Geometry Basics Lecture Notes

Key Concepts

Lines

• Definition: A line in geometry is represented with two arrows, extending infinitely in two directions.
• Naming: A line with points can be named in multiple ways, e.g., line AB, line BC, or line AC.

Rays

• Definition: A ray starts at a point and extends infinitely in one direction.
• Naming: A ray is named starting with its initial point, e.g., ray AB (not ray BC if A is the start).

Segments

• Definition: A segment has a definite beginning and end.
• Naming: A segment between points A and B is written as segment AB.

Angles

Types of Angles

• Acute Angle: Measures between 0 and 90 degrees.
• Right Angle: Measures exactly 90 degrees.
• Obtuse Angle: Measures greater than 90 but less than 180 degrees.
• Straight Angle: Measures exactly 180 degrees.

Angle Formation

• An angle is formed by the union of two rays sharing a common endpoint.

Midpoints and Bisectors

Midpoint

• Definition: The middle point of a segment.
• Properties: Divides the segment into two congruent parts.

Segment Bisector

• Definition: A ray or line that divides a segment into two equal parts.

Angle Bisector

• Definition: A ray that divides an angle into two equal parts.

Parallel and Perpendicular Lines

Parallel Lines

• Properties: Never intersect and have the same slope.
• Symbol: Line A is parallel to line B is denoted as A || B.

Perpendicular Lines

• Definition: Intersect at right angles.
• Properties: Slopes are negative reciprocals of each other.

Complementary and Supplementary Angles

Complementary Angles

• Definition: Two angles that add up to 90 degrees.

Supplementary Angles

• Definition: Two angles that add up to 180 degrees.

Transitive Property

• Definition: If two angles are congruent to the same angle, they are congruent to each other.
• Example: If angle 1 = angle 2 and angle 3 = angle 2, then angle 1 = angle 3.

Vertical Angles

• Definition: Opposite angles formed by two intersecting lines are equal.
• Example: If angle 1 is 50 degrees, its opposite angle is also 50 degrees.

Medians and Altitudes

Medians

• Definition: A line segment from a vertex to the midpoint of the opposite side.

Altitudes

• Definition: A line segment from a vertex forming a right angle with the opposite side.

Perpendicular Bisector

• Definition: A line that is perpendicular to a segment and bisects it into two equal parts.
• Properties: Any point on it is equidistant to the endpoints of the segment it bisects.

Triangle Congruence

Postulates

1. SSS (Side-Side-Side): All three sides of one triangle are congruent to another.
2. SAS (Side-Angle-Side): Two sides and the included angle are congruent.
3. ASA (Angle-Side-Angle): Two angles and the included side are congruent.
4. AAS (Angle-Angle-Side): Two angles and a non-included side are congruent.

CPCTC

• Definition: Corresponding Parts of Congruent Triangles are Congruent.

Practice Problems

• The video links and practice problems are available in the description section of the video.

Additional Resources

• Geometry Video Playlists: Check the description for additional geometry content.

Conclusion

• Subscribe and click the notification bell for updates on new videos.