Answer
1. The median of a vertex of an isosceles triangle forms a right angle with the side opposite the vertex.
2. This means that two identical right triangles are formed, with each leg being the hypotenuse.
3. The hypotenuse of a right triangle is longer than the leg.
4. Thus, the legs of the isosceles triangle are longer than the median of the isosceles triangle.
Work Step by Step
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. $\square$
