ALEX | Alabama Learning Exchange

Grade 8 Mathematics Module 3, Topic B: Similar Figures

Classroom Resource Information

Title:

Grade 8 Mathematics Module 3, Topic B: Similar Figures

URL:

https://www.engageny.org/resource/grade-8-mathematics-module-3-topic-b-overview

Content Source:

EngageNY

Type:

Lesson/Unit Plan

Overview:

Module 3, Topic B begins with the definition of similarity and the properties of similarities. In Lesson 8, students learn that similarities map lines to lines, change the length of segments by factor r, and are degree-preserving. In Lesson 9, additional properties about similarity are investigated; first, students learn that congruence implies similarity (e.g., congruent figures are also similar). Next, students learn that similarity is symmetric (e.g., if figure A is similar to figure B, then figure B is similar to figure A) and transitive (e.g., if figure A is similar to figure B, and figure B is similar to figure C, then figure A is similar to figure C.) Finally, students learn about similarity with respect to triangles.

Lesson 10 provides students with an informal proof of the angle-angle criterion for similarity of triangles. Lesson 10 also provides opportunities for students to use the AA criterion to determine if a pair of triangles is similar. In Lesson 11, students use what they know about similar triangles and dilation to find an unknown side length of one triangle. Since students know that similar triangles have side lengths that are equal in ratio (specifically equal to the scale factor), students verify whether or not a pair of triangles is similar by comparing their corresponding side lengths.

In Lesson 12, students apply their knowledge of similar triangles and dilation to real world situations. For example, students use the height of a person and the height of his shadow to determine the height of a tree. Students may also use their knowledge to determine the distance across a lake, the height of a building, and the height of a flagpole.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 8

24. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Unpacked Content

Evidence Of Student Attainment:

Students:

Explain how transformations can be used to prove that two figures are similar.
Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.

Teacher Vocabulary:

Translation
Reflection
Rotation
Dilation
Scale factor

Knowledge:

Students know:

How to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
What makes figures similar and congruent.

Skills:

Students are able to:

Use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.

Understanding:

Students understand that:

There is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.24.1: Define similar.
M.8.24.2: Recognize dilations.
M.8.24.3: Recognize translations.
M.8.24.4: Recognize rotations.
M.8.24.5: Recognize reflections.
M.8.24.6: Identify similar figures.
M.8.24.7: Analyze an image and its dilation to determine if the two figures are similar.

Prior Knowledge Skills:

Define ordered pairs.
Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Identify which signs indicate the location of a point in a coordinate plane.
Recall how to plot ordered pairs on a coordinate plane.
Define reflections.
Calculate the distances between points having the same first or second coordinate using absolute value.

Mathematics
MA2019 (2019)
Grade: 8

25. Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

a. Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees.

Unpacked Content

Evidence Of Student Attainment:

Students:

Find missing angles when presented angles formed by a transversal cutting through parallel lines.
Write equations to find missing angles when an angle is represented by a variable expression.
Prove that all triangles have an interior angle sum of 180 degrees by using given angle relationships that form a triangle.

Teacher Vocabulary:

Transversal
Corresponding Angles
Vertical Angles
Alternate Interior Angles
Alternate Interior Angles
Supplementary
Adjacent

Knowledge:

Students know:

That a straight angle is 180 degrees
That a triangle has three interior angles whose sum is 180 degrees.
The definition of transversal.
How to write and solve two-step equations.

Skills:

Students are able to:

Make conjectures about the relationships and measurements of the angles created when two parallel lines are cut by a transversal.
Informally prove that the sum of any triangle's interior angles will have the same measure as a straight angle.

Understanding:

Students understand that:

Missing angle measurements can be found when given just one angle measurement along a transversal cutting through parallel lines.
Every exterior angle is supplementary to its adjacent interior angle.
Parallel lines cut by a transversal will yield specific angle relationships that are connected to the concepts of rigid transformations (i.e. vertical angles are reflections over a point. corresponding angles can be viewed as translations).
The sum of the interior angles of a triangle is 180 degrees.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.25.1: Define exterior angles, interior angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, corresponding angles, and transversal.
M.8.25.2: Identify attributes of triangles.
M.8.25.3: Identify exterior angles, interior angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, and corresponding angles.
M.8.25.4: Identify a transversal.
M.8.25.5: Apply properties to find missing angle measures.
M.8.25.6: Discover the Angle Sum Theorem (sum of the interior angles of a triangle equal 180 degrees).

Prior Knowledge Skills:

Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
Discuss strategies for solving mulit-step problems and equations.
Identify all types of angles.
Identify right angles and straight angles.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.8.25 Compare any angle to a right angle using greater than, less than, or congruent to the right angle.

Tags:

angle sum, dilations, exterior angle, figure, geometry, parallel lines, reflections, rotations, similar, translations, transversal, triangles, twodimensional

License Type:

Custom Permission Type
See Terms: https://www.engageny.org/terms-of-use
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Text Resources: Content is organized under headings and subheadings

Comments

There are five lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site.

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Grade 8 Mathematics Module 3, Topic B: Similar Figures