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Holt McDougal Geometry
7-3-ext Providing the Pythagorean Theorem7-3-ext Providing the Pythagorean Theorem
Holt Geometry
Lesson PresentationLesson Presentation
Holt McDougal Geometry
Holt McDougal Geometry
7-3-ext Providing the Pythagorean Theorem
Prove the Pythagorean Theorem using similar Triangles.
Objectives
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 TheoremExample 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:
Find f:
322 + 242 = b2
1024 + 576 = b2
1600 = b2
40=b
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:
Find c:
f2 + 122 = 152
f2 + 144 = 225
f2 = 81
f = 9
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
Carla needs to run about 5.1 miles.
a2 + b2 = c2
42 + b2 = 6.52
16 + b2 = 42.25
b2 = 26.25
b 5.1 ~~
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?
The school is approximately 5.8 miles from her home.
a2 + b2 = c2
52 + 32 = c2
25 + 9 = c2
34 = c2
c 5.8~~