Question

ABCD is a rhombus. Explain why TRIANGLE ABC =~ TRIANGLE CDA.thank you ! :)

Answer 1

Explanation

From the statement, we know that:

• ABCD is a rhombus,

,

• we have the triangles ΔADC and ΔABC,

,

• the triangles share the side AC.

We must prove that the triangles are congruent.

In a rhombus all the 4 sides are equal, so we have:

• AC = AC,

,

• AD = BC,

,

• AB = DC.

Therefore, we have two triangles with equal sides that share the side AC. From SSS we know that the triangles are congruent.

Answer

We have two triangles with equal sides that share the side AC. From SSS we know that the triangles are congruent.