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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: “∠A≅∠B if and only if m∠A=m∠B”.

Step by step solution

01

Step 1. Define the congruent angles.

Congruent angles are angles that have equal measures.

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

∠A≅∠Bor m∠A=m∠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 “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”.

03

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∠Bare equivalent.

Therefore, the bi-conditional statement is:

∠A≅∠Bif and only if m∠A=m∠B.

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Most popular questions from this chapter

Copy everything shown and supply missing statements and reasons.

Given:

m∠1=m∠3;

m∠2=m∠4

Prove: m∠ABC=m∠DEF

Proof:

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

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

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

BD+DC=BC

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a number is divisible by 4, then it is divisible by 6.

Provide a counterexample to show that each statement is false.

Statement: If n2=5nthen n=5.
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