Question

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. hector wrote the following proof for his geometry homework for the given problem. statements reasons segment ln is congruent to segment np given ∠1 ≅ ∠2 given ∠n ≅ ∠n reflexive property Δlno ≅ Δpnm ∠nlo ≅ ∠npm corresponding parts of congruent triangles are congruent which of the following completes hector's proof? (6 points) angle-angle-side postulate angle-side-angle postulate side-angle-side postulate side-side-side postulate

1) angle-angle-side postulate
2) angle-side-angle postulate
3) side-angle-side postulate
4) side-side-side postulate

Answer 1

The correct completion of Hector's proof for the given problem is the angle-side-angle postulate.

Step-by-step explanation:

The correct completion of Hector's proof would be the angle-side-angle postulate (2).

The angle-side-angle postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

In this case, since segment ln is congruent to segment np (given), and angle 1 is congruent to angle 2 (given), the angle-side-angle postulate can be used to conclude that angle nlo is congruent to angle npm.