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Illustrative Mathematics - Geometry - Unit 7 - Lesson 12

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Last updated about 3 years ago
7 questions
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Question 1
1.

Match each diagram showing a sector with the measure of its central angle in radians.

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Question 2
2.

In the circle, sketch a central angle that measures \frac{2\pi}{3} radians.

Question 3
3.

Angle AOC has a measure of \frac{5\pi}{6} radians. The length of arc AB is 2\pi units and the radius is 12 units.
What is the area of sector BOC?

Question 4
4.

Lin thinks that the central angle in circle A is congruent to the central angle in circle B.
Do you agree with Lin? Show or explain your reasoning.

Question 5
5.

Question 6
6.

Match each arc length and radius with the measure of the central angle that defines the arc.

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arc length 9\pi cm, radius 12 cm
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angle: 30 degrees
arc length 4\pi cm, radius 10 cm
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angle: 72 degrees
arc length 3\pi cm, radius 18 cm
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Question 7
7.

Quadrilateral ABCD is shown with the given angle measures.
Select all true statements.

This lesson is from Illustrative Mathematics. Geometry, Unit 7, Lesson 12. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/7/12/preparation.html ; accessed 29/July/2021.

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diagram C
\frac{3\pi}{2}
diagram B
\pi
diagram E
\frac{\pi}{3}
diagram A
\frac{\pi}{2}
diagram F
2\pi
diagram D
\frac{2\pi}{3}
The fraction of the circumference taken up by the arc outlining circle A’s sector is smaller than the fraction of the circumference taken up by the arc in circle B.
The ratio of the area of circle A’s sector to its total area is \frac{1}{6}.
Not taking into account the sectors, circle A and circle B are similar.
The ratio of circle A’s area to circle B’s area is \frac{5}{9}.
angle: 135 degrees
arc length 5\pi cm, radius 5 cm
angle: 180 degrees
Angle A measures 55 degrees.
The measures of angle A and angle D must add to 180 degrees.
Angle D measures 40 degrees.
Angle A measures 140 degrees.
Angle D measures 55 degrees.