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Chapter 2: Q29 (page 35)

Write a definition of congruent angles as a biconditional.

Short Answer

Expert verified

The definition of congruent angles as a biconditional is: 鈥�鈭�A鈮�鈭�B if and only if m鈭�A=m鈭�B鈥�.

Step by step solution

01

Step 1. Define the congruent angles.

Congruent angles are angles that have equal measures.

Let鈭�A and鈭�B both have equal measure then:

鈭�A鈮�鈭�Bor m鈭�A=m鈭�B.

02

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 鈥渋f and only if鈥�. Such a statement containing the words 鈥渋f and only if鈥� is defined as a biconditional. For example, 鈥�p if and only if q鈥�.

03

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

The definition of congruent angles tells us that the two statements鈭�A鈮�鈭�B or m鈭�A=m鈭�Bare equivalent.

Therefore, the bi-conditional statement is:

鈭�A鈮�鈭�Bif and only if m鈭�A=m鈭�B.

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Most popular questions from this chapter

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

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State the hypothesis and the conclusion of each conditional.

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Justify each step.

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