Question

consider the statement \an acute angle, a, measures 0° < m∠a < 90°.\. a. write the statement as a conditional statement. b. if the conditional statement is true, write the converse of the conditional. c. if the conditional statement is false, give a counter - example for the conditional. d. if the converse statement is true, write a true biconditional statement. e. if the converse statement is false, give a counter - example for the converse. b. if the conditional statement is true, which of the following is the converse of the conditional? a. if 0° < m∠a < 90°, then ∠a is not an acute angle. b. if 0° < m∠a < 90°, then ∠a is an acute angle. c. if 90° > m∠a > 90°, then ∠a is an acute angle. d. the conditional statement is false.

Explanation:

Step1: Recall conditional statement form

A conditional statement is of the form "if p, then q". Here, p is "an angle is acute" and q is "the measure of the angle \(m\angle A\) satisfies \(0^{\circ}

Step2: Recall converse of a conditional statement

The converse of a conditional statement "if p, then q" is "if q, then p". So the converse of "If \(\angle A\) is an acute - angle, then \(0^{\circ}

Step3: Analyze truth - value of conditional and converse

The conditional statement "If \(\angle A\) is an acute - angle, then \(0^{\circ}

Answer:

a. If \(\angle A\) is an acute - angle, then \(0^{\circ}b. B. If \(0^{\circ}c. The conditional statement is true, so no counter - example.
d. \(\angle A\) is an acute angle if and only if \(0^{\circ}e. The converse statement is true, so no counter - example.