"
">

If $Δ\ ABC$ and $Δ\ AMP$ are two right triangles, right angled at $B$ and $M$, respectively such that $∠MAP\ =\ ∠BAC$. Prove that:
(i) $ΔABC\ ∼\ ΔAMP$(ii) $\frac{CA}{PA}\ =\ \frac{BC}{MP}$
"

Academic Mathematics NCERT Class 10

Given:

$Δ\ ABC$ and $Δ\ AMP$ are two right triangles, right-angled at $B$ and $M$, respectively such that $∠MAP\ =\ ∠BAC$.

To do:

We have to prove that:

(i) $ΔABC\ ∼\ ΔAMP$

(ii) $\frac{CA}{PA}\ =\ \frac{BC}{MP}$

Solution:

(i) In $\vartriangle AMP$ and $\vartriangle ABC$,

$\angle AMP = ∠ABC = 90^o$

$\angle MAP = \angle BAC$ (Vertically opposite angles)

Therefore,

$\vartriangle ABC ∼ \vartriangle AMP$ (By AA similarity)

(ii) $\vartriangle ABC ∼ \vartriangle AMP$

This implies,

$\frac{CA}{PA} = \frac{BC}{MP}$ (Corresponding sides are proportional)

Hence proved.

Simply Easy Learning

Updated on: 10-Oct-2022

17 Views

Kickstart Your Career

Get certified by completing the course

Advertisements