Definition: A line extends in both directions infinitely.
Naming: Can be named as line AB, line BC, or line AC.
Rays
Definition: A ray starts at a point and extends infinitely in one direction.
Naming: Named using the starting point first, e.g., ray AB (not ray BC).
Segments
Definition: A segment has a definite starting and ending point.
Naming: E.g., 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.
Midpoints
Definition: The midpoint divides a segment into two equal segments.
Notation: If B is the midpoint of segment AC, then segment AB is congruent to segment BC.
Bisectors
Segment Bisector: A ray that bisects a segment into two equal parts.
Angle Bisector: A ray that divides an angle into two equal angles.
Parallel Lines
Definition: Two lines that never intersect and have the same slope.
Notation: Line A is parallel to line B (A || B).
Perpendicular Lines
Definition: Two lines that intersect at right angles (90 degrees).
Slopes: The slopes of perpendicular lines are negative reciprocals.
Notation: Line A is perpendicular to line B (A ⊥ B).
Complementary Angles
Definition: Two angles that sum to 90 degrees.
Supplementary Angles
Definition: Two angles that sum to 180 degrees.
Transitive Property
Definition: If two angles are congruent to the same angle, then they are congruent to each other.
Vertical Angles
Definition: Angles opposite each other when two lines intersect; they are congruent.
Medians
Definition: A median of a triangle is a line segment from a vertex to the midpoint of the opposite side.
Altitudes
Definition: An altitude is a segment from a vertex perpendicular to the opposite side.
Perpendicular Bisector
Definition: A line that bisects a segment at a right angle.
Triangle Congruence Postulates
SSS Postulate: If all three sides of one triangle are congruent to the corresponding 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 triangle, 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 triangle, the triangles are congruent.
AAS Postulate: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
Proof Techniques
CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
Use appropriate postulates and properties to prove triangles are congruent.
Conclusion
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