Question

Как решить задачу: На биссектрисе BM равнобедренного треугольника ABC с основанием AC отмечена точка D , на отрезке AM - точка E и на отрезке CM - точка F , причём EM = FM. Найдите угол CFD , если угол FDE = 80 градусов

Answer 1

FDE + CFD = 180, ЯК СУМІЖНІ

80 + х = 180

х = 100 - CFD

Answer 2

The Problem:

The problem asks us to find the measure of angle CFD, given that we are given a right isosceles triangle ABC with bisector DM of the right angle B, and points D, E, and F marked on the bisector, the segment AM, and the segment CM respectively such that the length EM equals the length FM.

Additional Information:

The question also provides that the measure of angle FDE is 80 degrees.

Solution:

Triangle AEM is isosceles with AM = EM. Therefore, the angle at M is also 80 degrees. Triangle CFM is also isosceles with CM = FM. Therefore, the angle at M is also 80 degrees Since corresponding angles of intersecting lines are equal, angle FMD = angle EMD = 80 degrees. Also, since DM is the angle bisector, angle MDB = angle MDC. Therefore, by angle-angle-side property of congruent triangles, triangle BMD is congruent to triangle CMD. Hence, angle CFD = angle BMD = 40 degrees.