Summary
Highlights
A line extends infinitely in opposite directions, represented with two arrows; it can be named using any two points on it. A ray has one endpoint and extends infinitely in one direction. A segment has a defined beginning and end.
Acute angles measure between 0 and 90 degrees. Right angles are exactly 90 degrees. Obtuse angles are greater than 90 but less than 180 degrees. Straight angles measure 180 degrees and resemble a straight line.
A midpoint divides a segment into two congruent parts. A segment bisector is a line or ray that passes through the midpoint, dividing the segment into two equal parts.
An angle bisector is a ray that divides an angle into two equal parts. For example, if a ray bisects a 60-degree angle, it creates two 30-degree angles. When naming an angle, the vertex must be in the middle (e.g., angle ABC).
Parallel lines never intersect and have the same slope. Perpendicular lines intersect at a 90-degree angle. Their slopes are negative reciprocals of each other.
Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees, often forming a straight line.
The transitive property states that if two angles are congruent to the same angle, they are congruent to each other (e.g., if A=B and C=B, then A=C). Vertical angles are opposite angles formed by two intersecting lines and are always congruent.
A median is a line segment from a triangle's vertex to the midpoint of the opposite side. An altitude is a line segment from a vertex that forms a right angle with the opposite side (or its extension).
A perpendicular bisector is a line that intersects a segment at its midpoint and forms a right angle with it. Any point on a perpendicular bisector is equidistant from the segment's endpoints.
Four postulates are used to prove triangle congruence: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side). After proving congruence, corresponding parts of congruent triangles are congruent (CPCTC).
Given two sides are congruent, and the triangles share a common side (reflexive property), the triangles can be proven congruent by SSS. Then, CPCTC can be used to prove other corresponding parts are congruent.
Using given angles and sides, plus identifying vertical angles, two triangles can be proven congruent by ASA. Subsequently, CPCTC allows proving that other corresponding parts, such as angles, are congruent.
Given an altitude and an angle congruence, knowing that altitudes form right angles, we can establish angle-angle-side conditions to prove triangles congruent by AAS. This then allows the use of CPCTC to prove congruence of other corresponding parts.