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

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

Question

(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 = \

Vedclass · Accepted Answer

$5, 2$

Vedclass · Answer

(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 $cm$).

Similar Questions

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

If $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow ZYX$,and given $PQ = 6$,$QR = 8$,and $XY = 12$,find the length of $YZ$.

In the figure,$ABD$ is a triangle right-angled at $A$ and $AC \perp BD$. Show that $AD^{2} = BD \cdot CD$.

$A$ $15\, m$ high tower casts a shadow $24\, m$ long at a certain time. At the same time,a telephone pole casts a shadow $16\, m$ long. Find the height of the telephone pole (in $m$).

In the given figure,$BD$ and $CE$ intersect each other at the point $P$. Is $\triangle PBC \sim \triangle PDE$ ? Why?

Vedclass Test Series

Exam Paper Generator

Online Exam Module