Questions: Two angles have the same measure if and only if they are congruent. Is the above statement simple or compound? A. The statement is a compound statement because it combines two or more simple statements. B. The statement is a simple statement because it combines two or more simple statements. C. The statement is a compound statement because it has only one idea. D. The statement is a simple statement because it has only one idea.

Two angles have the same measure if and only if they are congruent.

Is the above statement simple or compound?
A. The statement is a compound statement because it combines two or more simple statements.
B. The statement is a simple statement because it combines two or more simple statements.
C. The statement is a compound statement because it has only one idea.
D. The statement is a simple statement because it has only one idea.

Transcript text: Two angles have the same measure if and only if they are congruent. Is the above statement simple or compound? A. The statement is a compound statement because it combines two or more simple statements. B. The statement is a simple statement because it combines two or more simple statements. C. The statement is a compound statement because it has only one idea. D. The statement is a simple statement because it has only one idea.

Solution

Solution Steps

Step 1: Understand the Statement

The given statement is: "Two angles have the same measure if and only if they are congruent." This statement is a biconditional statement, which means it is composed of two conditional statements: "If two angles have the same measure, then they are congruent" and "If two angles are congruent, then they have the same measure."

Step 2: Determine the Type of Statement

A simple statement is one that does not contain any other statements as parts. A compound statement is one that is made up of two or more simple statements. Since the given statement is a biconditional statement, it is composed of two conditional statements, making it a compound statement.

Final Answer

The answer is \(\boxed{\text{A}}\).

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