Cevians and parallels
Altitude--------> Orthocenter-------> can be outside or inside a triangle
Median---------> only inside the triangle and divides median into a 1:2 ratio
Angle Bisector-------> incenter---------> can only be inside a triangle and center of inscribed circle
Perpendicular Bisector------>circumcenter--------> can be inside or outside a triangle and center of circumscribed circle
Alternate interior angles are congruent
Alternate exterior angles are congruent
Corresponding angles are congruent
Same side interior angles are supplementary
Transversal symmetry- If two parallel lines are cut by a transversal then each pair of ________________ are _______________.
Converse of transversal symmetry: If two lines are cut by a transversal such that the______ are ______ then the lines are parallel.
Side Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally.
Three Parallels Theorem: Three or more parallel lines divide all the transversals proportionally.
Substitution: If a congruent segment is substituted in for a congruent segment then the proportion remains equivalent.
Midsegment Theorem: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and it’s length is one half the length of the third side.
Transitive Property of Parallel Lines: If two lines are parallel to a third line, they are parallel to each other.
Altitude Theorem- If it is an altitude then it forms a congruent linear pair.
Median Theorem- If it is a median then it divides the opposite side into congruent parts.
Angle Bisector Theorem- If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.
GAGS Theorem (Greatest Angle Greatest Side):
In a triangle the greatest angle is opposite from the greatest side.
The sum of any two sides of a triangle must be greater than the third