Question

In Fig, 7.244, if ∠A =∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = _______ and CD = _________.

Answer 1

In ∆ABP and ∆CDP,

∠A = ∠C (Given)

∠APB = ∠CPD (Vertically opposite angles)

∴ ∆ABP $~$ ∆CDP (AA similarity)

$\Rightarrow \frac{\mathrm{BP}}{\mathrm{PD}}=\frac{\mathrm{AB}}{\mathrm{CD}}=\frac{\mathrm{AP}}{\mathrm{PC}}$ (If two triangles are similar, then their corresponding sides are proportional)

$$\begin{gathered} \Rightarrow \frac{15\mathrm{cm}}{\mathrm{PD}}=\frac{6\mathrm{cm}}{\mathrm{CD}}=\frac{12\mathrm{cm}}{4\mathrm{cm}} \\ \Rightarrow \frac{15\mathrm{cm}}{\mathrm{PD}}=3\mathrm{and}\frac{6\mathrm{cm}}{\mathrm{CD}}=3 \\ \Rightarrow \mathrm{PD}=5\mathrm{cm}\mathrm{and}\mathrm{CD}=2\mathrm{cm} \end{gathered}$$

In Fig, 7.244, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = ___5 cm___ and CD = ___2 cm___.