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 ∆PQR, we 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, $\frac{D E}{Q R}=\frac{D F}{Q P}=\frac{E F}{P R}$
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