Question

It is given that ΔABC ~ ΔEDF. Which of the following is not true?

Options

• `("Perimeter of"  ΔABC)/("Perimeter of"  ΔEDF) = (AB)/(ED)`

• `(AB)/(ED) = (AC)/(EF)`

• ∠A = ∠D, ∠C = ∠F

• `(AB + BC)/(AC) = (DE + DF)/(EF)`

Answer 1

∠A = ∠D, ∠C = ∠F

Explanation:

Given: △ABC ∼ △EDF

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

Corresponding side ratios are: `(AB)/(ED) = (BC)/(DF) = (AC)/(EF) = k`.

(A) True: The ratio of perimeters is equal to the ratio of corresponding sides.

(B) True: `(AB)/(ED) = (AC)/(EF)` is a correct pair of corresponding sides.

(C) False: 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 `(AB)/(ED) = (BC)/(DF) = (AC)/(EF) = k`, then AB = k · ED, BC = k · DF, and AC = k · EF.

Substituting these: `(k · ED + k · DF)/(k · EF) = (k(ED + DF))/(k · EF) = (ED + DF)/(EF)`. This holds true.

The statement ∠A = ∠D, ∠C = ∠F is not true.