7.5 - Proportions in Triangles

7.5 - Proportions in Triangles

By Steve Dull

Objective

• ​To use the Triangle Proportionality Theorem

• To use the Triangle Angle Bisector Theorem​

Essential Understanding

When two or more parallel lines intersect other lines, proportional segments are formed.

Open Ended

Determine the value of x in the diagram.

Multiple Select

What proportion could NOT be used to determine the value of x in the diagram?

• $$\frac{30}{x+7}=\frac{25}{15}$$  

• $$\frac{x+7}{15}=\frac{30}{25}$$  

• $$\frac{30}{15}=\frac{x+7}{25}$$  

• All three proportions could be used to solve the problem.

The Triangle Proportionality Theorem has a corollary

Let's try one

Open Ended

Determine the value of x in the diagram.

One last theorem

Multiple Choice

If $$KM$$   is an angle bisector, determine the value of x in the diagram.

• 4.8

• 9.6

• 2.4

• 7.2

Complete #6-12 on the last page of the

7.5 Notes packet.

​Independent Practice

Open Ended

How would you explain the Triangle Proportionality Theorem to a friend who didn't understand today's lesson?