Geometry: Points, Lines, and Angles

Collinear and Concurrent

• Collinear points are three or more points lying on the same line.
• Concurrent lines are three or more lines that intersect at a single point.

Geometric Relations

• Point B is between points A and C if A, B, and C are distinct collinear points with AB + BC = AC.
• Points B and C are on the same side of point A if A, B, and C are collinear and A does not lie between B and C.

Line and Its Components

• A line segment consists of two endpoints and all points in between.
• A ray has a fixed starting point and extends infinitely in one direction.
• Opposite rays share a common endpoint and extend in opposite directions.

Angles

• An angle is formed by two rays that meet at a common endpoint known as the vertex.
• A point lies in the interior of an angle if two points exist on each ray, and the interior point lies between them.

Congruence

• Congruent line segments are those of equal length.
• Congruent angles measure the same, indicating equality in angle size.

Midpoints and Bisectors

• The midpoint of a line segment is the point dividing it into two congruent segments.
• A line segment bisector intersects a segment at its midpoint.

Angle Types

• A right angle measures exactly 90 degrees.
• Acute angles measure less than 90 degrees and more than 0 degrees.
• Obtuse angles are greater than 90 degrees but less than 180 degrees.

Angle Relationships

• Complementary angles' measures sum to 90 degrees.
• Supplementary angles' measures add up to 180 degrees.

Intersections and Perpendicularity

• Lines intersect if they share at least one point.
• Perpendicular lines intersect at a right angle (90 degrees).

Angle and Line Segment Properties

• An angle bisector divides an angle into two congruent angles and originates from the angle's vertex.
• A reversed midpoint and segment bisector principles affirm congruence in segments created through division.

Angular Relationships and Properties

• Adjacent angles share a vertex and a side but do not overlap.
• Linear pairs consist of two adjacent angles whose non-shared sides are opposite rays, forming a straight line together.