Triangle Congruence: Proving ΔADB≅ΔCBD with Parallel Lines

AD = BC

AD || BC

According to which theorem are the triangles ΔADB≅ΔCBD congruent?

AAABBBCCCDDD

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Step-by-step written solution

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1

Understand the problem

AD = BC

AD || BC

According to which theorem are the triangles ΔADB≅ΔCBD congruent?

AAABBBCCCDDD

2

Step-by-step solution

We are given: AD=BC

The angle ADB is equal to the angle CBD since AD is parallel to BC and the corresponding angles are equal between parallel lines.

DB=DB since it is a common side.

Therefore, we have two triangles that are congruent according to the S.A.S. (side, angle, side) theorem.

3

Final Answer

According to the S.A.S. theorem

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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