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Inscribed Angles Theorem Activity

Author:Jasmin Trujillo
Topic:Geometry

PART 1: Observe the following circle. Move the points around

Which angles do you think are congruent?

Select all that apply
  • A
  • B
  • C
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PART 2: Theorem: Angles subtended by the same arc are congruent. See for yourself.

Which arc subtends the congruent angles above?

Select all that apply
  • A
  • B
  • C
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PART 3: Now move points A and C around

What happens to the congruent angles as arc AC gets bigger?

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PART 4: Observe the following inscribed angles

Finish the sentence:

Angles subtended by the same ARC are always ___________

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PART 5: Angle <CEB is called the central angle because point E is at the center of the circle

INSCRIBED ANGLE THEOREM

What do you notice about angle <CEB and angle <CAB ?

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  • A
  • B
  • C
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PART 6: Observe, what happens to the inscribed angle <CAB when the central angle is 180 degrees

What is another name for the central angle <CEB?

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  • A
  • B
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PART 7: So, an inscribed angle across a circle's diameter is always a right angle.

What do all of the inscribed angles above form with the diameter?

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PART 8: Now, using all the above information, solve the following

Approximately, what is the measure of angle <BCD

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  • A
  • B
  • C
  • D
Check my answer (3)

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