Definition: In geometry, a line has two arrows and extends in opposite directions forever.
Naming: A line can be named in multiple ways using points on the line, such as line AB, BC, or AC.
Rays
Definition: A ray has a starting point and extends forever in one direction.
Naming: The starting point must be first in the name (e.g., ray AB, not ray BC).
Segments
Definition: A segment has a definite beginning and end (e.g., segment AB).
Naming: Use two endpoints to name a segment.
Angles
Types of Angles
Acute Angle: Measures between 0 and 90 degrees.
Right Angle: Measures exactly 90 degrees.
Obtuse Angle: Measures greater than 90 and less than 180 degrees.
Straight Angle: Measures exactly 180 degrees.
Midpoint
Definition: The middle point of a segment, dividing it into two congruent segments.
Notation: Segment AB is congruent to segment BC if B is the midpoint of segment AC.
Segment Bisector
Definition: A ray that passes through the midpoint of a segment, dividing it into two congruent parts.
Angle Bisector
Definition: A ray that divides an angle into two equal parts.
Parallel and Perpendicular Lines
Parallel Lines
Properties: Never intersect, have the same slope.
Notation: Line A is parallel to line B.
Perpendicular Lines
Properties: Intersect at right angles.
Notation: The slopes are negative reciprocals.
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.
Vertical Angles
Definition: Angles that are opposite each other when two lines intersect; they are congruent.
Triangles
Medians
Definition: A line segment from a vertex to the midpoint of the opposite side.
Altitudes
Definition: A line segment from a vertex perpendicular to the opposite side.
Perpendicular Bisector
Definition: A line that is perpendicular to a segment at its midpoint.
Congruent Triangles
Postulates
SSS Postulate: If three sides of one triangle are congruent to three sides of another, the triangles are congruent.
SAS Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another, the triangles are congruent.
ASA Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another, the triangles are congruent.
AAS Postulate: If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another, the triangles are congruent.
CPCTC
Definition: Corresponding parts of congruent triangles are congruent.
Practice and Resources
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