choose the paragraph proof that correctly completes the two column proof. given= m is the midpoint of kl prove= jkm=jlm
Statement | Reason
1. m is the midpoint of kl | Given
2. km = ml | Definition of midpoint
3. kjm ≅ ljm | Segment Addition Postulate
4. Angle addition postulate | Definition of Congruent Angles
5. ∠jkm = ∠jlm | Definition of Congruent Angles
To prove that JKM is congruent to JLM, we can use the fact that M is the midpoint of KL. Here is a paragraph proof:
Paragraph Proof:
Given: M is the midpoint of KL
To prove: JKM = JLM
Proof:
1. Draw line segment KM and line segment LM.
2. Since M is the midpoint of KL, KM = ML because the midpoint divides the line segment into two congruent parts.
3. Angle JKM = Angle JLM because they are vertical angles formed by intersecting line segments KM and LM.
4. Side KM = Side LM because KM = ML (given) and sides opposite congruent angles in a triangle are congruent.
5. Therefore, by the side-angle-side (SAS) congruence postulate, JKM is congruent to JLM.
Therefore, JKM is congruent to JLM, as we have proved using the given information and the congruence postulates.
To prove that JKM is congruent to JLM using the information that M is the midpoint of KL, we can use a paragraph proof. Here's one possible way to complete the proof:
Paragraph Proof:
Given: M is the midpoint of KL
To Prove: JKM ≅ JLM
Since M is the midpoint of KL, we know that KM is congruent to ML by the definition of a midpoint.
Now, let's consider triangle JKM and triangle JLM. We have the following:
1. Side KM is congruent to side LM (as we established earlier).
2. Side JK is common to both triangles.
3. Angle JKM is congruent to angle JLM because they are vertical angles (it can also be proven with the given information, if we assume that JL and KL are straight lines).
Using the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle JKM is congruent to triangle JLM.
Therefore, we can state that JKM is congruent to JLM, as desired.
Note: It's important to keep in mind that there might be alternative proofs that could also prove the congruence of JKM and JLM, depending on the specific guidelines and assumptions given in the problem statement.