   Chapter 5.5, Problem 19E 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

In Exercises15 to 19, create drawing as needed. Given: Square A B C D with diagonals D B ¯ and A C ¯ intersecting at E D C = 5 3 Find: D B

To determine

To find:

DB of a square ABCD with diagonals DB¯ and AC¯ intersecting at E and DC=53.

Explanation

Approach:

For a right triangle for which the measure of the interior angles 45°, 45°, and 90°, if ‘a’ is the length of measure of one of the leg; opposite to the angle 45°, then the length of the other two sides is given by

Length of the other leg =a

Length of the hypotenuse =a2

In general

Length of the legs are equal.

Length of the hypotenuse =2× (Length of one of the legs)

Calculation:

Given,

ABCD is a square DB¯ and AC¯ intersecting at E and DC=53..

By the property of a square that all the sides and diagonals are of equal in length and the diagonals bisect each other at right angle, we have

AB¯BC¯CD¯DA¯,

AE¯BE¯CE¯DE¯,

DB¯AC¯, and

DBAC.

Thus,

Now, consider the right triangle ADE of the square ABCD, having right angle at E.

Since, two of the sides of the right triangle are congruent, the angles opposite to the sides must be equal and should be 45° each.

Thus, the ADE become

Here, AD is the hypotenuse of the ADE.

By the application of 45°-45°-90°

45°-45°-90° theorem.

In a right triangle whose angle measures 45°, 45°, and 90°, the legs are congruent and the hypotenuse has a length equal to the product of 2 and the length of either leg

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

Find all possible real solutions of each equation in Exercises 3144. y32y22y3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 4562, find the values of x that satisfy the inequality (inequalities). 55. (x + 3)(x 5) 0

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

What are the two requirements for a random sample?

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integral. 27. dx1+ex

Single Variable Calculus: Early Transcendentals

True or False: , for –π ≤ t ≤ π, is smooth.

Study Guide for Stewart's Multivariable Calculus, 8th

Explain how an artifact can limit the validity and reliability of a measurement.

Research Methods for the Behavioral Sciences (MindTap Course List) 