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Answer:
TRUE
Step-by-step explanation:
Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.
We know that corresponding angles formed by transversal line are congruent.
Hence ∠JKL = ∠ MLK ...(i)
Now consider triangles JKL and MLK
JK = LM {Given}
∠JKL = ∠ MLK { Using (i) }
KL = KL {common sides}
Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congurent.
Hence given statement is TRUE.
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Rewritten by : Barada
The statement that if JK and LM are congruent and parallel, then angles JKL and MLK are congruent is false. Congruency of angles depends on more than just the congruency and parallelism of two lines.
In the field of geometry, just because two lines are congruent and parallel, this does not necessarily mean that the angles formed by the intersection of the lines with a third line are congruent. The statement 'If JK and LM are congruent and parallel, then JKL and MLK are congruent' is false. Congruency of angles JKL and MLK depends on the relationship between the two other sides of the angles, not solely the lines JK and LM. Therefore, for the angles to be congruent, additional conditions besides the congruency and parallelism of JK and LM must be satisfied.
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