Question

Given: A regular hexagon; M is the midpoint of angle NO and RP. Prove: Angle NRM = Angle OPM

Answer 1

Explanation:

Since it is a regular hexagon, the length of its sides are equal. And same as the distance across its flats.

So that;

NR ≅ OP (property of a regular polygon)

PM ≅ RM (half of the distance across flats of a polygon)

NM ≅ OM (half of the distance across flats of a polygon)

<NMR ≅ <PMO (vertically opposite angles)

<NRM ≅ <OPM (alternate angle property)

<RNM ≅ <POM (alternate angle property)

This therefore proves that: ΔNRM = ΔOPM