The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.
Key Terms:
Ray: a "line" that starts at a point and then goes on in one direction (different from a line that goes on in two directions).
Vertex: the "corner" of an angle where a ray "starts."
Intersect: when two lines cross each other and form an "X."
Adjacent: when two things are side-by-side (e.g., the doors for Room 8 and Room 10 are adjacent because they're next to each other). For angles, this is when two angles share a vertex (corner) and a side (ray). Adjacent angles cannot overlap each other; they must be side-by-side.
Nonadjacent: when two things are not side-by-side. For angles, it is when they don't share a vertex and a side (they can share one or the other, but not both).
Measure: how "wide" an angle is (e.g., 46°).
Acute: an angle with a measure less than 90°.
Right: an angle with a measure of exactly 90°.
Obtuse: an angle with a measure between 90° and 180°.
Straight: an "angle" with a measure of 180° (basically, a straight line through a vertex).
Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. Vertical angles are directly across (opposite) the vertex from each other (e.g., on a clock, 6 and 12 would be considered "vertical," as well as 9 and 3 because they are across from each other). Vertical angles also must be congruent.
Complementary angles: any two angles that have a sum of 90°.
Supplementary angles: any two angles that have a sum of 180°.
Caution: Complementary and supplementary angles do not have to be adjacent; the only requirement is that the measures of the angles add up to 90° (complementary) or 180° (supplementary).
Memory trick: complementary angles and supplementary angles can be confusing to students. Here are 3 tips to help you remember which one is which:
Shape:
Complementary begins with a "c" just like "corner."
Supplementary begins with an "s" just like "straight."
P's:
Complementary has a single "p" in its name.
Supplementary has two "p's" in its name.
Curves:
"Complementary" begins with a "c."
"Supplementary" begins with an "s" (which is kind of like putting two "c's" together).
Either way, supplementary angles (180°) are twice as large as complementary angles (90°).
Identify and describe the vertical, adjacent, supplementary, and complementary angles.
Use the relationships between supplementary, complementary, vertical, and adjacent angles to solve problems (including finding the measure of unknown angles).
6.CC.2,314-17
7.W.2,16-17
8.O.13-14
Art of Problem Solving
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