Chapter 4.3, Problem 42E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# a) Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing.b) Use the relationship from part a) to find CM, the length of the median to the hypotenuse of right △ A B C , in which m ∠ C = 90 ∘ , AC = 6, and BC = 8.

To determine

(a)

To argue:

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

Explanation

Calculation:

We have to use the fact that the congruent diagonals of a rectangle bisect each other.

Consider the rectangle ABCD whose congruent diagonals are AC and BD.

â–³ABC is right triangle. Since it is a midpoint, clearly it is equidistant from the vertices that are opposite the 90 degree angle. Thus, we must prove that triangle AOB is isosceles. Since angle A and angle B are both bisected 90 degree angles, they have equal measures. Since the base angles are the same, it is isosceles.

â–³ABC is right angled with hypotenuse = AC, as per the question

To determine

(b)

To find:

CM, the length of the median to the hypotenuse of right ABC.

### 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

#### In Exercises 2336, find the domain of the function. 30. g(x)=2x2+3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Exercises 1-6, simplify the expression. 3+(1)2

Calculus: An Applied Approach (MindTap Course List)

#### Using n = 4 and midpoints for xi, then Riemann sum for 17x2 dx is a) 3443 b) 72 c) 168 d) 112

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

#### The graph of is: a) b) c) d)

Study Guide for Stewart's Multivariable Calculus, 8th

#### In Exercises 116, determine whether the argument is valid. pqqrpr

Finite Mathematics for the Managerial, Life, and Social Sciences