Question

# Statement I: Two triangles are similar if two corresponding angles are equal. Statement II: The sum of internal angles in a triangle is 180∘.

A
Statement I is true. Statement II is true. Statement II is the correct explanation of Statement I.
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B
Statement I is true. Statement II is true. Statement II is not the correct explanation of Statement1.
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C
Statement I is true. Statement II is false.
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D
Statement I is false. Statement II is true.
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Solution

## The correct option is B Statement I is true. Statement II is true. Statement II is not the correct explanation of Statement1.Consider two triangles, Δ ABC and Δ DEF in which ∠A=∠D,∠B=∠E. We know that sum of internal angles in a triangle is 180∘. The third angle can be obtained by ∠C=180∘−∠A−∠B. Similarly the third angle in Δ DEF is ∠F=180∘−∠D−∠E=180∘−∠A−∠B=∠C. Hence the three angles are equal and by AAA similarity the two triangles are similar.

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