# If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM. Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM.

**Solution:**

Overlapping triangles LNO and PNM.

The triangles intersect at point Q on segment LO of triangle LNO and segment MP of the triangle

By using the congruence property in triangles, we can prove ∠NLO ≅ ∠NPM

Statements | Reasons |
---|---|

segment LN ≅ segment NP | Given |

∠ 1 ≅ ∠ 2 | Given |

∠ N ≅ ∠ N | Reflexive Property |

∠ NLO ≅ ∠ NPM | By using Angle-Angle-Side Postulate |

∠NLO ≅ ∠NPM | Corresponding Parts of Congruent Triangles Are Congruent(CPCTC) |

Thus ∠NLO ≅ ∠NPM using the congruence property known as Angle-Angle-Side Postulate of Hector geometry

## If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM. Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM.

**Summary:**

By using Angle-Angle-Side Postulate of Hector geometry it is proved that∠ NLO ≅ ∠ NPM, if segment LN is congruent to segment NP and ∠1 ≅ ∠2, Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM.