Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 3 - Section 3.5 - Inequalities in a Triangle - Exercises - Page 160: 37


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. $\square$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.