Provide the reasons for the following proof . Given : overline JK cong overline KL , overline NK cong overline KM Prove : triangle NKJ cong triangle MLK Statements Reasons 1. overline JK cong overline KL .; overline NK cong overline KM 1. Given. 2. angle JKW cong angle LKM 2 3 3. triangle NKJ cong triangle MLK (1 point ) Reflexive Property of cong;SAS Reflexive Property of cong:ASA Vertical angles are congruent ASA Vertical angles are congruent SAS

Question

Provide the reasons for the following proof . Given : overline JK cong overline KL , overline NK cong overline KM Prove : triangle NKJ cong triangle MLK Statements Reasons 1. overline JK cong overline KL .; overline NK cong overline KM 1. Given. 2. angle JKW cong angle LKM 2 3 3. triangle NKJ cong triangle MLK (1 point ) Reflexive Property of cong;SAS Reflexive Property of cong:ASA Vertical angles are congruent ASA Vertical angles are congruent SAS

Answer 1

4. Triangle NKJ congruent triangle MLK

Reason: By the Reflexive Property of congruence, line segment JK is congruent to itself and line segment KL is congruent to itself.

5. Angle JKW congruent angle LKM

Reason: By the Vertical Angles Theorem, angle JKW is congruent to angle LKM because they are vertical angles.

6. Triangle NKJ congruent triangle MLK

Reason: By the SAS (Side-Angle-Side) Congruence Postulate, triangle NKJ is congruent to triangle MLK because side NK is congruent to side KM (by given information), angle JKW is congruent to angle LKM (by reasoning from statement 2), and side JK is congruent to side KL (by given information).