Q3. Write the biconditional as two c... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q3. (page 68)

Write the biconditional as two conditionals that are converse of each other:
Angles are congruent if and only if their measures are equal.

Short Answer

Expert verified

The conditionals that are converse of each other are:

Angles are congruent or equal if their measures are alike.

Measures of angles are equal if they are congruent.

Step by step solution

Step 1. State the biconditional statement.

Angles are congruent if and only if their measures are equal.

Step 2. Define a biconditional statement.

A biconditional statement is the combination of a conditional statement and its opposite written in if and only if form.

Step 3. State the conclusion.

The biconditional statement is 鈥淎ngles are congruent if and only if their measures are equal鈥�.

Therefore, this statement can be written as a combination of two conditional statements written as follows:

Angles are congruent or equal if their measures are alike.

Measures of angles are equal if they are congruent.

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Statement	Reasons
1. $\overset{鈫�}{B X}$ is the bisector of $鈭� A B C$	1. ?
2. $鈭� A B X 鈮�$ ?, or $m 鈭� A B X =$ ?	2. ?
3. $m 鈭� A B X + m 鈭� X B C = m 鈭� A B C$	3. ?
4. $m 鈭� A B X + m 鈭� A B X = m 鈭� A B C$ , or $2 m 鈭� A B X = m 鈭� A B C$	4. ?
5. $m 鈭� A B X = \frac{1}{2} m 鈭� A B C$	5. ?
6. $m 鈭� X B C = \frac{1}{2} m 鈭� A B C$	6. Substitution Prop. (Steps ? and ?)

91影视

Write the biconditional as two conditionals that are converse of each other:
Angles are congruent if and only if their measures are equal.

Short Answer

Step by step solution

Step 1. State the biconditional statement.

Step 2. Define a biconditional statement.

Step 3. State the conclusion.

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91影视

Write the biconditional as two conditionals that are converse of each other:Angles are congruent if and only if their measures are equal.

Short Answer

Step by step solution

Step 1. State the biconditional statement.

Step 2. Define a biconditional statement.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Calculus

Discrete Mathematics

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Write the biconditional as two conditionals that are converse of each other:
Angles are congruent if and only if their measures are equal.