Choose the paragraph proof that correctly completes the two-column proof. Given: M is the midpoint of . Prove: Statement Reason Given ? Definition of Midpoint ? ? ? (1 point) Responses It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SSS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SSS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SSS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: angle JMK is congruent to angle JML . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SSS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SAS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SAS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SAS Angle Theorem.

Question

Choose the paragraph proof that correctly completes the two-column proof. Given: M is the midpoint of . Prove: Statement Reason Given ? Definition of Midpoint ? ? ? (1 point) Responses It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SSS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SSS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SSS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: angle JMK is congruent to angle JML . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SSS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SAS Angle Theorem. It is given that Image with alt text: segment KJ is congruent to segment LJ . Because M is the midpoint of Image with alt text: segment KL , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexing Property of Congruence, we can state that Image with alt text: segment MJ is congruent to segment MJ . Therefore, we can state that Image with alt text: triangle JKM is congruent to triangle JLM by the SAS Angle Theorem. It is given that . Because M is the midpoint of , we know that . Knowing the Reflexing Property of Congruence, we can state that . Therefore, we can state that by the SAS Angle Theorem.

Answer 1

The correct paragraph proof that completes the two-column proof is:

It is given that M is the midpoint of LK. Because M is the midpoint of LK, we know that KM is congruent to ML. Knowing the Reflexive Property of Congruence, we can state that KM is congruent to KM. Therefore, we can state that triangle KLM is congruent to triangle KLM by the SSS Angle Theorem.

Answer 2

that's wrong

Answer 3

I apologize for the mistake.

The correct paragraph proof that completes the two-column proof is:

It is given that M is the midpoint of KL. Because M is the midpoint of KL, we know that KM is congruent to ML. Knowing the Reflexive Property of Congruence, we can state that KJ is congruent to LJ. Therefore, we can state that triangle KJM is congruent to triangle LJM by the SSS Angle Theorem.

Answer 4

choose one of the answers given

Answer 5

I apologize for the confusion. Based on the given options, the correct paragraph proof that completes the two-column proof is:

It is given that segment KJ is congruent to segment LJ. Because M is the midpoint of segment KL, we know that segment KM is congruent to segment LM. Knowing the Reflexive Property of Congruence, we can state that segment MJ is congruent to segment MJ. Therefore, we can state that triangle JKM is congruent to triangle JLM by the SSS Angle Theorem.

Answer 6

The paragraph proof that correctly completes the two-column proof is:

It is given that segment KJ is congruent to segment LJ. Because M is the midpoint of segment KL, we know that segment KM is congruent to segment LM. Knowing the Reflexive Property of Congruence, we can state that segment MJ is congruent to segment MJ. Therefore, we can state that triangle JKM is congruent to triangle JLM by the SAS Angle Theorem.

Answer 7

The correct paragraph proof that completes the two-column proof is:

It is given that segment KJ is congruent to segment LJ. Because M is the midpoint of segment KL, we know that segment KM is congruent to segment LM. Knowing the Reflexive Property of Congruence, we can state that segment MJ is congruent to segment MJ. Therefore, we can state that triangle JKM is congruent to triangle JLM by the SAS (Side-Angle-Side) Congruence Theorem.

To understand why this paragraph proof is correct, let's break it down step by step:

1. Given: segment KJ is congruent to segment LJ: This is a given statement.

2. Because M is the midpoint of segment KL, we know that segment KM is congruent to segment LM: Definition of midpoint states that the point M divides segment KL into two equal parts.

3. Knowing the Reflexive Property of Congruence, we can state that segment MJ is congruent to segment MJ: The Reflexive Property of Congruence states that any segment is congruent to itself.

4. Therefore, we can state that triangle JKM is congruent to triangle JLM by the SAS Congruence Theorem: Using the SAS Congruence Theorem, which states that if two triangles have two sides and the included angle congruent, then the triangles are congruent, we can conclude that triangle JKM is congruent to triangle JLM.

By following these steps, we have provided a logical proof to show that triangle JKM is congruent to triangle JLM using the given information and known principles of congruence.