SOLUTION: In parallelogram ABCD, AE is perpendicular to BC and AF is perpendicular to CD. Prove that triangle ABE is similar to triangle ADF.

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Question 969188: In parallelogram ABCD, AE is perpendicular to BC and AF is perpendicular to CD. Prove that triangle ABE is similar to triangle ADF.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


Given: parallelogram ABCD, AE ⊥ BC, AF ⊥ CD. 
To prove: ΔABE ∽ ΔADF.

1. m∠AEB = 90°      Given AE ⊥ BC.
2. m∠AFD = 90°      Given AF ⊥ CD. 
3.  ∠AEB ≅ ∠AFD    Both have equal measures. 1,2
4.    ∠B ≅ ∠D      Opposite interior ∠s of parallelogram ABCD are ≅.
5.  ΔABE ∽ ΔADF    If 2 ∠s of one Δ are ≅ 2 ∠s of another Δ the Δs are ∽. 3,4

Edwin