Navigation

9-12 Integrated Math 2 Unit 7 Lesson 8

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 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 permission of Illustrative Mathematics.

This site includes 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.

Settings

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 7, Lesson 8

Quadrilaterals in Circles

$Course Icon$

Integrated Math 2

Practice

Problem 1

Student Task Statement

A quadrilateral has the given angle measures. Select all measurements that could come from a cyclic quadrilateral.

Angle is 90, angle is 90, angle is 90, and angle is 90.
Angle is 80, angle is 80, angle is 100, and angle is 100.
Angle is 70, angle is 110, angle is 70, and angle is 110.
Angle is 60, angle is 50, angle is 120, and angle is 130.
Angle is 50, angle is 40, angle is 120, and angle is 150.

to access Practice Problem Solutions.

Problem 2

Student Task Statement

Quadrilateral is cyclic with given angle measures.

What is the measure of angle ?
What is the measure of angle ?

<p>Quadrilateral A B C D. Angle A B C is 75 degrees and angle B A D is 135 degrees.</p>

to access Practice Problem Solutions.

Problem 3

Student Task Statement

Lin is looking at cyclic quadrilateral . She says, “I’m not convinced that opposite angles of cyclic quadrilaterals always add up to 180 degrees. For example, in this diagram, suppose we moved point to a different spot on the circle. Angle would still measure 100 degrees, but now angle would have a different measure, and they wouldn’t add up to 180.”

Do you agree with Lin? Explain or show your reasoning.

<p>Quadrilateral A B C D inscribed in a circle. Angle B A D is 80 degrees, angle B C D is 100 degrees, given angles are opposite each other.</p>

to access Practice Problem Solutions.

Problem 4

ForLesson 7: Tangent Lines

Student Task Statement

Line is tangent to the circle centered at with radius 3 units. The length of segment is 4.5 units. Find the length of segment .

<p>Circle with center O. Triangle ACO. AC = 4.5.</p>

units

to access Practice Problem Solutions.

Problem 5

ForLesson 7: Tangent Lines

Student Task Statement

Technology required. Line is tangent to a circle of radius 1 unit centered at . The length of segment is 1.2 units. The length of segment is 1.7 units. Han is trying to figure out if or is closer to . He uses the Pythagorean Theorem to find the length of . Then he subtracts 1 from the length of to determine how far is from point .

How far is from point ?
Which point is closest to ? Explain your reasoning.

<p>Circle with points and lines.</p>

to access Practice Problem Solutions.

Problem 6

ForLesson 6: Inscribed Angles

Student Task Statement

In the diagram, the measure of angle is 25 degrees. What is the measure of angle ?

Circle, center O. Points A, B and C lie on circle. Angles A O B and A C B.

to access Practice Problem Solutions.

Problem 7

ForLesson 5: Lines, Angles, and Curves

Student Task Statement

Which statement must be true?

A diameter is a chord.
A chord is a radius.
A chord is a diameter.
A central angle’s vertex is on the circle.

to access Practice Problem Solutions.

Problem 8

ForLesson 4: Intersection Points

Student Task Statement

A circle and line are drawn. How many intersection points are possible? Select all possible answers.

0
1
2
3
4

to access Practice Problem Solutions.

Lesson 8 Resources

Student Materials

units

units

26.25 units