## Elementary Geometry for College Students (6th Edition)

1-Given an isosceles triangle ABC with vertex C. 2-drawing a median(CM), where M is a point of the side AB. 3- the median from the vertex of an isosceles triangle is also the altitude to the base of the triangle ABC so $\angle CMA= \angle CMB= 90^{\circ}$ 4-the median CM separates the triangle ABC into two congruent right triangles $\triangle AMC = \triangle BMC$ by SSS. 4-by lemma 3.5.7 side $AC \gt CM$ And side $CB \gt CM$ 5- therefore the median CM from the vertex C of an isosceles triangle is less than the length of either of the legs AC and CB. $\square$