Question

Given: ∠XMA ≅ ∠DNY Prove: ∠AMN ≅ ∠CNY

Proof: It is given that ∠XMA ≅ ∠DNY.
So, line AB is parallel to line CD by converse of the alternate exterior angles theorem. Since lines AB and CD are parallel, ∠AMN and ∠MND are congruent by the alternate interior angles theorem. Also, ∠MND ≅ ∠CNY by the consecutive interior angles theorem. Therefore, ∠AMN ≅ ∠CNY by the transitive property of equality.

Identify the flaw in the proof and the appropriate correction.




A.
Flaw: ∠AMN ≅ ∠MND by the alternate interior angles theorem.
Correction: ∠AMN and ∠MND by the consecutive interior angles theorem.
B.
Flaw: ∠MND ≅ ∠CNY by the consecutive interior angles theorem.
Correction: ∠MND ≅ ∠CNY by the alternate interior angles theorem.
C.
Flaw: ∠AMN ≅ ∠MND by the alternate interior angles theorem.
Correction: ∠AMN and ∠MND by the corresponding angles postulate.
D.
Flaw: ∠MND ≅ ∠CNY by the consecutive interior angles theorem.
Correction: ∠MND ≅ ∠CNY by the vertical angles theorem.

Answer 1

D

Explanation:

Since lines CD and XY intersect at point N, ∠MND and ∠CNY are vertical angles.

The vertical angles theorem states that vertical angles are congruent.

So, ∠MND ≅ ∠CNY by the vertical angles theorem.