9.1 (old geometry book)

Similar Triangles

5.4-9.1 HW Quiz: Wednesday

Special Triangles Test: FRIDAY!

Similar Triangles

In order for two triangles to be

similar:1. Their angles must be _____________

2. Their ___________ sides must be ____________

congruent

corresponding

proportional

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:

A

D

C

B

perpendicular

vertex opposite

Theorem 9.1

• 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:

B

A

D

C

altitude

rightsimilar

original

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.

7.8 m 12.3 mh

14.6 m

D CA

B

Example 1 cont’d:

7.8 m 12.3 mh

14.6 m

D CA

B

Theorem 9.2 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:

AD BD

BD DC

D

B C

A

1

2

Part Altitude

Altitude Part

right hypotenuse

geometric mean

Theorem 9.3 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:

AC AB

AB AD D

B C

A

hyp leg

leg part

right

hypotenuse

geometric meanhypotenuse

adjacent

Example 2:

• Solve for the missing variable:

x

106

y

8

5

Homework

9.1 Worksheet