Triangle Congruence Theorem: Identifying the Proof for ADE ≅ BCE

EDC is an isosceles triangle.

ADE=BCE ∢ADE=∢BCE

AC=BD AC=BD

ΔADEΔBCE ΔADE≅ΔBCE

According to which theorem are the triangles congruent?

AAADDDCCCBBBEEE

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1

Understand the problem

EDC is an isosceles triangle.

ADE=BCE ∢ADE=∢BCE

AC=BD AC=BD

ΔADEΔBCE ΔADE≅ΔBCE

According to which theorem are the triangles congruent?

AAADDDCCCBBBEEE

2

Step-by-step solution

ΔEDC is an isosceles triangle.

DE = EC

D=C ∢D=∢C

EDC=ECD ∢\text{EDC}=∢\text{ECD}

ADE=BCE ∢\text{ADE}=∢\text{BCE} (A)

E1=E2 ∢E1=∢E2 (A)

Reasoning:

In an isosceles triangle there are 2 equal sides.

The base angles of an isosceles triangle are equal.

DEDC=CECD ∢D-∢\text{EDC}=∢C-∢ECD

Therefore, the triangles are congruent according to the theorem S.A.S. theorem.

3

Final Answer

A.S.A.

Practice Quiz

Test your knowledge with interactive questions

Look at the triangles in the diagram.

Which of the statements is true?

727272727272131313222131313222AAABBBCCCDDDEEEFFF

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