6
QuizMultiple Choice

Logic and Reasoning — Quiz

Question 6 • MASTER COURSE Geometry

Holly wrote the statement Polygon R S T U V is regular if it has congruent sides and congruent angles. Which statements are true regarding her work? Choose three correct answers.

Answer
A
The hypothesis of the statement is "it has congruent sides and congruent angles."
B
It is a conditional statement.
C
The statement cannot be proven true or false.
D
The conclusion of the statement is "Polygon R S T U V is regular."
E
An equivalent statement is "If polygon R S T U V has congruent sides, then it has congruent angles."

Explanation

“P is true if Q” means “If Q, then P.” Here, the hypothesis is that polygon R S T U V has congruent sides and congruent angles, so A is true. The conclusion is that the polygon is regular, making D true, and the statement is conditional, making B true. Choice E is not equivalent: it says congruent sides alone imply congruent angles.

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