M2 T1 L1 Running Circles around Geometry
CL Module 2 Topic 1 Lessons 1-5
Table of Contents
- Review
- Defining Angle Pairs in Parallel Lines
- Getting Started
- Drawing a Circle
- Activity 1
- Central Angle
- Activity 2
- M2T1L1A2
- Activity 3
- M2T1L1A3
- M2T1L1A3b
- M2T1L1A3c
- Talk the Talk
- Poorly Drawn Quadrilaterals
Defining Angle Pairs in Parallel Lines
This Quick sketch illustrates the relationships between angle pairs in parallel lines.
Select the individual angle pair types and observe the angles that appear. Write your definition for the angle pair types based on what you observed.
[u][b]Define Corresponding Angles:[/b][/u]
[b][u]Define Alternate Interior Angles:[/u][/b]
[b][u]Define Alternate Exterior Angles:[/u][/b]
[b][u]Define Consecutive Interior Angles:[/u][/b]
[b][u]Define Consecutive Exterior Angles:[/u][/b]
List the angle pairs that are congruent?
List the angle pairs that are supplementary?
Drawing a Circle
Explore this applet to draw a circle. Use it to help write a definition of a circle.
What equation would give you a circle?
Central Angle
Definition of Central Angle
A central angle is an angle whose vertex is the center of a circle, and whose sides are radii.
Central Angle Theorem
The measure of a central angle is always equal to the degree measure of the intercepted arc. In the figure below, m [math]\angle[/math]A = m arc BC
Try It !
Drag points C and D to change the measure of the central angle and the arc. Look at the relationship between the angle A and arc CD.
Try These Questions
[math]\angle[/math] PQR is a central angle that measures 42[math]^\circ[/math], what is the measure of arc PR ?
In circle O, arc FG measures 84[math]\circ[/math], what is the measure of arc FOG ?
M2T1L1A2
M2T1L1A3
Poorly Drawn Quadrilaterals
Determine the best possible name for the poorly drawn quadrilateral below. Base your reasoning on how the quadrilateral is marked, and not on how it looks. Check your answer. Some quadrilaterals can not be determined, and others may be impossible!