Transcript Geo 9.1-9.2

9.1 Similar Right Triangles
GOAL
1
PROPORTIONS IN RIGHT TRIANGLES
THEOREM 9.1
If the altitude is drawn to the hypotenuse of a right triangle,
then the two triangles formed are similar to the original
triangle and to each other.
EXAMPLE 1
Extra 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 h of the roof.
B
7.8 m
A
h
D
14.6 m
12.3 m
C
Checkpoint
The diagram shows the approximate dimensions of a right
triangle.
a. Identify the similar triangles in the diagram.
b. Find the height h of the triangle.
R
U
6.8 in.
S
T
12.7 in.
9.1 Similar Right Triangles
GOAL
2
USING A GEOMETRIC MEAN TO SOLVE
PROBLEMS
Study the Geometric Mean Theorems on page 529 before
going on!
EXAMPLE 2
Extra Example 2
Find the value of each variable.
a.
5
b.
y
x
6
10
8
Checkpoint
Find the value of each variable.
a.
b.
5
18
x
24
14
y
9.2 The Pythagorean Theorem
GOAL
2
USING THE PYTHAGOREAN THEOREM
If ΔABC is a right triangle, then c2 = a2 + b2.
B
c
a
C
b
EXAMPLE 1
A
Extra Example 1
Find the length of the
hypotenuse of the right
triangle. Tell whether the side
lengths form a Pythagorean
triple.
7
x
24
Checkpoint
Find the length of the
hypotenuse of the right
triangle. Tell whether the side
lengths form a Pythagorean
triple.
x
3
2
2
Extra Example 2
Find the length of the leg of the right triangle.
12
x
6 5
Checkpoint
Find the length of the
leg of the right triangle.
9
21
x
Extra Example 3
Find the area of the triangle to
the nearest tenth of a meter.
8m
8m
h
10 m
Extra Example 4
The two antennas shown
in the diagram are
supported by cables 100
feet in length. If the cables
are attached to the
antennas 50 feet from the
ground, how far apart are
the antennas?
Checkpoint
Find the missing side of the
12 m
triangle. Then find the area
to the nearest tenth of a
10.8 m
meter.
12 m