It is given that ∆ ABC ∼∆ EDF. Which of the ...

CBSE Class 10 Standard Math 2026 All Sets Solved Paper

Question : 10 of 20

Marks: +1, -0

It is given that ∆ ABC ∼∆ EDF. Which of the following is not true?

$\; \frac{\text{Perimeter\, of\, }\triangle ABC}{\text{Perimeter\, of\, }\triangle EDF} = \; \frac{AB}{ED}$
$\; \frac{AB}{ED} = \; \frac{AC}{EF}$
$\angle A = \angle D, \angle C = \angle F$
$\; \frac{AB + BC}{AC} = \; \frac{DE + DF}{EF}$

Solution:

Given: ∆ ABC ∼∆ EDF.

Corresponding angles are: ∠A = ∠E, ∠B = ∠D, ∠C = ∠F.

Corresponding side ratios are:

\; \frac{AB}{ED} = \; \frac{BC}{DF} = \; \frac{AC}{EF} = k.

(A) True

The ratio of perimeters is equal to the ratio of corresponding sides.

(B) True

\; \frac{AB}{ED} = \; \frac{AC}{EF}

is a correct pair of corresponding sides.

According to the order of vertices, ∠A corresponds to ∠E. Therefore, ∠A = ∠E is true, but ∠A = ∠D is generally not true.

(D) True

Since

\; \frac{AB}{ED} = \; \frac{BC}{DF} = \; \frac{AC}{EF} = k

, then AB = k . ED, BC = k. DF and AC = k. EF.

The statement (C) is not true.

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