Question

What theorem is used to prove △ABC≅△DEC given that C is the midpoint of EB?

Answer 1

The theorem is used to prove △ABC≅△DEC is Side-Angle-Side(SAS) theorem

The two triangles are

△ABC and △DEC

Here we have to prove that the △ABC and △DEC are congruent

It is given that

The length of AC = The length of CD

The angle ACB = The angle ECD

The point C is the midpoint of EB

Therefore,

The length of BC = The length of EC

Therefore, the two sides and one angle of triangle ABC is equal to the two sides and one angle of triangle DEC, so the both triangles are congruent by SAS rule

Hence, the theorem is used to prove △ABC≅△DEC is Side-Angle-Side(SAS) theorem.

Learn more about congruence of triangle here

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