# Review 5.7 _ Pythagorean Theorem.ppt by malj

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```									                 Bell Work 1/25
1) Find the value of x. Give the answer in simplest radical
form                    9
5

x
y
x

5√
3
Review 5.7 & 5.8
1/25
5.7: Pythagorean Theorem
 What is the Pythagorean Theorem?
 a2 + b 2 = c 2

 Pythagorean triple
 Classifying triangles
 Right, obtuse and acute
 Right: c2 = a2+b2
 Obtuse: c2 > a2+b2
 Acute: c2 < a2+b2
Example 1: Together
Find the value of x. Give your
form.                                                 x
2     2    2                                6
a +b =c                    Pyth. Thm.

62 + 32 = x2
Substitution                                 3
45 = x2
Simplify
x = 3√5                                 Find the
positive
square root & simplify
Example 2: Together
Find the missing side length.
Tell if the sides form a                       2
Pythagorean triple. Explain
1.6

a2 + b 2 = c 2   Pyth. Thm.
a2 + (1.6)2 = 22              Substitution
a2 = 1.44           Solve for a2
a = 1.2          Find the positive square root.

The side lengths do not form a Pythagorean triple
because 1.2 and 1.6 are not whole numbers
Find the value of x.        1)                        2)       14
8

6                          x
Find the missing side length. Tell if the sides
x
form a Pyth. triple.                           3)
2        32
Tell if the measures can be the side length of a            4
triangle. If so, is it right, acute, or obtuse

4)    9, 12, 16                5)        11, 14, 27

6)    1.5, 3.6, 3.9            7)        2, 3.7, 4.1
5-8: Applying Special Right
 45°-45°-90° Theorem
Triangle

 30°-60°-90° Theorem
Examples: Together
x
1)
This is a 45°-45°-45° triangle.
45°           x = 19√2           Hyp.=leg√2
19
This is a 45°-45°-45° triangle.
45°         x
15 = x√2         Hyp.=leg√2
15
2)                                        15 = x          Divide both sides √2
45°                45°         √2

15√2 = x        Rationalize the
x                             √2              denominator

3)                                     This is a 30°-60°-90° triangle.
y
22 = 2x       Hyp.=2(shorter leg)
x
60°             30°          11 = x        Divide both sides by 2
22                    Y = 11√3      Longer leg = (shorter leg √3
1)           26             2)
1                 3)
45°
2
x
45°                          x           16√2

x                             x                            45°

4)
y
60°        5)           y
x                                        30°
30°        4                   6
8                               x

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