Unit 1 Foundations of Geometry: Undefined Terms, Naming, and Slope

A comprehensive set of flashcards covering undefined terms (point, line, plane), naming conventions, angle relationships, segment addition, perpendicular/parallel concepts, and slope-related forms and forms of line equations as introduced in Unit 1 (Day 1–3).

What are the three undefined terms in Euclidean geometry?

Point, Line, and Plane.

How is a point denoted and what are its dimensions?

A point is designated by a capital letter, has no dimensions, and serves as the foundation for geometry.

How is a line named?

By two points on the line (e.g., PR) or by a designated letter (e.g., line m); lines extend forever.

What does it mean for points to be collinear?

They lie on the same line.

How is a plane named?

By three non-collinear points or by a designated letter (often in cursive); it extends forever.

What does it mean for points to be coplanar?

They lie on the same plane.

What is a ray?

A portion of a line that has one endpoint and extends forever in one direction.

How do you name a ray?

Start with the endpoint, then a second point along the ray (e.g., ray QP).

What is a line segment?

A portion of a line between two endpoints; has a definite length; named by its endpoints with no arrows.

What is an angle?

Formed by the intersection of two lines, rays, or segments; has a vertex and sides; named with three letters when needed.

What is the vertex of an angle?

The intersection point of the sides of the angle (the middle letter in a three-letter angle name).

What are vertical angles?

Angles formed by two intersecting lines that are opposite each other; they are congruent.

What does congruent mean?

Two objects have the same size and shape; symbol ≅.

What is the Segment Addition Postulate?

If B lies between A and C on a segment, then AB + BC = AC (e.g., AB=5, BC=10 implies AC=15).

What is a bisector?

A line or segment that cuts a segment or an angle into two congruent parts.

Define complementary angles.

Two or more angles whose measures sum to 90°.

Define supplementary angles.

Two or more angles whose measures sum to 180°.

Define adjacent angles.

Two angles that share a vertex and a common side.

Define a linear pair.

Two adjacent angles whose measures sum to 180°.

What is the slope formula?

For points (x1,y1) and (x2,y2), slope m = (y2 - y1) / (x2 - x1).

What is slope-intercept form?

y = mx + b, where m is the slope and b is the y-intercept.

What is point-slope form?

y - y1 = m(x - x1), given a point (x1,y1) and slope m.

What is Standard Form of a line?

Ax + By = C, with A, B, C as integers; solve for y to resemble slope-intercept form.

What is the rule for perpendicular slopes?

Slopes are opposite reciprocals; m1 · m2 = -1.

What is the relationship between parallel lines and slopes?

Parallel lines have the same slope (and different intercepts).

What is the slope of a horizontal line?

0.

What is the slope of a vertical line?

Undefined.

How do you indicate a line’s direction when naming it by two points?

Use a double-headed arrow over the line’s name to show it extends in both directions.

When multiple angles share a vertex, how should you name them?

Use the three-letter naming with the vertex as the middle letter.

What is the difference between collinear and coplanar?

Collinear means points lie on the same line; coplanar means points lie on the same plane.