# Section 8-5 Proportions in Triangles SPI 22B: apply ratio and proportion to solve real-world problems involving polygons - PowerPoint PPT Presentation

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## Section 8-5 Proportions in Triangles SPI 22B: apply ratio and proportion to solve real-world problems involving polygons

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Title: Section 8-5 Proportions in Triangles SPI 22B: apply ratio and proportion to solve real-world problems involving polygons

1
Section 8-5 Proportions in
Triangles SPI 22B
apply ratio and proportion to solve real-world
problems involving polygons
• Objectives
• Use Side-splitter Theorem and the
Triangle-Angle-Bisector Theorem

Similar triangles can be used to solve a variety
of problems.
2
Side-Splitter Theorem
Theorem 8-4 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.
3
Apply the Side-Splitter Theorem
Find the length of VX by using the side splitter
theorem.
4
Corollary to Side-Splitter Theorem
Theorem 8-4 Corollary to Side-Splitter Theorem
If three parallel lines intersect two
transversals, then the segments intercepted on
the transversals are proportional.
5
Apply the Corollary to the Side-Splitter Theorem
Find the value of x from the diagram below.
6
Real-world Connection
Sail makers sometimes use a computer to create
patterns for sails. After the panels are cut
out, they are sown together to form the sail.
The edges of the panels in the sail to the right
are parallel. Find the lengths of x and y.
7
Triangle-Angle Bisector Theorem
Theorem 8-5 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.
CA DB CD BA
8
Using the Triangle-Angle Bisector Theorem
Find the unknown value for the given information.