Angle at the Center Theorem

Part 1: Pizza

The pizza has a radius of about 4 inches.[br]Point C (0,0) is the center of the pizza.

Graph 1

MOVE [b]POINT E[/b] and find out how big you want your slice pizza.[br]Answer in terms of degrees and give the coordinates of E .[br] [br]Example: Pizza Slice Size is 180 degrees and coordinate E (-4,0).

Part 2: Best Guess

The circle below has center A (0,0) and radius 4.[br][br]Angle BAC is called the central angle and the measurement of central angle BAC is 90 degree.[br][br]Angle BDC is called the inscribed angle.[br]

Graph 2

Give me your best guess on the measurement of the inscribed angle BDC (the angle in pink).

Part 3: Learning Time

Let's find out what is the relationship between the central angle and the inscribed angle! :)

Please watch this video.

This is a circle with center A (0,0) and radius 4.[br][br]Move point C (color blue) to create different measurements for central angle BAC.[br]Observe what happen between the measurement of central angle BAC and the measurement of inscribed angle BDC.

Graph 3

If the central angle BAC is 90 degrees, then what is the measurement of the inscribed angle BDC? [br]Explain your reasoning.

Using Graph 3 above[br] If the measurement of the [b]central angle BAC[/b] is [b]240 degrees[/b],[br] what is the measurement of the [b]inscribed angle BDC[/b]?

Using Graph 3 above[br] If the measurement of the [b]inscribed angle BDC[/b] is [b]64 degrees[/b],[br] what is the measurement of the [b]central angle BAC[/b]?

Angle at the Center Theorem

What is the relationship between the measurement of central angle BAC and the measurement of inscribed angle BDC?[br]Select all that apply.

inscribed angle BDC [math]=2x[/math] central angle BAC central angle BAC [math]=2x[/math] inscribed angle BDC the measurement of the central angle BAC is half of the measurement of the inscribed angle BDC the measurement of the central angle BAC is [math]3x[/math] (three times bigger) of the measurement of the inscribed angle BDC the measurement of the inscribed angle BDC is half of the measurement of the central angle BAC central angle BAC [math]=\frac{1}{2}x[/math] inscribed angle BDC inscribed angle BDC [math]=\frac{1}{2}x[/math] central angle BAC the measurement of the central angle BAC is [math]2x[/math] (two times bigger) of the measurement of the inscribed angle BDC

Please watch this video

Graph 4

If your friend, cut the pizza from [b]DB [/b]and from [b]DC[/b], what is the measurement of angle [b]BDC[/b] (angle in red)?

Identify the central angle:

angle CAB angle BDC angle DBA angle ACD

Identify the inscribed angle:

angle ACD angle BDC angle DBA angle CAB

Part 4: Reflection Time

Reflection

1. What was your favorite part of this activity?[br]2. What did you not like about this activity?[br]3. Write your own definition of what it means to be an inscribed angle and a central angle.[br]4. Bonus Question: What is your favorite pizza toppings?[br][br]Please number your responses:

On a scale of 1-5, was this activity helpful in learning the ANGLE at the CENTER THEOREM?[br]1: meaning not very helpful[br]5: meaning very helpful

2 - somewhat helpful 4 - moderately helpful 3 - neutral 5 - very helpful 1 - not very helpful

Angle at the Center Theorem

Part 1: Pizza

Graph 1

Part 2: Best Guess

Graph 2

Part 3: Learning Time

Please watch this video.

Graph 3

Angle at the Center Theorem

Please watch this video

Graph 4

Part 4: Reflection Time

Reflection

Information: Angle at the Center Theorem