Transcript 9.1 ( ) Similar Triangles

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:
congruent
1. Their angles must be _____________
corresponding sides must be
2. Their ___________
____________
proportional
Geometric Mean
• The Altitude of a triangle is the
perpendicular segment from a
_____________
vertex
opposite
_____________
to the ____________
side.
• The Altitude is called the Geometric Mean.
Draw a picture: B
D
A
C
Theorem 9.1
altitude
• If the ______________
is drawn to the
hypotenuse of a ___________
triangle, then the
right
similar
two triangles formed are ____________
to the
original
____________
triangle and to each other.
• Draw a picture and write the three SIMILARITY
STATEMENTS:
B
D
A
C
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
b) Find the height of h.
12.3 m
7.8 m
A
h
C
D
14.6 m
Example 1 cont’d:
B
12.3 m
7.8 m
A
h
C
D
14.6 m
Theorem 9.2
 In a right triangle, the altitude from the
hypotenuse divides
_____________
angle to the ____________
right
the hypotenuse into two segments. The length of
mean
the altitude is the ___________
of
geometric _____________
the lengths of the two segments.
 In the diagram:
AD BD

BD DC
 In other words:
Part1
Altitude

Altitude
Part 2
A
D
B
C
Theorem 9.3
right
 In a right triangle, the altitude from the ___________
angle to the _____________
hypotenuse divides the hypotenuse
into two segments. The length of each leg of the
right triangle is the _________________
_________
geometric
mean
of the lengths of the ____________
hypotenuse and the
adjacent
segment of the hypotenuse that is _____________
to the leg.
A
 In the diagram: AC  AB
AB
D
AD
 In other words:
hyp leg

leg part
B
C
Example 2:
• Solve for the missing variable:
8
x
6
10
5
y
Homework
9.1 Worksheet