Question

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)

Answer 1

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.