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Q5

Expert-verified

Geometry

Found in: Page 34

Book edition Student Edition

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

Pages 227 pages

ISBN 9780395977279

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Short Answer

State the hypothesis and the conclusion of each conditional.
if

The hypothesis is and the conclusion is .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Hypothesis and the conclusion.

The hypothesis and the conclusion of a conditional statement are where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

Step 2. Symbolic representation.

If p represents the hypothesis and q represents the conclusion, then the basic form of an if-then statement is “If p, then q”. For example, in the statement “If today is Friday, then tomorrow is Saturday”, “today is Friday” is the Hypothesis, and “tomorrow is Saturday” is the Conclusion.

Step 3. Rewrite the statement.

The given statement “ if ” can be rewritten as “If , then ”.

Step 4. Identification of Hypothesis and the conclusion.

Since, “” is followed by “If” and “” is followed by then “then” thus, the hypothesis is and the conclusion is .

Hence, the hypothesis is and the conclusion is .

Most popular questions for Math Textbooks

Rewrite each pair of conditionals as a biconditional.

If then is a straight angle. If is a straight angle, then .

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with $b > a$ , and the midpoint M of $\bar{A B}$ has coordinate x, then prove $x = \frac{a + b}{2}$ .

Proof:

Statement	Reasons
1. A, M, and B have coordinated a, x, and b respectively; $b > a$ .	1. ?
2. $A M = x - a; M B = b - x$	2. ?
3. M is the midpoint of $\bar{A B}$ .	3. ?
4. $\bar{A M} ≅ \bar{M B}$ , or $A M = M B$	4. ?
5. $x - a = b - x$	5. ?
6. $2 x =$ ?	6. ?
7. $x = \frac{a + b}{2}$	7. ?

State the hypothesis and the conclusion of each conditional.

implies

Justify each statement with a property from algebra or property of congruence.

$2 (a + b) = 2 a + 2 b$

It is known that has a supplement, but $∠ H O K$ can’t have a complement. Name one possible measure for $∠ H O K$ .

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