Geometry Basics: Points, Lines, Planes & Angles

31 question-and-answer flashcards covering undefined terms, basic definitions, postulates, theorems, and angle relationships from Lessons 1–3.

What are the three undefined terms in Euclidean geometry?

Point, line, and plane

How is a point represented and named in geometry?

As an infinitely small dot, named with a single capital letter

Describe a line in geometry.

A straight path made of infinitely many points that extends in two opposite directions forever and has no thickness; named with two points

Describe a plane in geometry.

A flat surface that extends indefinitely with length and width but no thickness; named with three non-collinear points

At what do two distinct lines intersect (if they intersect)?

A point

At what do two distinct planes intersect (if they intersect)?

A line

Define collinear points.

Points that lie on the same line

Define coplanar points.

Points that lie on the same plane

What is a ray?

Part of a line with one endpoint that extends infinitely in one direction

What is a line segment?

Part of a line between two endpoints; finite length

What forms an angle?

Two different rays that share the same initial point

In an angle, what are the sides and the vertex?

The rays are the sides; the shared endpoint is the vertex

What is a construction in geometry?

A geometric drawing made using only a compass and a straightedge

What is a postulate (axiom)?

A statement accepted without proof

State the Ruler Postulate in simple terms.

Points on a line can be matched one-to-one with real numbers so distances can be measured

State the Segment Addition Postulate.

If B is between A and C on a line, then AB + BC = AC

State the Linear Pair Postulate.

If two angles form a linear pair, they are supplementary (their measures sum to 180°).

State the Vertical Angle Theorem.

Vertical angles are congruent

State the Pythagorean Theorem.

In a right triangle, a² + b² = c², where c is the hypotenuse

Give the distance formula between points (x₁, y₁) and (x₂, y₂).

√[(x₂ − x₁)² + (y₂ − y₁)²]

Give the midpoint formula for a segment with endpoints (x₁, y₁) and (x₂, y₂).

((x₁ + x₂)/2 , (y₁ + y₂)/2)

Define an acute angle.

An angle whose measure is greater than 0° and less than 90°

Define a right angle.

An angle whose measure is exactly 90°

Define an obtuse angle.

An angle whose measure is greater than 90° and less than 180°

Define a straight angle.

An angle whose measure is exactly 180°

When are two angles supplementary?

When the sum of their measures is 180°

When are two angles complementary?

When the sum of their measures is 90°

Define adjacent angles.

Two angles that share a common vertex and side but have no common interior points

Define vertical angles.

The non-adjacent angles formed by two intersecting lines

Define a linear pair of angles.

Adjacent angles whose non-common sides form a straight line (sum to 180°)

How many letters are typically used to name a point, a line, and a plane respectively?

1 letter for a point, 2 letters for a line, and 3 letters for a plane