Question

Assertion (A): Two isosceles triangles with equal vertical angles are similar.

Reason (R): If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional then the two 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. In each isosceles triangle, the two sides including the vertical angle are equal. Thus, the ratios of the corresponding sides are equal, and the included angles are equal.

Step 2 – Reason: R is true. It states the SAS similarity criterion.

Step 3 – Link: The equal vertical angles and equal pairs of equal sides satisfy SAS similarity, so R explains A.