Students use their understanding of angles formed by intersecting lines and extend their thinking to triangles. Students determine whether a triangle exists given three measures of angles or sides. Students explore the various relationships that exist between angles (supplementary, complementary, vertical, and adjacent) to write equations to solve multistep problems.
Key Concepts:
 Intersecting lines produce angles with important relationships, including supplementary angles, complementary angles, adjacent angles, and vertical angles.
 The sum of the lengths of two sides of a triangle must be greater than the length of the third side, and this can be informally proven.
 The sum of the angles of a triangle is 180 degrees, and this can be informally proven using the idea of parallel lines.
 Given particular information about attributes of a triangle, it may be possible to construct a unique triangle, more than one triangle, or no triangle. (For instance, given that two angles of the triangle are 57 degrees and 60 degrees, we can construct infinitely many triangles that fit that description, even though the third angle must measure 63 degrees.)
Prior Knowledge Needed:
 4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.
 4.G.A.2: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.
 4.MD.C.6: Geometric measurement: understand concepts of angle and measure angles. Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.
 4.MD.C.7: Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Units on the Horizon:
 Geometric Relationships; (Grade 8, Unit 13)
 Geometry or Math II in High School
Lessons

Lesson objective: Understand that intersecting lines produce angles that have important relationships. Students bring prior knowledge of drawing and identifying angles as right, acute, or obtuse, from 4.G.A.1. This prior knowledge is extended to recogni...

Lesson objective: Find the measures of unknown angles in geometric figures using relationships that exist among complementary, supplementary, vertical, and adjacent angles. This lesson helps to build procedural skill with these special angle relationshi...

Lesson objective: Connect their understanding of special angles formed by intersecting lines to street intersections on a town that they have designed. This lesson provides an opportunity for students to apply their knowledge and understanding of supple...

Lesson objective: Understand that when given three side lengths of a triangle, the sum of the lengths of two sides must be greater than the length of the third side in order for the triangle to form. Students bring prior knowledge of triangles that can ...

Lesson objective: Understand that the sum of the angles of a triangle is 180°. Students bring prior knowledge that angle measure is additive from 4.MD.C.7. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole angle is t...

Lesson objective: Find missing angle measures in a triangle using the angle sum for triangles. In addition, students will use the Triangle Inequality Theorem to determine if a triangle will form when given the measures of the three sides. This lesson he...

Lesson objective: Make a connection to a relationship between the size of an angle and the size of the side opposite that angle. This lesson provides an opportunity for students to apply their knowledge and understanding of the sum of the angles of a tr...

Lesson objective: Understand that when given particular information about attributes of a triangle, it may be possible to construct a unique triangle, more than one triangle, or no triangle. Students bring prior knowledge of triangles that can be catego...

Lesson objective: Determine if a given set of attributes for a triangle produce a unique triangle, more than one triangle, or no triangle. This lesson helps to build procedural skill with using the triangle angle sum and the Triangle Inequality Theorem....

Lesson objective: Apply their understanding of the Triangle Inequality Theorem to determine an efficient design for a kitchen. This lesson provides an opportunity for students to apply their knowledge and understanding the the sum of any two lengths of ...