• ## Course 3, Module 1: Transforming Geometric Objects

In this module, students build on their experience with rational numbers, proportionality, scale drawings, triangles, and angle pairs formed when two lines intersect. They will use patty paper to investigate transformations of geometric objects to develop an understanding of congruence and similarity. Students will then use this new knowledge about transformations to establish facts about triangles and relationships between special angle pairs.

• In this topic, students use patty paper and the coordinate plane to investigate congruent figures. Throughout the topic, students are expected to make conjectures, investigate conjectures, and justify true results about transformations.
• MATHia Workspaces (5)
• Experimenting with Rigid Motions
• Translating Plane Figures
• Reflecting Plane Figures
• Rotating Plane Figures
• Describing Rigid Motions Using Coordinates

Topic 2: Similarity

• In this topic, students investigate the fourth common transformation: dilation. Students will make connections between scale factors and dilation factors by examining worked examples of Euclidean dilations.
• MATHia Workspaces (5)
• Defining Similarity
• Dilating Plane Figures
• Performing One Transformation
• Performing Multiple Transformations
• Describing Transformations Using Coordinates

Topic 3: Line and Angle Relationships

• In this topic, students use their knowledge of transformations, congruence, and similarity to establish the Triangle Sum Theorem, the Exterior Angle Theorem, relationships between angles formed when parallel lines are cut by a transversal, and the Angle-Angle Similarity Theorem for similarity of triangles. Students determine and informally prove the relationships between the special angle pairs formed when parallel lines are cut by a transversal and use these relationships to solve mathematical problems, including writing and solving equations.
• MATHia Workspaces (4)
• Introduction to Triangle Sum and Exterior Angle Theorems
• Classifying Angles Formed by Transversals
• Reasoning about Angles Formed by Transversals
• Calculating Angle Measures Formed by Transversals