Overview
This lesson introduces basic geometry concepts, focusing on measuring segments and angles, key terminology, and using postulates to find unknown values.
Undefined and Defined Terms
- Undefined terms: point, line, and plane have accepted meanings without formal definitions.
- A point is drawn as a dot, labeled with a capital letter (e.g., A).
- A line extends infinitely, drawn with arrows on both ends, named by two points or a lowercase letter.
- A plane is a flat surface extending infinitely, named by a letter or three non-collinear points.
- Collinear points lie on the same line; non-collinear points do not.
Segments, Rays, and Angles
- A line segment has two endpoints and is drawn without arrows.
- A ray starts at an endpoint and extends infinitely in one direction (one arrow).
- Opposite rays share an endpoint and extend in opposite directions.
- Angles are named by the vertex, a number, or three points (vertex in the middle).
Measuring Segments
- Segment length is always positive and measured in units.
- Use absolute value to ensure positive distance: |coordinate1 − coordinate2|.
- Segment Addition Postulate: the sum of smaller segments equals the total segment (e.g., CD + DE = CE).
Segment Addition & Examples
- To find missing segment lengths, set up equations using given values and solve for unknowns.
- Combine like terms and solve algebraically for variables.
- Label segment results in units (e.g., 16 units).
Angle Addition Postulate & Examples
- Angle Addition Postulate: the sum of adjacent angles equals the total angle (e.g., angle 1 + angle 2 = whole angle).
- Plug in angle measures or algebraic expressions, combine, and solve for variables.
- Use "m∠" for measure of an angle (no degree symbol with "m", use degree symbol otherwise).
Congruence and Perimeter
- Segments/angles marked with the same symbol are congruent (equal in measure).
- Add lengths or measures as needed to find totals or missing values.
- Perimeter is the distance around the outside of a shape.
Key Terms & Definitions
- Point — a location with no size, labeled by a capital letter.
- Line — extends infinitely in both directions; named by two points or a lowercase letter.
- Plane — a flat, infinite surface; named by a letter or three non-collinear points.
- Collinear — points on the same line.
- Line segment — part of a line with two endpoints.
- Ray — part of a line with one endpoint, extending infinitely.
- Opposite rays — two rays sharing an endpoint but extending in opposite directions.
- Angle — formed by two rays with a common endpoint (vertex).
- Segment Addition Postulate — the sum of part lengths equals the whole segment.
- Angle Addition Postulate — adjacent angle measures add to the total angle.
- Congruent — identical in measure or length.
Action Items / Next Steps
- Practice finding segment and angle measures using the postulates.
- Complete assigned problems from the lesson.
- Review key terms and definitions for next class.