Question

select whether each statement is always true, sometimes true, or never true.
a radius is a segment.
always true
sometimes true
never true
an arc measuring 100° has an acute corresponding central angle.
always true
sometimes true
never true
the measure of an arc is less than 90°.
always true
sometimes true
never true

Explanation:

• For "A radius is a segment": A radius is defined as a line segment from the center of a circle to any point on its circumference. So by definition, it is always a segment.
• For "An arc measuring \(100^{\circ}\) has an acute corresponding central angle": An acute angle is an angle that measures less than \(90^{\circ}\). Since \(100^{\circ}>90^{\circ}\), an arc of \(100^{\circ}\) can never have an acute corresponding central angle (because the measure of an arc is equal to the measure of its corresponding central angle).
• For "The measure of an arc is less than \(90^{\circ}\)": Arcs can have measures ranging from \(0^{\circ}\) to \(360^{\circ}\). For example, a semic - circle has a measure of \(180^{\circ}\), a major arc can have a measure greater than \(180^{\circ}\). But there are also arcs (like some minor arcs) that can have measures less than \(90^{\circ}\). So the measure of an arc is sometimes less than \(90^{\circ}\).

Answer:

1. Always true
2. Never true
3. Sometimes true