This unit builds on studentsâ€™ 7thgrade work with angle relationships. Students extend their work with similar triangles to prove informally the angle sum of a triangle. Students also extend their previous work with angle relationships to discover angle relationships formed by parallel lines cut by a transversal and use those to prove informally the angle sum of a triangle.
Key Concepts:
 Angles created when parallel lines are cut by a transversal have special relationships, including congruence, and we can use the idea of translating the parallel lines to other parallel lines that are closer and closer to one another.
 The angle sum for any triangle is 180 degrees, and we can informally prove this using the relationships of angles. (In this lesson, use three similar triangles.)
 The angle sum for any triangle is 180 degrees, and we can informally prove this using the relationships of angles. (In this lesson, incorporate a triangle and parallel lines.)
Prior Knowledge Needed:
 7.G.A.2: Recognize when conditions determine a unique triangle, more than one triangle, or no triangle; Grade 7, Unit 14
 7.G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations; Grade 7, Unit 14
 8.G.A.5: Use and apply angleangle criterion: Grade 8, Unit 3
 8.G.B: Apply the properties of triangles (Pythagorean Theorem); Grade 8, Unit 5
Units on the Horizon:
 HSGCO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
 HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Lessons

Lesson objective: Understand angle relationships formed from parallel lines and a transversal. Students bring prior knowledge of angle relationships formed with two intersecting lines from 7.G.B.5 and transformations in 8.G.3. This prior knowledge is ex...

Lesson objective: Find missing angles formed when a transversal crosses parallel lines. This lesson helps to build procedural skill with writing equations to represent equivalent angle measures formed from congruent angle relationships. Equations are us...

Lesson objective: Determine if lines are parallel using angle relationships. This lesson helps to build procedural skill with determining parallelism of lines. Game cards are used here because it highlights students' ability to recognize what an angle r...

Lesson objective: Justify angle relationships of a triangle. This lesson provides an opportunity for students to apply their knowledge and understanding of angle relationships to a mathematical situation. Students are asked to provide a justification of...

Lesson objective: Understand the triangle angle sum using similar triangles. Students bring prior knowledge of similarity from 8.G.4 and angleangle criterion from 8.G.B.5. This prior knowledge is extended to the sum of the interior angles of a triangle...

Lesson objective: Determine missing angles using the triangle angle sum. This lesson helps to build procedural skill with triangle sum of triangles. Visual representations are used here to support students as they determine angle relationships that help...

Lesson objective: Apply the triangle angle sum to polygons. This lesson provides an opportunity for students to apply their knowledge and understanding of triangle angle sum to a mathematical situation. Students are asked to determine the interior angle...

Lesson objective: Extend understanding of angle relationships to informally prove the angle sum of triangles. Students bring prior knowledge of angle relationships from 7.G.B.5 and 8.G.B.5. This prior knowledge is extended to triangles formed from two t...

Lesson objective: Compute missing angles using angle relationships formed from transversals. This lesson helps to build procedural skill with angle relationships. Task Cards (with visual representations of parallel lines and transversals) are used here ...

Lesson objective: Solve problems using angle relationships and auxiliary lines. This lesson provides an opportunity for students to apply their knowledge and understanding of angle relationships formed from parallel lines and transversals to a reallife...
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