Triangle Theorems and Proportionality Notes

Vocabulary review of geometric theorems regarding triangle midsegments, proportionality, parallel lines, transversals, and angle bisectors.

Side Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Triangle Midsegment Theorem

If a segment joins the midpoint of two sides of a triangle, the the segment is parallel to the third side and is half as long.

Line dividing two sides of a triangle proportionally

If a line divides two sides of a triangle proportionally, then it is parallel to the

Corollary to the Side Splitter Theorem

If three parallel lines interest two transversals, then the segments intercept on the transversals proportional.

Triangle Angle Bisector Theorem

If a ray bisects an angle of a triangle then it divides the opposite sides into two segments such that the ratio between the segments is in the same as the ratio between the sides adjacent to each segment.