BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

In Exercises 25 and 26, complete each proof shown on page 160.

Given: Equilateral Δ A B C and D - B - C
Prove: D A > A C

Chapter 3.5, Problem 26E, In Exercises 25 and 26, complete each proof shown on page 160. Given: Equilateral ABC and D-B-C

PROOF
Statements Reasons
1. ? 1. Given
2. Δ A B C is equiangular, so m A B C = m C 2. ?
3. m A B C > m D ( D of Δ A B D ) 3. The measure of an exterior of a Δ is greater than the measure of either nonadjacent interior
4. ? 4. Substitution
5. ? 5. ?

To determine

To prove:

The side DA is greater than the side AC.

Explanation

Given:

Consider the figure,

Figure (1)

From figure (1),

Equilateral ΔABC and D-B-C

If the measure of one angle of a triangle is greater than the measure of a second angle, than the side opposite to the larger angle is longer than the side opposite to the smaller angle.

The measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle of a triangle.

Definition:

The triangle whose all the sides are equal and the measures of all the angle are same, that triangle is called equilateral or equiangular triangle.

Approach:

Consider an equilateral ΔABC,

Since, in equilateral triangle the measures of all the angle are same, then

mABC=mC(1)

Consider the triangle ΔABD,

Since, the measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle of a triangle. Then,

mABC>mD(2)

Substitute equation (1) in equation (2).

mC>mD(3)

Consider the triangle ΔADC,

Since, the measure of one angle of a triangle is greater than the measure of a second angle, than the side opposite to the larger angle is longer than the side opposite to the smaller angle. Then, from equation (3) the side DA is greater than the side AC. So,

DA>AC

PROOF
Statements Reasons
1. Equilateral ΔABC and D-B-C 1

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
Sect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.2 P-37ESect-3.2 P-38ESect-3.2 P-39ESect-3.2 P-40ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 P-46ESect-3.3 P-47ESect-3.3 P-48ESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.CR P-1CRSect-3.CR P-2CRSect-3.CR P-3CRSect-3.CR P-4CRSect-3.CR P-5CRSect-3.CR P-6CRSect-3.CR P-7CRSect-3.CR P-8CRSect-3.CR P-9CRSect-3.CR P-10CRSect-3.CR P-11CRSect-3.CR P-12CRSect-3.CR P-13CRSect-3.CR P-14CRSect-3.CR P-15CRSect-3.CR P-16CRSect-3.CR P-17CRSect-3.CR P-18CRSect-3.CR P-19CRSect-3.CR P-20CRSect-3.CR P-21CRSect-3.CR P-22CRSect-3.CR P-23CRSect-3.CR P-24CRSect-3.CR P-25CRSect-3.CR P-26CRSect-3.CR P-27CRSect-3.CR P-28CRSect-3.CR P-29CRSect-3.CT P-1CTSect-3.CT P-2CTSect-3.CT P-3CTSect-3.CT P-4CTSect-3.CT P-5CTSect-3.CT P-6CTSect-3.CT P-7CTSect-3.CT P-8CTSect-3.CT P-9CTSect-3.CT P-10CTSect-3.CT P-11CTSect-3.CT P-12CTSect-3.CT P-13CTSect-3.CT P-14CTSect-3.CT P-15CTSect-3.CT P-16CTSect-3.CT P-17CTSect-3.CT P-18CTSect-3.CT P-19CT

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Given: ABDEmBAC+mCDE=93 Find: mACD See Hint in Exercise 26.

Elementary Geometry For College Students, 7e

For the following set of stores, find the value of each expression: a. X b. (X) c. (X 3) d. (X 3) X 4 5 2 1 3

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

What is wrong with the equation? 21x4dx=x33]21=38

Single Variable Calculus: Early Transcendentals

The simplified form of the derivative of y=(x+11−x2)3.

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 1520, simplify the expression. 19. (3xy24x3y)2(3xy32x2)3

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

The moment about the xz-plane of solid E whose density is ρ(x, y, z) = x is:

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: If converges absolutely, then it converges conditionally.

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

Explain how the existence of an interaction can influence the interpretation of main effects.

Research Methods for the Behavioral Sciences (MindTap Course List)