Question

Assertion (A): In the given figure, if $$\triangle ABC\sim\triangle DEF$$ then $$x = 5$$.

Reason (R): $$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$$.

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

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

Explanation:

Step 1 – Assertion: A is false. Substituting the corresponding side lengths shown in the figure into the proportionality equations gives $$x=1$$, not $$x=5$$.

Step 2 – Reason: R is true. For similar triangles, corresponding side lengths are proportional.