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Q29

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Geometry
Found in: Page 35
Geometry

Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Illustration

Short Answer

Write a definition of congruent angles as a biconditional.

The definition of congruent angles as a biconditional is: “∠A≅∠B if and only if m∠A=m∠B”.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Define the congruent angles.

Congruent angles are angles that have equal measures.

Let ∠A and ∠B both have equal measure then:

∠A≅∠B or m∠A=m∠B.

Step 2. Define the biconditional.

If a conditional and its converse are both true then they can be combined into a single statement by using connector “if and only if”. Such a statement containing the words “if and only if” is defined as a biconditional. For example, “p if and only if q”.

Step 3. Write the biconditional for the definition of congruent angles.

The definition of congruent angles tells us that the two statements ∠A≅∠B or m∠A=m∠B are equivalent.

Therefore, the bi-conditional statement is:

∠A≅∠B if and only if m∠A=m∠B.

Most popular questions for Math Textbooks

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 AB¯ has coordinate x, then prove x=a+b2.

Proof:

Statement

Reasons

1. A, M, and B have coordinated a, x, and b respectively; b>a.

1. ?

2. AM=x−a ; MB=b−x

2. ?

3. M is the midpoint of AB¯.

3. ?

4. AM¯≅MB¯, or AM=MB

4. ?

5. x−a=b−x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

State the converse of each conditional. Is the converse true or false?

If a number is divisible by 6, then it is divisible by 3.

State which postulate, definition, or theorem justifies the statement about the diagram.

If E is the midpoint of AF¯, then EC¯, bisects AF¯ .

State the hypothesis and the conclusion of each conditional.

If , then is a right angle.

State the hypothesis and the conclusion of each conditional.

if

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