Question

select whether each statement is always true, sometimes true, or 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 a diameter is a chord. always true sometimes true never true

Explanation:

• For "An arc measuring \(100^{\circ}\) has an acute corresponding central angle":
• An acute angle is less than \(90^{\circ}\). The measure of an arc is equal to the measure of its corresponding central angle. Since \(100^{\circ}>90^{\circ}\), this statement is never true.
• For "The measure of an arc is less than \(90^{\circ}\)":
• Arcs can have measures from \(0^{\circ}\) to \(360^{\circ}\). Some arcs (e.g., minor arcs in some cases) can be less than \(90^{\circ}\), but there are also arcs (e.g., major arcs, semicircles) that are not. So, this statement is sometimes true.
• For "A diameter is a chord":
• A chord is a line segment joining two points on a circle. A diameter is a chord that passes through the center of the circle. So, by definition, a diameter is a chord, and this statement is always true.

Answer:

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