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.

Navigation

9-12 Geometry Unit 1 Lesson 5

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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 Lesson 19 Lesson 20 Lesson 21 Lesson 22

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

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 19
Lesson 20
Lesson 21
Lesson 22

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 1, Lesson 5

Construction Techniques 3: Perpendicular Lines and Angle Bisectors

Geometry

Practice

Problem 1
Student Task Statement

This diagram is a straightedge and compass construction of a line perpendicular to line passing through point . Explain why it is helpful to construct points and to be the same distance from .

Three circles. Two large congruent circles intersect at point E. Smaller circle, center C, in the intersection of two larger circles. Small circle intersects one circle at Point A and the other circle at Point D. Segment A B passes through C and D. Segment E C is drawn.

to access Practice Problem Solutions.

Problem 2

Student Task Statement

This diagram is a straightedge and compass construction.

Select all true statements.

<p>Three circles</p>

Line is the bisector of angle .
Line is the perpendicular bisector of segment .
Line is the perpendicular bisector of segment .
Line is the perpendicular bisector of segment .
Line is parallel to line .

to access Practice Problem Solutions.

Problem 3

ForLesson 4: Construction Techniques 2: Equilateral Triangles

Student Task Statement

This diagram is a straightedge and compass construction. is the center of one circle, and is the center of the other. A rhombus is a quadrilateral with 4 congruent sides. Explain why quadrilateral is a rhombus.

<p>Two congruent circles, with centers A and B, each pass through the center of the other and intersect at C and D. Radii AC, CB, DA and BD form quadrilateral ACBD.</p>

to access Practice Problem Solutions.

Problem 4

ForLesson 4: Construction Techniques 2: Equilateral Triangles

Student Task Statement

, , and are the centers of the three circles. Which line segment is congruent to ?

<p>Three intersecting circles.</p>

to access Practice Problem Solutions.

Problem 5

ForLesson 2: Constructing Patterns

Student Task Statement

In the construction, is the center of one circle, and is the center of the other. Explain why segment is the same length as segment .

<p>A diagram of circles and line segments.</p>

to access Practice Problem Solutions.

Problem 6

ForLesson 3: Construction Techniques 1: Perpendicular Bisectors

Student Task Statement

Two intersecting line segments.

In this diagram, line segment is the perpendicular bisector of line segment . Assume the conjecture that the set of points equidistant from and is the perpendicular bisector of is true. Is point closer to point , closer to point , or the same distance from both points? Explain how you know.

to access Practice Problem Solutions.

Problem 7

ForLesson 3: Construction Techniques 1: Perpendicular Bisectors

Student Task Statement

A sheet of paper with points and is folded so that and match up with each other.

<p>Two points, A and B.</p>

Explain why the crease in the sheet of paper is the perpendicular bisector of segment

. (Assume the conjecture that the set of points equidistant from

and

is the perpendicular bisector of segment

is true.)

to access Practice Problem Solutions.

Problem 8

ForLesson 1: Build It

Student Task Statement

Here is a diagram of a straightedge and compass construction. is the center of one circle, and is the center of the other. Explain why the length of segment is the same as the length of segment .

<p>Two circles, one large centered at point C. Points A, B, and D lie on the large circle. The smaller circle centered at point B intersects larger circle at points A and D. Radii CA, CB, and CD are drawn. Radii BA and BD are drawn.</p>

to access Practice Problem Solutions.

Lesson 5 Resources

Student Materials