From point M of the bisector of an obtuse angle, perpendiculars MA and MK are drawn

From point M of the bisector of an obtuse angle, perpendiculars MA and MK are drawn to the sides of this angle. Prove that MA = MK.

Given:
obtuse angle AOK,
OM – bisector,
MA perpendicular to OA,
AK perpendicular OK.
Prove that MA = MK
Proof:
Consider triangles AMO and MKO. These triangles are rectangular, since AM is perpendicular to OA and AK is perpendicular to OK. The MO side is the hypotenuse for these triangles. Angle MOA = angle MOA because OM is the bisector of angle O. Therefore, according to the hypotenuse and acute angle, triangle MOA = triangle MOA. Equal triangles have equal sides and angles. Then MA = MK, as required.