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Answer :
We have proven that ∠AJLK is congruent to ∠ALNM based on the SAS congruence criteria, the definition of midpoint, and the corresponding angles theorem.
To prove that ∠AJLK = ∠ALNM, we can use the SAS (Side-Angle-Side) congruence criteria along with the definitions of midpoint and corresponding angles theorem.
JK || LM. (Given)
JK = LM. (Given)
L is the midpoint of JN. (Given)
JL = LN. (Definition of midpoint)
By using the SAS congruence criteria, we can establish the congruence of triangles JKL and LNM.
Triangle JKL ≅ Triangle LNM. (SAS congruence)
According to the corresponding angles theorem, corresponding angles of congruent triangles are congruent.
∠AJK = ∠ALM. (Corresponding angles of congruent triangles)
Since L is the midpoint of JN, we can infer the following:
∠AJL = ∠ALN. (Definition of midpoint)
Combining statements 6 and 7, we can conclude:
∠AJLK = ∠ALNM. (Angle addition)
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