Geometry – Section 7.5 Day 1
Proportions in Triangles
Name:_______________________
Date:____________ Period:______
Target Goals:
1. To use the Side-Splitter Theorem
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 PROPORTIONATELY.
What does that mean?
Since RS // XY , then according to the
Side splitter theorem we know that…
Examples: Find the value of x.
1.)
2.)
Old Method:
New Method:
3.)
Corollary to the SIDE SPLITTER THEOREM
If three parallel lines intersect two transversals, then the segments intercepted
on the transversals are PROPORTIONAL.
What does that mean?
By the Corollary to the Side Splitter Theorem we
know that…
Examples: Solve for the missing variables in each picture.
1.)
2.
3.)
Triangle Angle Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into
two segments that are proportional to the other two sides of the triangle.
What does that mean?
Since we know that AD bisects CAB then by
the Triangle Angle Bisector Theorem we know…
Examples: Find the value of the missing variable.
1.)
2.)
3.)