1. Section 8.6 Proportions and Similar Triangles
OBJECTIVE:
To use the Triangle Proportionality Theorem and the Triangle-Angle-Bisector Theorem
BIG IDEAS: Visualization and Proportionality
ESSENTIAL UNDERSTANDINGS:
When two or more parallel lines intersect other lines, proportional segments are formed
The bisector of an angle of a triangle divides the opposite side into two segments with lengths proportional to the sides of the triangle that form the angle
MATHEMATICAL PRACTICE:
Construct viable arguments and critique the reasoning of others

2. Proportionality Theorems
Triangle Proportionality Theorem:
If a line is ____________________ to one side of a triangle and ____________________ the other two sides, then it divides those sides _________________________
Converse of the Triangle Proportionality Theorem:
If a line ____________________ two sides of a triangle _________________________, then it is ____________________ to the third side

3. Proportionality Theorems
Corollary to the Triangle Proportionality Theorem:
If _______________ parallel lines ____________________ two transversals, then the ____________________ intercepted on the transversals are _________________________
Triangle-Angle-Bisector Theorem:
If a _______________ bisects an angle of a triangle, then it divides the ____________________ side into two segments that are _________________________ to the other two sides of the triangle

4. Examples
1. In the diagram,
What is the length of ?

5. Examples
2. In the diagram,
What is the lengths of ?

6. Examples
3. In the diagram,
What is the length of ?

7. Examples
4. In the diagram, Find

8. Examples
5. Find the value of x