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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: 鈥�鈭�R is a right angle if and only if m鈭�R=90鈭�鈥�.

Step by step solution

01

Step 1. Define the right angle.

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

Let鈭�R measure 90掳then, the angle鈭�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 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 right angles.

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

Therefore, the bi-conditional statement is:

鈭�Ris a right angle if and only if m鈭�R=90掳.

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