About This Chapter
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)
About This Chapter
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.
1. Reflection, Rotation & Translation
This lesson will define reflection, rotation, and translation as they relate to math. It will also show you an example of each one so that you can perform these transformations on your own.
2. Line and Rotational Symmetries of 2-D Shapes
One of the most important concepts in geometry is the idea of symmetry. But what does it actually mean? This lesson explains the difference between line symmetry and rotational symmetry.
3. Graphing Translations & Finding a Set of Coordinates
In this lesson, you're going to learn how to translate figures by counting boxes, find the coordinates of points, and learn how to translate a figure more quickly using simple math.
4. Rotating Shapes by Degrees, Center & Direction
In this lesson, you're going to learn about the definition and basic concept of rotation as well as how to rotate any shape about the origin in a coordinate plane. Finish up the lesson, then test your understanding with a quiz!
5. How to Graph Reflections Across Axes, the Origin, and Line y=x
A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.
6. Congruence in Geometric Shapes
Watch this video lesson to learn how you can determine whether two shapes are congruent or not. You will learn what the one criterion is when determining congruency between two shapes.
7. Similarity in Geometric Shapes
View this lesson to learn how you can determine whether shapes are similar. Find out how to use the one rule that tells you when your two shapes are geometrically similar.
8. Similarity Transformations in Corresponding Figures
Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.
9. Practice Proving Relationships using Congruence & Similarity
In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.
10. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
11. Angles Formed by a Transversal
When you have a pair of parallel lines and a transversal, something very interesting happens to the angles that are formed. You can see this happen in real life at street intersections and such. Watch this video lesson to learn about all of this.
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Other chapters within the Common Core Math Grade 8 - Geometry: Standards course