If in two Δ DEF and Δ PQR,

Question:

If in two Δ DEF and Δ PQR,∠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) Given,in ΔDEF,∠D =∠Q,∠R = ∠E

$\therefore$ $\triangle D E F \sim \triangle Q R P$ [by AAA similarity criterion]

$\Rightarrow$ $\angle F=\angle P$ [corresponding angles of similar triangles]

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

 

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