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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 itâ€™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.

Triangle Inequality:

The sum of any two sides of a triangle must be greater than the third