   Chapter 5.3, Problem 42E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Prove that the line segment joining the midpoints of two sides of a triangle determines a triangle that is similar to the original triangle.

To determine

To prove:

The statement “The line segment joining the midpoints of two sides of a triangle determines a triangle that is similar to the original triangle.”

Explanation

Definition:

SSS:

If the three sides of one triangle are proportional (in length) to the three corresponding sides of a second triangle, then the triangle are similar.

Description:

Draw the line segment joining the midpoints of two sides as shown below.

Figure

From the given figure, it is observed that the line segment DE joining the two sides of AB and AC. In the triangle ABC, D is the midpoint of AB and E is the midpoint of AC.

By the definition of midpoint, AD=12AB and AE=12AC.

It is known that the line segment DE joins the midpoints of two sides a triangle, its length DE is half the length of BC. That is, DE=12BC

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 8596 radical form. 34/5

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 62. d1+cos2

Single Variable Calculus: Early Transcendentals

In Exercises 1-22, evaluate the given expression. P(5,2)

Finite Mathematics for the Managerial, Life, and Social Sciences

For a given M 0, the corresponding in the definition of limx012x4= is: a) 2M4 b) 2M4 c) 12M4 d) 12M4

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 