Proportions in Triangles.

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Proportions and Similar Triangles

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Presentation transcript:

Proportions in Triangles

Side-Splitter Theorem Theorem 7-4: 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. OR

Side-Splitter Proof Statements Reasons 1. 2. 3. 4. 5. 6. 7.

Side-Splitter Theorem Find the value of x. Find the value of x.

Corollary to Side-Splitter Theorem Corollary to Theorem 7-4: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

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

You wanna try one? Too bad! ;) Find the values of the variables in the following figure.

Triangle-Angle-Bisector Theorem 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.

Triangle-Angle-Bisector Theorem Find the value of x in the following figure. Find the value of x in the following figure.

Kick it up a notch!!! Find the value of x.

Kick it up a notch!!! Find the value of x.