Question

Cut out two identical right angled triangles. Name the vertices of the A, B, C on both sides .Draw the altitude on the hypotenuse of one of the foot of the perpendicular as D. cut the triangle on its altitude an triangles. state the correspondences by which the three triangle an one another.

Answer 1

We have,

Given that:-

$\Delta ABC$ right angled at point $B$.and perpendicular from $B$ intersecting $AC$ at point $D$.

To prove :-

$\Delta ADB\sim \Delta ABC$

$\Delta BDC\sim \Delta ABC$

$\Delta ADB\sim \Delta BDC$

Proof:-

$In\Delta BDCand\Delta ABC$

$\angle C=\angle C\left(Common\right)$

$\angle BDC=\angle ABC\left(Each{90}^o\right)$

$\text{Then,}$

$\Delta BDC\sim \Delta ABC\left(ByAAsimilarity\right)$

$In\Delta ADBand\Delta ABC$

$\angle A=\angle A\left(Common\right)$

$\angle ADB=\angle ABC\left(Each{90}^o\right)$

$\text{Then,}$

$\Delta ADB\sim \Delta ABC\left(ByAAsimilarity\right)$

Hence proved.