1. 9.1 (old geometry book) Similar Triangles
HW Quiz: Wednesday
Special Triangles Test: FRIDAY!

2. Similar Triangles In order for two triangles to be similar:
Their angles must be _____________
Their ___________ sides must be ____________
congruent
corresponding
proportional

3. Geometric Mean
The Altitude of a triangle is the _____________ segment from a _____________ to the ____________ side.
The Altitude is called the Geometric Mean.
Draw a picture:
perpendicular
vertex
opposite B D C A

4. Theorem 9.1
altitude
If the ______________ is drawn to the hypotenuse of a ___________ triangle, then the two triangles formed are ____________ to the ____________ triangle and to each other.
Draw a picture and write the three SIMILARITY STATEMENTS:
right
similar
original B A D C

5. Example 1:
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section.
a) Identify the similar triangles in the diagram.
b) Find the height of h.

6. Example 1 cont’d:

7. Theorem 9.2 In the diagram: In other words:
In a right triangle, the altitude from the _____________ angle to the ____________ divides the hypotenuse into two segments. The length of the altitude is the ___________ _____________ of the lengths of the two segments.
In the diagram:
In other words:
hypotenuse
right
mean
geometric

8. Theorem 9.3
right
In a right triangle, the altitude from the ___________ angle to the _____________ divides the hypotenuse into two segments. The length of each leg of the right triangle is the _________________ _________ of the lengths of the ____________ and the segment of the hypotenuse that is _____________ to the leg.
In the diagram:
In other words:
hypotenuse
geometric
mean
hypotenuse
adjacent

9. Example 2:
Solve for the missing variable:

10. Homework
9.1 Worksheet