If in two triangles DEF and PQR,angle D = ang | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given,in $	riangle DEF$ and $	riangle PQR$,$\angle D = \angle Q$ and $\angle E = \angle R$.By the $AA$ similarity criterion,$	riangle DEF \sim

Vedclass · Accepted Answer

$\frac{DE}{PQ} = \frac{EF}{RP}$

Vedclass · Answer

(D) Given,in $	riangle DEF$ and $	riangle PQR$,$\angle D = \angle Q$ and $\angle E = \angle R$.By the $AA$ similarity criterion,$	riangle DEF \sim 	riangle QRP$.Since the triangles are similar,the ratios of their corresponding sides are equal:$\frac{DE}{QR} = \frac{EF}{RP} = \frac{DF}{QP}$.Now,let's check the given options:Option $A$: $\frac{EF}{PR} = \frac{DF}{PQ}$ is equivalent to $\frac{EF}{RP} = \frac{DF}{QP}$,which is true.Option $B$: $\frac{EF}{RP} = \frac{DE}{QR}$ is true.Option $C$: $\frac{DE}{QR} = \frac{DF}{PQ}$ is equivalent to $\frac{DE}{QR} = \frac{DF}{QP}$,which is true.Option $D$: $\frac{DE}{PQ} = \frac{EF}{RP}$. From the similarity ratio,$\frac{DE}{QR} = \frac{EF}{RP}$. Thus,$\frac{DE}{PQ} = \frac{EF}{RP}$ is not necessarily true because $PQ 
eq QR$ in general.Therefore,option $D$ is not true.

If in two triangles $DEF$ and $PQR$,$\angle D = \angle Q$ and $\angle R = \angle E$,then which of the following is not true?

Similar Questions

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YP}$ is a median. If $YP = 6$,then $XZ = \ldots$

In $\Delta ABC$,$\angle B$ is a right angle. Then,according to Pythagoras' theorem,$\ldots \ldots \ldots$ holds good.

In $\Delta ABC$,$\overline{AD}$ is a median. The bisectors of $\angle ADB$ and $\angle ADC$ intersect $\overline{AB}$ and $\overline{AC}$ at $E$ and $F$ respectively. Prove that $\overline{EF} \parallel \overline{BC}$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $PM = 8$ and $RM = 12$,then $QM = \dots$

Find the value of $x$ for which $DE \parallel AB$ in the given figure.

Vedclass Test Series

Exam Paper Generator

Online Exam Module