Overview
This lecture covers the types of angles, pairs of angles, and angle relationships formed when parallel lines are intersected by a transversal, with examples to illustrate how to find unknown angles.
Types of Angles
- Acute angle: less than 90°.
- Right angle: exactly 90°.
- Obtuse angle: between 90° and 180°.
- Straight angle: exactly 180°.
- Reflex angle: between 180° and 360°.
- Complete angle: exactly 360°.
Pairs of Angles
- Complementary angles: sum to 90°.
- Supplementary angles: sum to 180°.
Angle Pairs with Parallel Lines and a Transversal
- Linear pair: Adjacent angles on a straight line, sum to 180° (supplementary).
- Vertically opposite angles: Angles opposite each other when two lines cross, always equal.
- Corresponding angles: Same position on parallel lines, always equal.
- Alternate interior angles: On opposite sides of transversal, inside parallel lines, equal (form Z shape).
- Co-interior (consecutive interior) angles: On the same side inside parallel lines, supplementary (sum to 180°).
- Alternate exterior angles: On opposite sides of transversal, outside parallel lines, equal.
- Co-exterior angles: On the same side outside parallel lines, supplementary (sum to 180°).
Solving for Unknown Angles (Examples)
- Use vertically opposite, corresponding, and alternate interior angles to find unknowns (e.g., Y = 57° if vertically opposite 57°).
- Linear pairs: Angles on a straight line sum to 180°; can have more than two angles (e.g., x + 82 + 82 = 180).
- For three angles adding to a straight line or 90°, do not use "pair" terminology; just state the sum.
- Be cautious with identifying angle relationships; not all angles that look opposite are vertically opposite.
Key Terms & Definitions
- Transversal — A line that intersects two or more parallel lines.
- Linear Pair — Two adjacent angles whose non-common sides form a straight line.
- Vertically Opposite Angles — Angles opposite each other at the intersection of two lines.
- Corresponding Angles — Angles on the same side of the transversal and in the same relative position.
- Alternate Interior Angles — Interior angles on opposite sides of the transversal.
- Co-interior Angles — Interior angles on the same side of the transversal.
- Alternate Exterior Angles — Exterior angles on opposite sides of the transversal.
- Co-exterior Angles — Exterior angles on the same side of the transversal.
- Complementary Angles — Two angles whose sum is 90°.
- Supplementary Angles — Two angles whose sum is 180°.
Action Items / Next Steps
- Practice identifying and calculating angle pairs from diagrams.
- Review and memorize angle pair rules for parallel lines and transversals.
- Prepare for the next session: "Angles in a Triangle."
- Complete assigned worksheet problems on angles and their pairs.