Chapter 7.4 Notes: Special Right Triangles

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Chapter 7.4 Notes Special Right Triangles

• Goal You will use the relationships among the
  sides in special right triangles.

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• Part I
• Draw an isosceles right triangle.
• What do you know about the two legs?
• What do you know about the measures of the acute
  angles of an isosceles right triangle?
• Another name for an isosceles right triangle is a
  
• 45o-45o-90o triangle.

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• Theorem 7.8 45o-45o-90o Triangle Theorem
• In a 45o-45o-90o triangle, the hypotenuse is
• times as long as each leg.
• hypotenuse ________________
• Find the length of the hypotenuse.
• Ex.1 Ex.2

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• Find the lengths of the legs in the triangle.
• Ex.3 Ex.4
• 
  
• 
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• Part II
• Draw an equilateral triangle with side length of
  6 cm
• What do you know about an equilateral triangle?
• 1. ________________________________
• 2. ________________________________
  

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• When you divide an equilateral triangle in half,
  the two triangles formed are called a 30o-60o-90o
  triangle.
• Theorem 7.9 30o-60o-90o Triangle Theorem
• In a 30o-60o-90o triangle, the hypotenuse is
  twice as long as the shorter leg, and the longer
  leg is
• times as long as the shorter leg.
• hypotenuse _______________
• longer leg ________________

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• Ex.5 Find the values of x and y. Write your
  answer in simplest radical form.
• Find the value of the variable.
• Ex.6 Ex.7
• 60o
• y
• 
  30o
• x

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• Ex.8 The shorter leg of a 30-60-90 triangle has
  a length of . What are the lengths of the
  other two sides?
• Ex.9 A baseball diamond is a square. The
  distance from base to base is 90 feet. How far
  does the second baseman throw a ball to home
  plate?

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• Find the value of the variable.
• Ex.10 Ex.11
• Ex.12
• 60o
• 
  b
• a
• 
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