# ALEX Classroom Resource

## Grade 8 Mathematics Module 2, Topic C: Congruence and Angle Relationships

Classroom Resource Information

Title:

Grade 8 Mathematics Module 2, Topic C: Congruence and Angle Relationships

URL:

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 2, Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions are then inherited by congruence:  congruence moves lines to lines and angles to angles, and it is both distance- and degree-preserving (Lesson 11). In Grade 7, students used facts about supplementary, complementary, vertical, and adjacent angles to find the measures of unknown angles (7.G.5). This module extends that knowledge to angle relationships that are formed when two parallel lines are cut by a transversal. In Topic C, on angle relationships related to parallel lines, students learn that pairs of angles are congruent because they are angles that have been translated along a transversal, rotated around a point, or reflected across a line. Students use this knowledge of angle relationships in Lessons 13 and 14 to show why a triangle has a sum of interior angles equal to 180˚ and why the exterior angles of a triangle are the sum of the two remote interior angles of the triangle.

Content Standard(s):
 Mathematics MA2015 (2016) Grade: 8 17 ) 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. [8-G2] NAEP Framework NAEP Statement:: 4G2e: Match or draw congruent figures in a given collection. NAEP Statement:: 8G2e: Justify relationships of congruence and similarity and apply these relationships using scaling and proportional reasoning. NAEP Statement:: 8G3c: Represent problem situations with simple geometric models to solve mathematical or real-world problems. NAEP Statement:: 8G3f: Describe or analyze simple properties of, or relationships between, triangles, quadrilaterals, and other polygonal plane figures. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.17- Given a geometric figure and a vertical or horizontal translation and reflection across a vertical or horizontal line, identify the components (lines/sides, angles) of the two figures that are congruent (limited to non-equilateral rectangles and triangles). Mathematics MA2019 (2019) Grade: 8 25. Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures. a. Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees. Unpacked Content Evidence Of Student Attainment:Students: Find missing angles when presented angles formed by a transversal cutting through parallel lines. Write equations to find missing angles when an angle is represented by a variable expression. Prove that all triangles have an interior angle sum of 180 degrees by using given angle relationships that form a triangle.Teacher Vocabulary:Transversal Corresponding Angles Vertical Angles Alternate Interior Angles Alternate Interior Angles Supplementary AdjacentKnowledge:Students know: That a straight angle is 180 degrees That a triangle has three interior angles whose sum is 180 degrees. The definition of transversal. How to write and solve two-step equations.Skills:Students are able to: Make conjectures about the relationships and measurements of the angles created when two parallel lines are cut by a transversal. Informally prove that the sum of any triangle's interior angles will have the same measure as a straight angle. Understanding:Students understand that: Missing angle measurements can be found when given just one angle measurement along a transversal cutting through parallel lines. Every exterior angle is supplementary to its adjacent interior angle. Parallel lines cut by a transversal will yield specific angle relationships that are connected to the concepts of rigid transformations (i.e. vertical angles are reflections over a point. corresponding angles can be viewed as translations). The sum of the interior angles of a triangle is 180 degrees.Diverse Learning Needs: Essential Skills:Learning Objectives: M.8.25.1: Define exterior angles, interior angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, corresponding angles, and transversal. M.8.25.2: Identify attributes of triangles. M.8.25.3: Identify exterior angles, interior angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, and corresponding angles. M.8.25.4: Identify a transversal. M.8.25.5: Apply properties to find missing angle measures. M.8.25.6: Discover the Angle Sum Theorem (sum of the interior angles of a triangle equal 180 degrees). Prior Knowledge Skills:Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines. Discuss strategies for solving mulit-step problems and equations. Identify all types of angles. Identify right angles and straight angles. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.25 Compare any angle to a right angle using greater than, less than, or congruent to the right angle.
Tags: angle, congruent, exterior angle, figure, parallel lines, sum, transversal, triangles, twodimensional