Question

1. given: (overline{mp}) bisects (angle lmn) (overline{lm}congoverline{nm}) prove: (overline{lp}congoverline{np}) 1. (overline{mp}) bisects (angle lmn) 1. 2. 2. definition of bisect 3. 3. given 4. (overline{mp}congoverline{mp}) 4. 5. (\triangle lmpcong\triangle nmp) 5. 6. 6. cpctc

Explanation:

Step1: Definition of bisect

$$\angle NMP=\angle LMP$$

Step2: Given

$$\overline{LM}\cong\overline{NM}$$

Step3: Reflexive property

$$\overline{MP}\cong\overline{MP}$$

Step4: SAS (Side - Angle - Side) congruence

$$\triangle LMP\cong\triangle NMP$$

Step5: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

$$\overline{LP}\cong\overline{NP}$$

Answer:

$$\overline{LP}\cong\overline{NP}$$