Overview
This lecture covers the basics of angles in geometry, including types of lines, angle definitions, naming conventions, and classifications of angles.
Lines in Geometry
- Parallel lines never cross and go in the same direction, no matter how far extended.
- Intersecting lines cross at a single point called the intersection.
Angles: Definition and Naming
- Angles are the spaces formed between intersecting lines.
- Angles can be named using the points that create them (e.g., Angle DPB, Angle APD).
- The angle symbol (∠) can be used for shorthand.
- Angles can also be named by placing a letter near the arc indicating the angle.
Representing Angles
- Rotating a line segment around an intersection point forms an arc, which shows the angle.
- The arc close to the intersection and a labeled point visually defines the angle.
Types of Angles
- Right angles are formed by perpendicular lines and measure exactly 90°, indicated by a small square symbol.
- Acute angles are smaller than right angles (less than 90°).
- Obtuse angles are larger than right angles (greater than 90° but less than 180°).
- Straight angles measure exactly 180° and look like a straight line.
Complementary and Supplementary Angles
- Complementary angles add up to a right angle (90°).
- Supplementary angles add up to a straight angle (180°).
Key Terms & Definitions
- Parallel lines — lines that never cross and go in the same direction.
- Intersection — the point where two lines cross.
- Angle — the space between two intersecting lines or rays.
- Arc — part of a circle, representing an angle.
- Perpendicular lines — lines that intersect to form right angles.
- Right angle — an angle of exactly 90°.
- Acute angle — an angle less than 90°.
- Obtuse angle — an angle greater than 90° but less than 180°.
- Straight angle — an angle of exactly 180°.
- Complementary angles — two angles that add up to 90°.
- Supplementary angles — two angles that add up to 180°.
Action Items / Next Steps
- Watch the next video to learn how to measure angles.