In ∆DEF and ∆PQR, it is given that ∠D = ∠Q and ∠R = ∠E,

Question:

In ∆DEF and ∆PQR, it is given that ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

(a) $\frac{E F}{P R}=\frac{D F}{P Q}$

(b) $\frac{D E}{P Q}=\frac{E F}{R P}$

(c) $\frac{D E}{Q R}=\frac{D F}{P Q}$

(d) $\frac{E F}{R P}=\frac{D E}{Q R}$

Solution:

(b) $\frac{D E}{P Q}=\frac{E F}{R P}$

In ∆DEF and ∆PQRwe have:

$\angle D=\angle Q$ and $\angle R=\angle E$

Applying $A A$ similarity theorem, we conclude that $\triangle D E F \sim \triangle Q R P$.

Hence, $\frac{D E}{Q R}=\frac{D F}{Q P}=\frac{E F}{P R}$