Question

Proof point l is the midpoint of jkŽ¯Ž¯Ž¯Ž¯Ž¯. jkŽ¯Ž¯Ž¯Ž¯Ž¯ intersects mkŽ¯Ž¯Ž¯Ž¯Ž¯Ž¯ at k. if mkŽ¯Ž¯Ž¯Ž¯Ž¯Ž¯≅jlŽ¯Ž¯Ž¯Ž¯, complete the flow proof to prove that lkŽ¯Ž¯Ž¯Ž¯Ž¯≅mkŽ¯Ž¯Ž¯Ž¯Ž¯Ž¯. drag the statements and reasons to complete the proof.

Answer 1

A flow proof using the definition of midpoint and the transitive property of congruence shows segments LK and MK are congruent because L is the midpoint of JK and MK is congruent to JL.

Step-by-step explanation:

To prove that point L is the midpoint of segment JK, where segment JK intersects MK at K and given that segment MK is congruent to segment JL, we can use the properties of line segments and a flow proof. A flow proof is a type of proof formatted in connected statements and reasons, showing the logical order of the argument.

Here’s a step-by-step explanation:

1. Draw segments JK and MK with an intersection at point K.
2. Identify the given information: MK is congruent to JL, and L is the midpoint of JK.
3. Since L is the midpoint of JK, JL is congruent to LK (Definition of Midpoint).
4. It is given that MK is congruent to JL (Given).
5. By the Transitive Property of Congruence, if JL is congruent to LK, and JL is also congruent to MK, then MK must be congruent to LK (Transitive Property of Congruence).

This completes the proof that segments LK and MK are congruent.