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ASA Congruence Criterion

Two triangles...

Question

Two triangles are formed on the same base and equal angles at the ends of the base. The triangles are congruent by _____ criterion.

A

ASA

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B

RHS

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C

AAA

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D

SSS

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Solution

The correct option is A ASA
Since the base(one side) is common and the angles at the ends are also same, the figure will be as shown below.

The two triangles formed have,
$∠ B A C = ∠$ BAD .....(given)
AB = AB ......(common side)
$∠ A B C = ∠$ ABD ..... (given)

Therefore, by ASA criterion for congruency of triangles,
$△ C B A ≅ △ D B A .$

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