7-3-ext
Providingthe
thePythagorean
PythagoreanTheorem
Theorem
7-3-extProviding
Lesson Presentation
Holt
Holt
McDougal
Geometry
Geometry
Holt
McDougal
Geometry
7-3-ext
Providing the Pythagorean Theorem
Objectives
Prove the Pythagorean Theorem using
similar Triangles.
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
The Pythagorean Theorem is one of the most widely
used and well-known mathematical theorems. The
theorem has been proven in many different ways,
some of which involve subdividing the triangle in
some way. The following proof uses similar triangles.
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Example 1:Proving the Pythagorean Theorem Using
Similar Triangles
For the figure, find b, c, and f.
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Example 1: Continued
Find b:
322 + 242 = b2
1024 + 576 = b2
1600 = b2
40=b
Find f:
f2 + 242 = 302
f2 + 576 = 900
f2 = 324
f = 18
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Example 1: Continued
Find c:
c = 32 + f
c = 32 + 18
c = 50
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Check It Out! Example 1
In the figure, find c, e,
and f.
Find e:
e2 + 122 = 202
e2 + 144 = 400
e2 = 256
e = 16
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Check It Out! Example 1 Continued
Find f:
f2 + 122 = 152
f2 + 144 = 225
f2 = 81
f=9
Find c:
c=e+f
c = 16 + 9
c = 25
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Example 2: Applying the Pythagorean Theorem
Megan, Tia, and Carla are running a relay
race. Megan runs the first leg, 6.5 miles
northwest. Tia runs the second leg, 4.0
miles south. How far east does Carla need
to run to complete the race?
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Example 2 : Continued
a2 + b2 = c2
42 + b2 = 6.52
16 + b2 = 42.25
b2 = 26.25
b~
~ 5.1
Carla needs to run about 5.1 miles.
Holt McDougal Geometry
7-3-ext
Providing the Pythagorean Theorem
Check It Out! Example 2
Jackie drives 5 miles east and 3 miles north
from home to school. What is the shortest
distance from Jackie’s home to school?
a2 + b2 = c2
52 + 32 = c2
25 + 9 = c2
34 = c2
c ~
~ 5.8
The school is approximately 5.8 miles from her home.
Holt McDougal Geometry