The triangles have a common vertex angle, and a given pair of
corresponding and congruent angles, they are therefore similar triangles.
- <u>∠ABC ≅ ∠ADE</u> (CASTC)
Reasons:
The given parameters are;
∠AED ≅ ∠ACB
By observation, we have that ΔAED and ΔACB have ∠A = ∠DAE and ∠A =
∠BAC in common.
Therefore, ∠DAE ≅ ∠BAC, by reflexive property.
Two angles of ΔAED (∠AED and ∠DAE) are congruent to two angles in
ΔACB.
(∠ACB and ∠BAC), which gives that ΔAED and ΔACB are similar by AA
Angle-Angle similarity postulate, and by Corresponding Angles of Similar
Triangles are Congruent CASTC we have;
∠AED ≅ ∠ACB
∠DAE ≅ ∠BAC
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