Illustrative Mathematics - Geometry - Unit 7 - Lesson 12

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Illustrative Mathematics - Geometry - Unit 7 - Lesson 12

Last updated about 3 years ago

7 questions

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

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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?

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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.

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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.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

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

Draggable item		Corresponding Item
diagram B		\frac{3\pi}{2}
diagram D		\pi
diagram F		\frac{\pi}{3}
diagram C		\frac{\pi}{2}
diagram A		2\pi
diagram E		\frac{2\pi}{3}

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

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?

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.

The sector in circle B has a larger area than the sector in circle A.

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}.

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

Draggable item		Corresponding Item
arc length 4\pi cm, radius 10 cm		angle: 30 degrees
arc length 3\pi cm, radius 18 cm		angle: 72 degrees
arc length 5\pi cm, radius 5 cm		angle: 135 degrees
arc length 9\pi cm, radius 12 cm		angle: 180 degrees

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

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.

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.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

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

diagram B

\frac{3\pi}{2}

diagram D

\pi

diagram F

\frac{\pi}{3}

diagram C

\frac{\pi}{2}

diagram A

2\pi

diagram E 

\frac{2\pi}{3}

The sector in circle B has a larger area than the sector in circle A.

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}.

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

arc length 4\pi cm, radius 10 cm

angle: 30 degrees

arc length 3\pi cm, radius 18 cm

angle: 72 degrees

arc length 5\pi cm, radius 5 cm

angle: 135 degrees

arc length 9\pi cm, radius 12 cm

angle: 180 degrees

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

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.

Illustrative Mathematics - Geometry - Unit 7 - Lesson 12

Illustrative Mathematics - Geometry - Unit 7 - Lesson 12

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

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?

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.

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

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

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?

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.

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

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

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?

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.

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?

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.

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