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
2) Find the values of the variables. Give your answers in
   simplest radical form.
                                         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

— Simplifying radicals
— 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
 answer in simplest radical
 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
          Exercises: On Your Own!!
 Find the value of x.        1)                        2)       14
 Give your answer in                          2
                                                                          8
 simplest radical form         x

                                      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
 Find the values of the variables. Give your answers in simplest radical form.
                  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
        Exercises: On Your Own!
Find the values of the variables. Give your answers in
simplest radical form.
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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