In Delta ABC and Delta PQR,angle A cong angle | vedclass

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(D) Given that in $\Delta ABC$ and $\Delta PQR$,$\angle A = \angle R$ and $\angle B = \angle P$.By the $AA$ similarity criterion,$\Delta ABC \sim \Del

Vedclass · Accepted Answer

$12$

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(D) Given that in $\Delta ABC$ and $\Delta PQR$,$\angle A = \angle R$ and $\angle B = \angle P$.By the $AA$ similarity criterion,$\Delta ABC \sim \Delta R P Q$.Since the triangles are similar,the ratios of their corresponding sides are equal:$\frac{AB}{RP} = \frac{BC}{PQ} = \frac{AC}{RQ}$.We are given $AB = 6$,$BC = 8$,and $PR = 9$.Substituting the values into the ratio $\frac{AB}{RP} = \frac{BC}{PQ}$:$\frac{6}{9} = \frac{8}{PQ}$.Simplifying the fraction $\frac{6}{9}$ gives $\frac{2}{3}$.So,$\frac{2}{3} = \frac{8}{PQ}$.$2 	imes PQ = 8 	imes 3$.$2 	imes PQ = 24$.$PQ = \frac{24}{2} = 12$.Therefore,$PQ = 12$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle R$ and $\angle B \cong \angle P$. If $AB = 6$,$BC = 8$ and $PR = 9$,then $PQ = \ldots$

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