Question

Given MN is perpendicular to MP, PQ is perpendicular to MP, and NR is congruent to OR. Prove triangle NRP is congruent to triangle QRM

Answer 1

1.
`\overline{MN} \perp \overline{MP}`,
`\overline{PQ} \perp \overline{MP}` (given)

2.
`\angle NMP` and
`\angle MPQ` are right angles (definition of perpendicular lines)

3.
`\angle NMP \cong \angle MPQ` (all right angles are congruent)

4.
`\overline{NR} \cong \overline{QR}` (given)

5.
`\angle NRM \cong \angle QRP` (vertical angles)

6.
`\triangle PRQ \cong \triangle MRN` (AAS)

7.
`\overline{MR} \cong \overline{RP}` (CPCTC)

8.
`\angle NRP \cong \angle MRQ` (vertical angles)

9.
`\triangle NRP \cong \triangle QRM` (SAS)