Asked by Kayla Druery
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.
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.
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