ALEX Classroom Resource

Students:

• Find the values of angles using complementary and supplementary angle relationships and equations.
• Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
• Write equations to represent relationships between known and unknown angle measurements.
• Determine the measures of unknown angles and judge the reasonableness of the measures.

Students know:

• supplementary angles are angles whose measures add to 180 degrees.
• Complementary angles are angles whose measures add to 90 degrees.
• vertical angles are opposite angles formed when two lines intersect.
• Adjacent angles are non-overlapping angles which share a common vertex and side.

Students are able to:

• write a simple equation to find an unknown angle.
• Identify and determine values of angles in complementary and supplementary relationships.
• Identify pairs of vertical angles in angle diagrams.
• Identify pairs of complementary and supplementary angles in angle diagrams.
• Use vertical, complementary, and supplementary angle relationships to find missing angles.

Students understand that:

• vertical angles are the pair of angles formed across from one another when two lines intersect, and that the measurements of vertical angles are congruent.
• Complementary angles are angles whose measures add up to 90^o, and supplementary angles are angles whose measures add up to 180^o.
• Relationships between angles depends on where the angles are located.

Learning Objectives:
M.7.21.1: Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
M.7.21.2: Discuss strategies for solving multi-step problems and equations.
M.7.21.3: Identify all types of angles.
M.7.21.4: Identify right angles and straight angles.

Students:

• Find the values of angles using complementary and supplementary angle relationships and equations.
• Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
• Write equations to represent relationships between known and unknown angle measurements.
• Determine the measures of unknown angles and judge the reasonableness of the measures.

Students know:

• supplementary angles are angles whose measures add to 180 degrees.
• Complementary angles are angles whose measures add to 90 degrees.
• vertical angles are opposite angles formed when two lines intersect.
• Adjacent angles are non-overlapping angles which share a common vertex and side.

Students are able to:

• write a simple equation to find an unknown angle.
• Identify and determine values of angles in complementary and supplementary relationships.
• Identify pairs of vertical angles in angle diagrams.
• Identify pairs of complementary and supplementary angles in angle diagrams.
• Use vertical, complementary, and supplementary angle relationships to find missing angles.

Students understand that:

• vertical angles are the pair of angles formed across from one another when two lines intersect, and that the measurements of vertical angles are congruent.
• Complementary angles are angles whose measures add up to 90^o, and supplementary angles are angles whose measures add up to 180^o.
• Relationships between angles depends on where the angles are located.

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.

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.

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.

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.

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).