- Definition of Congruent- If measures are equal, two angles are congruent or if lengths are equal, segments are congruent.
- Definition of Bisect: Bisect means to cut something into two congruent parts.
- Angle Bistector- a segment, line, or ray that splits an angle into two congruent angles.
- Segment Bisector- a segment, line, or ray that splits a segment into two congruent parts.
- Definition of Midpoint- A midpoint splits a line segment into two congruent segments.
- Definition of Supplementary- Two or more angles whose sum is 180 degrees.
- Reflexive property- a line segment or angle is congruent to itself. Any value is equal to itself.
- Transitive property- If A=B and B=C, then A=C (also works for congruence).
- Substitution property of equality- If a=b, you can substitute a for b or b for a in any equation.
- Angle Addition Postulate- If an angle is split into parts, the sum of the measures of the parts equal the measure of the original angle
- Linear Pair Theorem- If two angles form a linear pair, then they are supplementary.
- Definition of Linear Pair-A linear pair is a pair of adjacent angles whose non common sides form a line.
- Definition of Vertical Angles- two nonadjacent angles formed by two intersecting lines.
- Vertical Angles Theorem- Vertical angles are congruent.
- Definition of Parallel lines- Parallel lines are lines that never intersect.
- Corresponding Angles Postulate- If the lines are parallel, then the corresponding angles are congruent.
- Converse: When corresponding angles are congruent, the lines are parallel.
- Alternate Interior Angles Theorem- If the lines are parallel, then the alternate interior angles are congruent.
- Converse: If the alternate interior angles are congruent, then the lines are parallel.
- Alternate Exterior Angles Theorem- If the lines are parallel, then the alternate exterior angles are congruent.
- Converse- If the alternate exterior angles are congruent, then the lines are parallel.
- Same Side Interior Angles Theorem- If the lines are parallel, then the SS Int angles are supplementary.
- Converse- If the SS Int angles are supplementary then the lines are parallel.
- Triangle Sum Theorem- All 3 angles add up to 180 degrees.
- 3rd Angles Theorem- If two pairs of angles are congruent between two triangles, then the third pair of angles must be congruent.
- Remote Angles- Two interior angles that are nonadjacent to a given exterior angle.
- Remote Angles Theorem- The measures of the two remote angles add up to the measure of the given exterior angle.
- SSS- Two triangles are congruent, if they have 3 pairs of congruent sides.
- SAS- Two triangles are congruent if they have two pairs of congruent sides, and the angles between those sides are also congruent.
- AAS- Two triangles are congruent if two angle pairs are congruent and a pair of sides are congruent, but not between the two congruent angles.
- ASA- Two triangles are congruent if two angle pairs are congruent and the sides between the two congruent angles are also congruent.
- CPCTC- Corresponding Parts of Congruent Triangles are Congruent.
- Definition of Isosceles Triangles- An isosceles triangle is a triangle with two congruent sides.
- Properties of Isosceles Triangles- The two base angles of an isosceles triangle are congruent.