Math 2 Side Splitter & Angle Bisector Theorems

Triangle Proportionality Theorem aka “The Side Splitter Theorem” If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the two sides proportionally.

Converse of the Triangle Proportionally Theorem If a line divides two sides of a triangle proportionally, then the line is parallel to the remaining side.

Solve for x

Solve for x

Show that DE // BC

Show that DE // BC

Theorem If three parallel lines are intersected by two lines, then the lines are divided proportionally.

Solve for x

Solve for x

Video Notes – Side Splitter https://safeshare.tv/x/igK6K_OsrHs

Triangle – Angle Bisector Theorem If a ray bisects one angle of a triangle, then it divides the sides proportional with the sides they are touching.

Solve for x

Solve for x

Video Notes – Angle Bisector https://safeshare.tv/x/Y13L0IxWbbY

Sample Practice Problems

Apply the Side-Splitter Theorem Find the length of VX by using the side splitter theorem.

Apply the Corollary to the Side-Splitter Theorem Find the value of x from the diagram below.

Using the Triangle-Angle Bisector Theorem Find the unknown value for the given information.

Application Given that the edges of the panels of the sails are parallel, find the values of the variables.

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.

Graded Assignment https://goo.gl/forms/YdybV1NLq0m6VzFu2 Click on the Google Doc to submit your answers. https://goo.gl/forms/YdybV1NLq0m6VzFu2

1 Solve for x.

2

3 Solve for x.

4 Solve for x.

5

6 Solve for x.

7 Find the missing length.

8 Solve for x.

9 Solve for x.

10 What is the sum of the answers for problem #s 1, 2, 7, & 9?

11 – Extra Credit