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.

This quiz covers essential concepts in geometry, including collinear points, concurrent lines, and the various components of angles. Test your understanding of geometric relationships and congruence. Perfect for students looking to solidify their knowledge in basic geometry.