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Given AE||FD, AE ≅FD and AC ≅BD. Prove ΔAEC≅ ΔDFB.

Given AE||FD, AE ≅FD and AC ≅BD. Prove ΔAEC≅ ΔDFB.-example-1
User Pablo Ramirez
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1 Answer

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28 votes

Since AE ≅FD and AC ≅BD are already given, we need to prove that Angle ADF and Angle CAE are also congruent.

Since we know that AE is parallel to FD and AD is also a straight segment that intersects both AE and FD, this will serve as our transversal segment. In this case, we have Angle ADF and Angle CAE as alternate interior angles. By definition, alternate interior angles are congruent. Hence, ∠ADF and ∠CAE are congruent with the reason that they are alternate interior angles.

From this, we can say that ΔAEC≅ ΔDFB is congruent by SAS Triangle Congruence Theorem stating that if two sides and an included angle are congruent to both triangles, then the two triangles are congruent.

Given AE||FD, AE ≅FD and AC ≅BD. Prove ΔAEC≅ ΔDFB.-example-1
User Paty
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