Justify the choice of personal referents for angles measuring $22.5°$, $30°$, $45°$, $60°$, $90°$, and $180°$ and use them to estimate angle measurements (e.g., a corner of a sheet of paper is $90°$ so $1/2$ of a corner is $45°$).

Sketch or draw angles of various measures, including acute, right, straight, obtuse, and reflex angles, and justify the choice of sketching or drawing in relation to the situation.

Explain, using examples, how to measure angles in different orientations using a variety of instruments such as a protractor, carpenter’s square, or dynamic software.

Explain and illustrate how angles can be replicated (e.g., Mira, protractor, compass and straightedge, carpenter’s square, and dynamic software).

Replicate angles in various orientations, with and without the use of technology.

Explain, using examples, the relationship between the bisecting of angles and axial symmetry.

Bisect angles in various orientations and explain the strategy used.

Observe and sort a set of pairs of lines as perpendicular, parallel, or neither, and justify.

Relate complementary and supplementary angles to parallel, perpendicular, and transversal lines.

Observe and identify in a situation relevant to self, family, or community adjacent angles that are complementary, supplementary, or neither, and explain the reasoning.

Generalize, develop, explain, and apply relationships between pairs of angles formed by parallel lines and a transversal, inclu

• corresponding angles
• vertically opposite angles
• alternate interior angles
• alternate exterior angles
• interior angles on the same side of the transversal
• exterior angles on the same side of the transversal.

Provide concrete and pictorial examples that show that there are no angle relationships (excluding vertically opposite angles) when two lines that are not parallel are crossed by a transversal.

Describe and apply strategies for determining if lines or planes are perpendicular or parallel in situations relevant to self, family, or community (e.g., are the walls perpendicular to the floor? Are the corners square? Are the seams on the duvet parallel? Are the joists parallel?).

Analyze personally relevant situations for the impact if lines or planes that are meant to be perpendicular or parallel are not (e.g., What would it be like if the stairs in a staircase were not parallel?).

Create and solve relevant situational questions that involve angles and/or parallel lines and transversals, including perpendicular transversals, and explain the reasoning.

Critique the statement “If two or more lines are perpendicular, then each is a transversal of the other and if two or more lines are transversals of each other, they are perpendicular”.

Critique the statement “All lines are either parallel or transversals”.

Analyze and describe the role of angles, parallel lines, perpendicular lines, and transversals in games and sports (e.g., chess, curling, pool, hockey, soccer, and basketball).