Chapter 10.4, Problem 17E

BuyFind*arrow_forward*

6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

1 views

*In Exercises 1 to 17, complete an analytic proof for each theorem.*

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

To determine

**To answer:**

The analytic proof for the given theorem “If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.”

Explanation

Given theorem is,

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

The above figure is drawn for the parallelogram ABCD with the diagonals perpendicular to each other.

Where, AC and BD are the diagonals of the parallelogram ABCD.

And

where, O is the mid point of the two diagonals.

Considering the two triangles ADO and CDO,

So, the triangles ADO and CDO are congruent.

Based on the Side-Angle-Side rule, the hypotenuses of the triangles are equal in length.

Sect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6ESect-10.1 P-7ESect-10.1 P-8ESect-10.1 P-9ESect-10.1 P-10E

Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.2 P-40ESect-10.2 P-41ESect-10.2 P-42ESect-10.2 P-43ESect-10.2 P-44ESect-10.2 P-45ESect-10.2 P-46ESect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-4ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-31ESect-10.3 P-32ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.5 P-37ESect-10.5 P-38ESect-10.5 P-39ESect-10.5 P-40ESect-10.5 P-41ESect-10.5 P-42ESect-10.5 P-43ESect-10.5 P-44ESect-10.5 P-45ESect-10.5 P-46ESect-10.5 P-47ESect-10.5 P-48ESect-10.5 P-49ESect-10.6 P-1ESect-10.6 P-2ESect-10.6 P-3ESect-10.6 P-4ESect-10.6 P-5ESect-10.6 P-6ESect-10.6 P-7ESect-10.6 P-8ESect-10.6 P-9ESect-10.6 P-10ESect-10.6 P-11ESect-10.6 P-12ESect-10.6 P-13ESect-10.6 P-14ESect-10.6 P-15ESect-10.6 P-16ESect-10.6 P-17ESect-10.6 P-18ESect-10.6 P-19ESect-10.6 P-20ESect-10.6 P-21ESect-10.6 P-22ESect-10.6 P-23ESect-10.6 P-24ESect-10.6 P-25ESect-10.6 P-26ESect-10.6 P-27ESect-10.6 P-28ESect-10.6 P-29ESect-10.6 P-30ESect-10.6 P-31ESect-10.6 P-32ESect-10.6 P-33ESect-10.6 P-34ESect-10.6 P-35ESect-10.6 P-36ESect-10.6 P-37ESect-10.6 P-38ESect-10.6 P-39ESect-10.6 P-40ESect-10.6 P-41ESect-10.6 P-43ESect-10.6 P-44ESect-10.6 P-45ESect-10.6 P-46ESect-10.6 P-49ESect-10.6 P-50ESect-10.CR P-1CRSect-10.CR P-2CRSect-10.CR P-3CRSect-10.CR P-4CRSect-10.CR P-5CRSect-10.CR P-6CRSect-10.CR P-7CRSect-10.CR P-8CRSect-10.CR P-9CRSect-10.CR P-10CRSect-10.CR P-11CRSect-10.CR P-12CRSect-10.CR P-13CRSect-10.CR P-14CRSect-10.CR P-15CRSect-10.CR P-16CRSect-10.CR P-17CRSect-10.CR P-18CRSect-10.CR P-19CRSect-10.CR P-20CRSect-10.CR P-21CRSect-10.CR P-22CRSect-10.CR P-23CRSect-10.CR P-24CRSect-10.CR P-25CRSect-10.CR P-26CRSect-10.CR P-27CRSect-10.CR P-28CRSect-10.CR P-29CRSect-10.CR P-30CRSect-10.CR P-31CRSect-10.CR P-32CRSect-10.CR P-33CRSect-10.CR P-34CRSect-10.CR P-35CRSect-10.CR P-36CRSect-10.CR P-37CRSect-10.CR P-38CRSect-10.CR P-39CRSect-10.CR P-40CRSect-10.CT P-1CTSect-10.CT P-2CTSect-10.CT P-3CTSect-10.CT P-4CTSect-10.CT P-5CTSect-10.CT P-6CTSect-10.CT P-7CTSect-10.CT P-8CTSect-10.CT P-9CTSect-10.CT P-10CTSect-10.CT P-11CTSect-10.CT P-12CTSect-10.CT P-13CTSect-10.CT P-14CTSect-10.CT P-15CTSect-10.CT P-16CTSect-10.CT P-17CTSect-10.CT P-18CTSect-10.CT P-19CTSect-10.CT P-20CTSect-10.CT P-21CTSect-10.CT P-22CT

Calculus: An Applied Approach (MindTap Course List)

Finite Mathematics

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

Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Calculus: Early Transcendental Functions

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Calculus: Early Transcendentals

Elementary Technical Mathematics

Mathematical Excursions (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Multivariable Calculus

Applied Calculus

Mathematical Applications for the Management, Life, and Social Sciences

Understanding Basic Statistics

Intermediate Algebra

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

Essentials Of Statistics

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Contemporary Mathematics for Business & Consumers

Finite Mathematics for the Managerial, Life, and Social Sciences

Calculus: Early Transcendental Functions (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Statistics for Business & Economics, Revised (MindTap Course List)

Multivariable Calculus

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

Research Methods for the Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Introduction To Statistics And Data Analysis

College Algebra (MindTap Course List)

Mathematics: A Practical Odyssey

Mathematics For Machine Technology

Study Guide for Stewart's Multivariable Calculus, 8th