# 9.3 Arcs & Angles

## Investigation 1

1. Use the angle tool to measure BAC.
2. Use the angle tool to measure BDC.
3. Use the arrow tool to drag points B, C, and D around the circle. Observe how the measures change.

## C-81 Inscribed Angle Conjecture

How is the measure of an inscribed angle related to the measure of the arc it intercepts? Remember that the measure of an arc is equal to the measure of the central angle it intercepts.

## Investigation 2

1. Use the angle tool to measure BED.
2. Use the angle tool to measure BCD.
3. Use the arrow tool to drag point B and point D around the circle. Observe how the measures change.

## C-82 Inscribed Angles Intercepting Arcs Conjecture

How are the measures of the angles that intercept the same arc on the circle related?

## Investigation 3

1. Use the point tool to construct 3 points: D, E, and F, on the same semicircle.
2. Use the line segment tool to create BDC, BEC, and BFC.
3. Use the angle tool to measure the angles you created in step 2.
4. Use the arrow tools to drag points B, D, E, and F. Observe how the measures change.

## C-83 Angles Inscribed in a Semicircle Conjecture

What is the measure of any angle inscribed in a semicircle?

## Investigation 4

1. Use the polygon tool to construct a quadrilateral that is inscribed in the circle (cyclic quadrilateral).
2. Use the angle tool to measure all 4 angles of the quadrilateral.
3. Use the arrow tool to move the vertices on the circle. Observe the relationship between opposite angles of the cyclic quadrilateral.

## C-84 Cyclic Quadrilateral Conjecture

How are the measures of the opposite angles of a cyclic quadrilateral related?

## Investigation 5

In the task below, BCDE.
1. Use the distance tool to measure the length of arc BD.
2. Use the distance tool to measure the length of arc CE.
3. Use the arrow tool to drag points B and D around the circle. Observe how the measures change.

## C-85 Parallel Lines Intercepted Arcs Conjecture

How are the arcs of a circle intercepted by parallel lines on a circle related?