Question

Is the following definition of complementary reversible? if yes, write it as a true biconditional. complementary angles are two angles whose sum measures to 90 degrees
a.this statement is not reversible
b.yes, if angles are complementary, than their sum measures to 90 degrees
c. yes, angles are complementary if (and only if) their sum measures to 90 degrees
d. yes, angles are complementary if their sum measures to 90 degrees 4. which biconditional is not a good definition?
a. a whole number is odd if and only if the number is not divisible by 2.
b. an angle is straight if and only if its measure is 180.
c. a whole number is even if and only if it is divisible by 2
d. a ray is a bisector of an angle if and only if it splits the angle into two angles.

Answer 1

Question 1: The answer is c. Yes, angles are complementary if (and only if) their sum measures to 90 degrees.

This definition of complementary is reversible because both parts of the sentence, whatever order they are put, are true. And we can be sure of it, when rewriting the sentence into both conditional statement and conditional converse. Both conditionals, have a part of a sentence that is called "hypothesis" and other that is called "conclusion".

• In conditional, the hypothesis clause comes first, and then the conclusion: If the angles are complementary, then their sum measures to 90 degrees.
• In converse, the conclusion clause comes first and then the hypothesis: If the sum of angles measures to 90 degrees, then the angles are complementary.

When both sentences in the conditional and in the converse are true, then it is can be a biconditional sentence. Furthermore, the general structure of this type of sentence is First clause + If (and only if) + Second clause.

Question 2: The answer is d. a ray is a bisector of an angle if and only if it splits the angle into two angles.

A ray is a bisector of an angle only when the line segment splits the angle into two equal parts.