MATH 2 SIDE SPLITTER ANGLE BISECTOR THEOREMS TRIANGLE

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

SHOW THAT DE // BC

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

SOLVE FOR X

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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

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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.