Question

in the given figure if,angle a =angle c,ab=6cm,bp=15cm,ap=12cm and cp=4cm then find the lengths of pd and cd​

Answer 1

pd = 5cm, cd = 2cm

Step-by-step explanation:

Here, ∠A = ∠C [As Given]

and ∠APB = ∠CPD [Vertically Opposite Angles]

∴∠APB ~ ∠CPD [by AA similarity criteria]

$Now, \: \frac{AP}{CP} = \frac{PB}{PD} = \frac{AB}{CD}$

$\frac{AP}{CP} = \frac{PB}{PD}$

$\frac{12cm}{4cm} = \frac{15cm}{PD}$

$PD = 5cm$

$Now, \: \frac{AP}{CP} = \frac{AB}{CD}$

$\frac{12cm}{4cm} = \frac{6cm}{CD}$

$CD = 2cm$