If AED and CED are both right triangles, what triangle congruence could be used to prove that the two triangles are congruent (Hint: it is not Hypotenuse leg)

Question

asked Aug 3, 2020 166k views

1 Answer

Thehhv · Answer 1 · 2020-08-09T04:21:56+0000

Answer:

The two triangles are congruent by AAS postulate.

Explanation:

From the figure,

$\angle AED=90$ °

$\angle CDE=90$ °

So,
$\angle AED \cong \angle CDE\cong 90$ °

For the given triangles
$\Delta AED\textrm{ and }\Delta CED$ ,

$\angle EAD\cong \angle ECD\\\angle AED \cong \angle CDE\\ED\cong ED(\textrm{common side})$

Therefore, the triangles are congruent by AAS postulate as two angles and one corresponding sides are congruent.