Geom ToF - Part 1

Geometry Level 1

True or False?

For any right triangle, if we draw the height from the hypotenuse to the vertex, we will get a pair of similar triangles

True always False always True only if the triangle is isosceles

2 solutions

Nihar Mahajan
Jul 10, 2015

If we let $m\angle ABC = x^\circ$ , clearly we can angle chase and get :

$m\angle BAD = (90-x)^\circ \\ m\angle CAD = x^\circ \\ m\angle ACB = (90-x)^\circ$

So by $A-A$ test of similarity , we can have following pairs of similar triangles:

$\Delta ABC \sim \Delta DBA \\ \Delta ABC \sim \Delta DAC \\\Delta DBA \sim \Delta DAC$

Thus the given statement is true.

Hadia Qadir
Jul 21, 2015