Lewis Harvey

## Answered question

2021-07-25

To find: congruent criteria used to prove that the triangles are congruent.
Given information:

### Answer & Explanation

BleabyinfibiaG

Skilled2021-07-26Added 118 answers

Consider $\mathrm{△}BAD,\mathrm{△}CAE$
As $\stackrel{―}{AD}\perp \stackrel{―}{DB},\mathrm{\angle }BDA={90}^{\circ }$
As $\stackrel{―}{AE}\perp \stackrel{―}{EC},\mathrm{\angle }CEA={90}^{\circ }$
So,
$\mathrm{\angle }CEA\stackrel{\sim }{=}\mathrm{\angle }BDA$ (i) (right angles are congruent to each other)
Also,
$\mathrm{\angle }BAD\stackrel{\sim }{=}\mathrm{\angle }CAE$ (ii) (common angles in $\mathrm{△}BAD,\mathrm{△}CAE$)
As $\mathrm{\angle }ABC\stackrel{\sim }{=}\mathrm{\angle }ACB$,
$\stackrel{―}{AB}\stackrel{\sim }{=}\stackrel{―}{AC}$ (iii)
(In a triangle, sides opposite to equal angles are equal)
From (i), (ii) and (iii),
$\mathrm{△}BAD\stackrel{\sim }{=}\mathrm{△}CAE$ (by AAS congruence criteria)

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