Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q21.

Expert-verified

Geometry

Found in: Page 212

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.
If $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Hence proved that if $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Define contrapositive statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

The given statement is if $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if $m ∠ D + m ∠ C = 180 °$ then $m ∠ A + m ∠ B = 180 °$ .

Step 3. Prove the statement

Since the sum of all angles of a quadrilateral is 360, therefore following will hold from the given figure as:

$\begin{matrix} m ∠ A + m ∠ B + m ∠ D + m ∠ C = 360 ° \\ m ∠ A + m ∠ B + 180^{o} = 360 ° \\ m ∠ A + m ∠ B = 360 ° - 180 ° \\ m ∠ A + m ∠ B = 180 ° \end{matrix}$

Most popular questions for Math Textbooks

For the following figure, find the value of x.

For the following figure, name the longest and the shortest side of the triangle.

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.

If $x^{2} \neq y^{2}$ , then $x \neq y$ .

For the following conditional statement, classify the statement as true or false.

If $x + 1 > 5$ , then $x > 4$ .

For the following figure, find the measures of $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ .

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free