Triangle Congruence in Isosceles Triangle: Proving ADC ≅ ADB

Given: ΔABC isosceles

and the line AD cuts the side BC.

Are ΔADC and ΔADB congruent?

And if so, according to which congruence theorem?

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Step-by-step written solution

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1

Understand the problem

Given: ΔABC isosceles

and the line AD cuts the side BC.

Are ΔADC and ΔADB congruent?

And if so, according to which congruence theorem?

AAABBBCCCDDD

2

Step-by-step solution

Since we know that the triangle is isosceles, we can establish that AC=AB and that

AD=AD since it is a common side to the triangles ADC and ADB

Furthermore given that the line AD intersects side BC, we can also establish that BD=DC

Therefore, the triangles are congruent according to the SSS (side, side, side) theorem

3

Final Answer

Congruent by L.L.L.

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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