides CDA.

Answer from: sebascarvallo2003

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.

Therefore 3 sides ABC would be equal to three other sides CDA.

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