The Main Idea 

A point is a location in space with no length, width, or height.

A line is an infinite collection of points extending infinitely in both directions.

A line segment is a finite portion of a line with two endpoints.

A ray is a part of a line that starts at an endpoint and extends infinitely in one direction.

Parallel lines are lines that lie in the same plane and move in the same direction, but never intersect.

Two lines that intersect at a [latex]90^\circ[/latex] angle are perpendicular lines.

The properties of planes include:

• Three points including at least one noncollinear point determine a plane.
• A line and a point not on the line determine a plane.
• The intersection of two distinct planes is a straight line.

The Main Idea 

An angle is formed when two lines, line segments, or rays meet at a common point called the vertex. The two lines or segments that form the angle are called the sides of the angle.

Measurement: Angles are measured in degrees ([latex]°[/latex]) or radians. We use a protractor to measure the size of an angle.

Types of Angles:

1. Right Angle: A right angle measures exactly [latex]90[/latex] degrees. It forms a perfect “L” shape.
2. Acute Angle: An acute angle measures less than [latex]90[/latex] degrees. It is smaller than a right angle. A key to remember acute angles is a small angle is “a cute” little angle.
3. Obtuse Angle: An obtuse angle measures more than [latex]90[/latex] degrees but less than [latex]180[/latex] degrees. It is larger than a right angle.
4. Straight Angle: A straight angle measures exactly [latex]180[/latex] degrees. It forms a straight line.
5. Reflex Angle: A reflex angle measures more than [latex]180[/latex] degrees but less than [latex]360[/latex] degrees. It is larger than a straight angle.

The Main Idea 

Degrees are the most common measurement of angles. A circle is divided into [latex]360^\circ[/latex]. The symbol for degrees is a small, raised circle: [latex]^\circ[/latex].

Radians are an alternative unit of angle measurement. In a circle, there are [latex]2π[/latex] radians, where [latex]π[/latex] (pi) is approximately [latex]3.14[/latex]. The symbol for radians is [latex]\text{rad}[/latex].

The conversion factor between degrees and radians is [latex]\frac{180}{π}[/latex].

[latex]\text{Angle in Degrees} = \text{Angle in Radians }\times\frac{180}{π}[/latex]

[latex]\text{Angle in Radians} = \text{Angle in Degrees }\times\frac{π}{180}[/latex]

Degrees are commonly used in everyday situations like navigation, construction, and basic geometry, while radians are more prevalent in advanced mathematics, physics, engineering, and other scientific fields.

The Main Idea 

Supplementary Angles: Two angles are considered supplementary when the sum of their measures is equal to 180 degrees. In other words, if you have two angles, and when you add their measures together, the result is 180 degrees, then those angles are supplementary.

Complementary Angles: Two angles are considered complementary when the sum of their measures is equal to 90 degrees. In other words, if you have two angles, and when you add their measures together, the result is 90 degrees, then those angles are complementary.

The Main Idea 

Vertical angles are a pair of opposite angles that are formed when two lines intersect. These angles are located across from each other and share a common vertex or point of intersection. Vertical angles have equal measures, which means they have the same angle measurement.

The Main Idea 

A transversal is a line that intersects two or more other lines. It cuts across these lines at different points, creating various angles.

Alternate interior angles are a pair of angles that lie on opposite sides of the transversal and are on the inside of the two other lines. These angles are equal in measure.

Alternate exterior angles are a pair of angles that lie on opposite sides of the transversal and are on the outside of the two other lines. These angles are equal in measure.

Corresponding angles are a pair of angles that are in the same relative position with respect to the transversal, but they are on different intersected lines. These angles are also equal in measure.