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Chapter 2: Q30 (page 35)

Write a definition of a right angle as a biconditional.

Short Answer

Expert verified

The definition of congruent angles as a biconditional is: “∠R is a right angle if and only if m∠R=90∘”.

Step by step solution

01

Step 1. Define the right angle.

The right angle is an angle that has measure 90o.

Let∠R measure 90°then, the angle∠R is a right angle.

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 right angles.

The definition of congruent angles tells us that the two statements∠R measure90° or the angle∠R is a right angle. are equivalent.

Therefore, the bi-conditional statement is:

∠Ris a right angle if and only if m∠R=90°.

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Most popular questions from this chapter

Fold down a corner of a rectangular sheet of paper. Then fold the next corner so that the edges touch as in the figure. Measure the angle formed by the fold lines. Repeat with another sheet of paper, folding the corner at a different angle. Explain why the angles formed are congruent.

The figure:

State the hypothesis and the conclusion of each conditional.

only if

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

If , then B is the midpoint of .

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

If ∠A≅∠B, then m∠A=m∠B.

State the hypothesis and the conclusion of each conditional.

I can’t sleep if I’m not tired.
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