Get the answer to "To find: congruent criteria used to prove that..."

Lewis Harvey

Answered question

2021-07-25

To find: congruent criteria used to prove that the triangles are congruent.
Given information:
$∠ A B C \tilde{=} ∠ A C B, \overset{―}{A E} ⊥ \overset{―}{E C} and \overset{―}{A D} ⊥ \overset{―}{D B}$

Answer & Explanation

BleabyinfibiaG

Skilled2021-07-26Added 118 answers

Consider $△ B A D, △ C A E$
As $\overset{―}{A D} ⊥ \overset{―}{D B}, ∠ B D A = 90^{\circ}$
As $\overset{―}{A E} ⊥ \overset{―}{E C}, ∠ C E A = 90^{\circ}$
So,
$∠ C E A \tilde{=} ∠ B D A$ (i) (right angles are congruent to each other)
Also,
$∠ B A D \tilde{=} ∠ C A E$ (ii) (common angles in $△ B A D, △ C A E$ )
As $∠ A B C \tilde{=} ∠ A C B$ ,
$\overset{―}{A B} \tilde{=} \overset{―}{A C}$ (iii)
(In a triangle, sides opposite to equal angles are equal)
From (i), (ii) and (iii),
$△ B A D \tilde{=} △ C A E$ (by AAS congruence criteria)

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