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. Given: JL = NM, K is the midpoint of JN and LM

Prove: AJKLANKM
Statements
JL = NM
K is the midpoint of JN and LM
JK = NK
LK = MK
AJKLANKM
3.
1. GIVEN
GIVEN
2.
4.
L
5.
Reasons
K
N
M

. Given: JL = NM, K is the midpoint of JN and LM Prove: AJKLANKM Statements JL = NM-example-1
User Amanni
by
8.3k points

1 Answer

6 votes

The student needs to prove the congruency of triangles AJKL and ANKM by using given information. The key steps involve using the fact that K is the midpoint of two segments and employing the Side-Side-Side (SSS) Postulate for congruence.

Step-by-step explanation:

The student is tasked with proving that two triangles, AJKL and ANKM, are congruent given a set of preconditions. The fact that JL = NM and K is the midpoint of both JN and LM leads to further steps in the proof:

Given: JL = NM.

K is the midpoint of JN and LM (Given).

From step 2, we can infer that JK = NK and LK = MK because the definition of a midpoint is such that it divides a segment into two equal parts.

With JK = NK and LK = MK, along with the matching sides JL = NM given initially, by the Side-Side-Side (SSS) Postulate, the triangles AJKL and ANKM are congruent.

User Anya Samadi
by
8.2k points
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