Transcript 7.5 Proportions in Triangles • Side-Splitter Theorem – If a line is parallel to one side of a triangle and intersects the other.

7.5 Proportions in Triangles
• 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.
Using the Side-Splitter Theorem
• What is the value of x in
the diagram at the right?
PK
NL

KM LM
x 1 x

12
9
9 x  9  12 x
9  3x
x3
Corollary to the Side-Splitter Theorem
• If three parallel lines intersect two transversals, then
the segments intercepted on the transversals are
proportional.
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.
Using the Triangle-Angle-Bisector
Theorem
• What is the value of x in
the diagram at the right?
RQ PR

QS PS
10 12

18 x
10 x  216
x  21.6
More Practice!!!!!
• Homework – Textbook p. 475 #9 – 22 ALL.