Question

In the given figure abcd is a rectangle prove that triangle abe is congruent to triangle cdf

Answer 1

Δ ABE  ≅ Δ CDF  In the given figure abcd is a rectangle

Step-by-step explanation:

ABCD is a rectangle

hence AB = CD  

∠DAB = 90°  & ∠ADC = 90°

in ΔOAD

∠DAE = ∠ODA + ∠AOD  ( Exterior angle = Sum of opposite two angles)

=> ∠DAB + ∠BAE = ∠ODA + ∠AOD

=> 90° + ∠BAE = ∠ODA + 90°

=>  ∠BAE = ∠ODA

now in Δ EAB  &  ΔODA

∠BEA = ∠AOD = 90°

∠BAE = ∠ODA

=> Δ EAB  ≈  ΔODA

Similarly we can show that

Δ FCD  ≈  ΔODA

Δ EAB  ≈  ΔODA & Δ FCD  ≈  ΔODA

=> Δ EAB  ≈ Δ FCD

AB = CD

hence Δ EAB  ≅ Δ FCD

=>  Δ ABE  ≅ Δ CDF

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