In the isosceles triangle KLM, point P is indicated on the base of KM. From this point, perpendiculars are drawn

In the isosceles triangle KLM, point P is indicated on the base of KM. From this point, perpendiculars are drawn to the two lateral sides, respectively PA and PB. Prove that these segments PA and PB are equal to each other.

Given:
isosceles triangle KLM;
KM – base;
point P belongs to CM;
RA and PB are perpendiculars to the two lateral sides.
Prove that these segments PA = PB
Evidence:
Consider triangles KRA and RMV. They are rectangular in the same way as RA and PB are perpendiculars. Hypotenuse KR = hypotenuse RM. Angle K = angle M. According to the hypotenuse and acute angle, the triangles KRA = PMA. Therefore AP = PM. Q.E.D.