In the figure,if angle A = angle C,AB = 6 , c | vedclass

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(D) Given,$\angle A = \angle C$,$AB = 6 \, cm$,$BP = 15 \, cm$,$AP = 12 \, cm$,and $CP = 4 \, cm$.In $	riangle APB$ and $	riangle CPD$:$\angle A = \

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$5, 2$

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(D) Given,$\angle A = \angle C$,$AB = 6 \, cm$,$BP = 15 \, cm$,$AP = 12 \, cm$,and $CP = 4 \, cm$.In $	riangle APB$ and $	riangle CPD$:$\angle A = \angle C$ [Given]$\angle APB = \angle CPD$ [Vertically opposite angles]Therefore,$	riangle APB \sim 	riangle CPD$ [By $AA$ similarity criterion]Since the triangles are similar,the ratios of their corresponding sides are equal:$\frac{AP}{CP} = \frac{BP}{PD} = \frac{AB}{CD}$Substituting the given values:$\frac{12}{4} = \frac{15}{PD} = \frac{6}{CD}$Taking the first two terms:$\frac{12}{4} = \frac{15}{PD} \implies 3 = \frac{15}{PD} \implies PD = \frac{15}{3} = 5 \, cm$Taking the first and last terms:$\frac{12}{4} = \frac{6}{CD} \implies 3 = \frac{6}{CD} \implies CD = \frac{6}{3} = 2 \, cm$Hence,the length of $PD = 5 \, cm$ and the length of $CD = 2 \, cm$.

In the figure,if $\angle A = \angle C$,$AB = 6 \, cm$,$BP = 15 \, cm$,$AP = 12 \, cm$,and $CP = 4 \, cm$,then find the lengths of $PD$ and $CD$ (in $cm$).

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