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 Reflexive 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 KM , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexive 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 Reflexive 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 KM , 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 KM , 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 Reflexive 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 KM , we know that Image with alt text: segment KM is congruent to segment LM . Knowing the Reflexive 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 Reflexive 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 KM , 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 KM , 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

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 KM , 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.

Answer 2

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 KM, 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 3

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 KM, 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.

To arrive at this proof, we need to follow the given information step by step. The given information states that segment KJ is congruent to segment LJ. Then, we use the fact that M is the midpoint of segment KM to conclude that segment KM is congruent to segment LM. This follows from the definition of a midpoint. From there, we can apply the Reflexive Property of Congruence, which states that any segment or angle is congruent to itself. Thus, we conclude that segment MJ is congruent to segment MJ.

Finally, to prove that triangle JKM is congruent to triangle JLM, we use the SSS Angle Theorem. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In our case, we have segment JK congruent to segment LJ, segment KM congruent to segment LM, and segment MJ congruent to segment MJ. Therefore, we can use the SSS Angle Theorem to establish the congruence of triangle JKM and triangle JLM.