9 Most Common Properties, Definitions & Theorems for Triangles

Reflexive Property

• AB = BA

• A(B + C) = AB + AC

• -AB = AB

• A+ (B + C) = (A + B) + C

Reflexive Property

• Results in two segments being congruent

• Results in two angles being congruent

• Results in two congruent segments and right angles

• When the triangles have an angle or side in common

Segment Bisector

• Results in two segments being congruent

• Results in two angles being congruent

• When two lines are intersecting

• When you are given right triangles and/or a square/rectangle

Vertical angles are

• similar

• different

• congruent

• perpendicular

3rd angle theorem

• is the same as AAA

• If 2 angles of a triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent

• is the same as alternate interior angles

• If 3 angles of a triangle are congruent, then the triangles are congruent

Angle Bisector

• Results in two segments being congruent

• When two lines are intersecting

• Results in two angles being congruent

• Results when you have alternate interior angles

Alternate Interior Angles are

• congruent when the givens inform you that two lines are parallel

• not congruent when the givens inform you that the two lines are parallel

• congruent when the givens inform you that two lines are perpendicular

• Results in 2 congruent segments and right angles

Vertical angles

• occur when two lines are intersecting

• occur when two lines are perpendicular

• occur when two lines are skew

• occur when there are two congruent segments

Perpendicular Bisector

• Results in two congruent angles

• Results in right angles

• Results when two lines intersect

• Results in two congruent segments and right angles

Midpoint

• Results in two congruent angles being congruent

• Results when triangles have an angle or side in common

• Results in two congruent segments being congruent

• Results when two lines intersect