Question

Assertion (A): In the given figure, if $$\angle AED=\angle ABC$$ then $$\triangle ADE\sim\triangle ACB$$.

 

Reason (R): If two corresponding angles of two triangles are equal then the triangles are similar.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The triangles share angle $$A$$ and the given equality provides a second pair of equal angles. Hence, $$\triangle ADE\sim\triangle ACB$$ by AA similarity.

Step 2 – Reason: R is true. Equality of two corresponding angles is sufficient for triangle similarity.

Step 3 – Link: The common angle at $$A$$ and the given angle equality meet the AA criterion, so R explains A.