7.5 proportions in triangles

7.5: Proportions in

TrianglesDone by

Rana Karout

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.

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.

a

bc

d

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

You wanna try one? Find the values of the variables in the following figure.

MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.

ALGEBRA Find x and y.

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.

In the figure, ΔLJK ~ ΔSQR. Find the value of x.

In the figure, ΔLJK ~ ΔSQR. Find the value of x.

Triangle-Angle-Bisector Theorem

Find the value of x in the following figure.

Find the value of x in the following figure.

Find x.

Find n.