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

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 ACD angle CAB angle BDC angle DBA

Identify the inscribed angle:

angle BDC angle ACD 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

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