Overview
This lecture covers types of lines, angle relationships created by transversals, properties of special angle pairs, and practice problems involving algebraic solutions for unknown angles.
Types of Lines
- Parallel lines never intersect and have the same slope.
- Perpendicular lines intersect at a right angle (90°), and their slopes are negative reciprocals.
Angles Formed by Transversals
- A transversal is a line that intersects two or more (usually parallel) lines.
- Interior angles are inside the parallel lines; exterior angles are outside.
- Alternate interior angles are on opposite sides of the transversal and inside the parallel lines; they are congruent.
- Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines; they are congruent.
- Corresponding angles are in the same position on each parallel line relative to the transversal; they are congruent.
- Consecutive (same-side) interior angles are inside the parallel lines on the same side of the transversal and are supplementary (sum to 180°).
- Vertical angles are formed by intersecting lines and are opposite each other; they are congruent.
Special Angle Pairs
- Complementary angles add up to 90°.
- Supplementary angles add up to 180°.
- Linear pair: two adjacent angles that form a straight line and are supplementary.
Angle Calculations & Practice Problems
- Use properties of congruent or supplementary angles to set up equations and solve for unknowns.
- In triangles, the sum of interior angles is always 180°.
- In quadrilaterals, the sum of interior angles is 360°.
- The formula for the sum of interior angles of an n-sided polygon is (n-2) × 180°.
Key Terms & Definitions
- Parallel Lines — lines that never meet and have the same slope.
- Perpendicular Lines — lines that meet at a 90° angle; slopes are negative reciprocals.
- Transversal — a line intersecting two or more lines.
- Interior Angles — angles between two lines cut by a transversal.
- Exterior Angles — angles outside two lines cut by a transversal.
- Alternate Interior Angles — non-adjacent interior angles on opposite sides of the transversal; congruent.
- Alternate Exterior Angles — non-adjacent exterior angles on opposite sides of the transversal; congruent.
- Corresponding Angles — angles in matching corners when two lines are crossed by a transversal; congruent.
- Consecutive Interior Angles — interior angles on the same side of the transversal; supplementary.
- Vertical Angles — opposite angles formed by two intersecting lines; always congruent.
- Complementary Angles — two angles that sum to 90°.
- Supplementary Angles — two angles that sum to 180°.
Action Items / Next Steps
- Review problems involving solving for unknown angles using angle relationships.
- Memorize key angle pair properties and the sum of interior angles formulas for polygons.
- Complete assigned homework or practice problems related to this topic.