Find the mistake made in the following proof. Explain why you think your colleague made this mistake.
Given: AB∣∣ED and AB≅ED
Prove: ΔABF≅ΔDEF
Proof:
It is given that AB∣∣ED so angle ∠DEB is congruent to angle ∠ABE, because parallel lines form congruent alternate interior angles with a transversal. It is also given that AB is congruent to ED and angle ∠AFB is congruent to angle ∠DFE because they are vertical angles and vertical angles are congruent. So, ΔABF is congruent to ΔDEF by ASA.
Gotta tell me where F is. You do know that ABDE is a rectangle.
F is the center point.
I have the same question and I'm really confused.
The mistake made in the proof is the incorrect use of the Angle-Side-Angle (ASA) congruence criterion. Here's why:
The ASA congruence criterion states that if two triangles have two pairs of corresponding congruent angles and a pair of corresponding congruent sides, then the triangles are congruent. However, in this proof, the triangles ΔABF and ΔDEF are not shown to have a pair of corresponding congruent sides.
The given information states that AB || ED (meaning AB is parallel to ED) and AB ≅ ED (meaning AB is congruent to ED). From this information, we can deduce that angle ∠DEB is congruent to angle ∠ABE due to the corresponding angles formed by parallel lines and a transversal.
Additionally, it is stated that angle ∠AFB is congruent to angle ∠DFE because they are vertical angles. While this statement is correct, it does not provide the necessary information to prove congruence between ΔABF and ΔDEF.
Therefore, the mistake in the proof lies in concluding that ΔABF is congruent to ΔDEF using the ASA congruence criterion when the necessary corresponding congruent sides have not been established.