# Ch 1: Common Core Math Grade 8 - Geometry: Congruence & Similarity

Use the resources in this collection to help your eighth graders meet the Common Core requirements in math. Teach students about congruence and similarity in geometry with these lessons, quizzes and teaching suggestions.

Standard: Verify experimentally the properties of rotations, reflections, and translations. (CCSS.MATH.CONTENT.8.G.A.1)

Standard: Lines are taken to lines, and line segments to line segments of the same length. (CCSS.MATH.CONTENT.8.G.A.1.A)

Standard: Angles are taken to angles of the same measure. (CCSS.MATH.CONTENT.8.G.A.1.B)

Standard: Parallel lines are taken to parallel lines. (CCSS.MATH.CONTENT.8.G.A.1.C)

Standard: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (CCSS.MATH.CONTENT.8.G.A.2)

Standard: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (CCSS.MATH.CONTENT.8.G.A.3)

Standard: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. (CCSS.MATH.CONTENT.8.G.A.4)

Standard: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. (CCSS.MATH.CONTENT.8.G.A.5)

Students who have mastered these Common Core standards in geometry are able to use physical models, transparencies and software to demonstrate their understanding of congruence and similarity. They should be able to verify the properties of reflections, rotations and translations and describe their effects on 2-dimensional figures. The lessons in this collection can be used to teach students about the following:

• Translation, reflection and rotation
• Rotational and line symmetry of 2-D shapes
• Shape rotation by degrees, direction and center
• Graphing reflections across origin, axes and line Y=X
• Finding coordinates and graphing rotations
• Congruence and similarity in geometric shapes
• Similarity transformations in corresponding figures
• Using congruence and similarities to prove relationships between figures
• Perpendicular, parallel and transverse lines
• Angles formed by transverse lines

You'll know your students have mastered these standards when they are able to make arguments to establish facts about angle sums, exterior angles and angles created when parallel lines are cut by transversals. They will also be able to describe sequences that show congruence between two figures.

### How to Use These Lessons in Your Classroom

Below are some ways to incorporate the resources in this collection into your classroom and help you meet the standards for the Common Core.

#### Assign Lessons and Quizzes as Homework

Use the lessons and quizzes as homework assignments. These tools can be used to supplement existing homework or as an assignment in and of themselves.

#### Play Simon Says

Watch the video 'Reflection, Rotation & Translation,' then play Simon Says. Call out the term, and have students act it out by making a flip, slide or turn.

#### Create and Identify Congruence Sequences

Have students view the lesson 'Congruence in Geometric Shapes.' Give each student a sheet of graph paper and a cutout shape. Ask them to trace the shape on the paper, then use a series of translations of reflections, rotations and/or translations to move the shape. End by tracing the final resting place of the shape. Afterwards, have students trade with one another and try to figure out and describe the sequence that moves the shape from the starting point to the ending point.

11 Lessons in Chapter 1: Common Core Math Grade 8 - Geometry: Congruence & Similarity
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.