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, ∠BAC=∠BAD .....(given) AB = AB ......(common side) ∠ABC=∠ABD ..... (given)
Therefore, by ASA criterion for congruency of triangles, △CBA≅△DBA.