Definition: A line extends in both directions with arrows at each end.
Naming Lines: Can be named in multiple ways (e.g., Line AB, Line BC, Line AC).
Rays
Definition: A ray has a starting point and extends infinitely in one direction.
Naming Rays: Must start from the initial point (e.g., Ray AB, Ray AC).
Segments
Definition: A segment has a specific beginning and end.
Naming Segments: Can be named based on endpoints (e.g., Segment AB or Segment BA).
Angles
Acute Angle: Measures between 0 and 90 degrees (less than 90).
Right Angle: Measures exactly 90 degrees.
Obtuse Angle: Measures more than 90 but less than 180 degrees.
Straight Angle: Measures exactly 180 degrees (looks like a line).
Midpoint and Segments
Midpoint: The point that divides a segment into two equal parts (e.g., if B is the midpoint of segment AC, then AB = BC).
Segment Bisector: A ray that passes through the midpoint of a segment, dividing it into two equal parts.
Angle Bisector
Definition: A ray that divides an angle into two equal angles.
Example: If Ray BD bisects angle ABC, then angle ABD = angle DBC.
Parallel Lines
Definition: Lines that never intersect and have the same slope.
Notation: A || B indicates that Line A is parallel to Line B.
Perpendicular Lines
Definition: Lines that intersect at right angles (90 degrees).
Slope Relationship: Slopes of perpendicular lines are negative reciprocals.
Complementary and Supplementary Angles
Complementary Angles: Two angles that add up to 90 degrees.
Supplementary Angles: 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: Angles opposite each other when two lines intersect; they are congruent.
Example: If angle 1 = 50 degrees, then angle 3 = 50 degrees.
Medians and Altitudes in Triangles
Median: A segment from a vertex to the midpoint of the opposite side.
Altitude: A segment from a vertex that forms a right angle with the opposite side.
Perpendicular Bisector
Definition: A line that is perpendicular to a segment at its midpoint, bisecting the segment into two equal parts.
Key Properties: Any point on the perpendicular bisector is equidistant to the endpoints of the segment.
Triangle Congruence Postulates
SSS (Side-Side-Side): If all three sides of triangle ABC are congruent to triangle DEF, then ABC ≅ DEF.
SAS (Side-Angle-Side): If two sides and the included angle of triangle ABC are congruent to triangle DEF, then ABC ≅ DEF.
ASA (Angle-Side-Angle): If two angles and the included side of triangle ABC are congruent to triangle DEF, then ABC ≅ DEF.
AAS (Angle-Angle-Side): If two angles and a non-included side of triangle ABC are congruent to triangle DEF, then ABC ≅ DEF.
CPCTC (Corresponding Parts of Congruent Triangles are Congruent): Once triangles are proven congruent, their corresponding angles and sides are also congruent.
Conclusion
This lecture provided essential geometry concepts needed for understanding basic geometric principles.
More practice problems available in the provided links.