Lines, line segments, and rays

Learning Objectives Define and differentiate between points, lines, line segments, and rays. Use correct geometric notation for lines, line segments, and rays. Identify and name lines, line segments, and rays from a complex geometric figure. Apply the Segment Addition Postulate to solve for unknown lengths involving algebraic expressions. Calculate the length of a line segment on a coordinate plane using the Distance Formula. Determine the coordinates of the midpoint of a line segment using the Midpoint Formula. Ever wonder how GPS pinpoints your location or how architects design stable buildings? 🗺️ It all starts with the simplest ideas: points, lines, and the paths between them! This tutorial will explore the fundamental building blocks of geometry: lines, line segments,...

TermDefinitionExample LineA straight, one-dimensional figure that has no thickness and extends infinitely in both directions. It is defined by any two points on it.A line passing through points A and B is denoted as $\overleftrightarrow{AB}$. Line SegmentA part of a line that is bounded by two distinct endpoints. It contains these endpoints and all the points on the line between them, and has a finite, measurable length.The segment with endpoints C and D is denoted as $\overline{CD}$. Its length is written as CD. RayA part of a line that has one endpoint and extends infinitely in one direction.A ray starting at endpoint E and passing through point F is denoted as $\overrightarrow{EF}$. The endpoint is always listed first. Collinear PointsA set of points that all lie on the same straight l...

Segment Addition Postulate If B is a point on $\overline{AC}$ and is between A and C, then $AB + BC = AC$. Use this postulate to find the length of a part of a segment or the whole segment when other lengths are known. It's a foundational rule for geometric proofs involving segments. Distance Formula The distance *d* between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Use this formula to calculate the precise length of a line segment when you know the coordinates of its endpoints on a coordinate plane. This is derived from the Pythagorean theorem. Midpoint Formula The midpoint M of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Use...