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Cevians and parallels Image result for triangle

Image result for parallel line

Altitude--------> Orthocenter-------> can be outside or inside a triangle

Image result for altitude and orthocenter


Median---------> only inside the triangle and divides median into a 1:2 ratio

Image result for median and centroid of a triangle


Angle Bisector-------> incenter---------> can only be inside a triangle and center of inscribed circle

Image result for angle bisector and incenter


Perpendicular Bisector------>circumcenter--------> can be inside or outside a triangle and center of circumscribed circle

Image result for perpendicular bisector and circumcenter

Alternate interior angles are congruent

Image result for alternate interior angles

Alternate exterior angles are congruent

Image result for alternate exterior angles 

Corresponding angles are congruent

Image result for corresponding angles 

Same side interior angles are supplementary

Image result for supplementary same side interior angles 

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. 


Triangle Inequality: 

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