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					Triangles
  November 2008
          Name this triangle
•     A




• B         C
            Name these sides
•       A           • There are 2 ways to
                      name sides:
                    • 1. a small letter
                    • 2. 2 capital letters




•   B        C
          Name these angles
•     A




• B         C
        Practice
              • A) Name the triangle.
•   S         • B) Name the angles
                (2 ways).
              • C) Name the sides (2
                ways).
•   T     P
              Angles
• An obtuse angle: • A right angle:



• An Acute angle:   • A straight angle:
• Complementary   • Supplementary
  Angles:           Angles:
         A triangle

•has 3        • has 3
 sides          angles
    • THE ANGLES OF A
  TRIANGLE ADD UP TO 180
          DEGRES.
         Classify triangles:
    We can categorize them 2 ways:
• Classified based on          • Classified based on
   SIDES
                                 ANGLES
• 1. An isosceles triangle
• 2. An equilateral triangle   • 1. An obtuse triangle
• 3. A scalene triangle        • 2. An acute triangle
                               • 3. A right angle
                                 triangle
   Triangles classified by sides:
• An isosceles    • An equilateral triangle
  triangle



• A scalene triangle
    Triangles classified by angle:

• An obtuse angle   • An acute angle triangle
  triangle



• A right angle triangle
                 Homework
• Sheet to complete.

• *** You cannot use a
  protractor because I
  changed the angles .
     The Pythagorean Theorem
• This theorem
  (formula) only works
  for right angle
  triangles.
                           hypotenuse
• Why? Right angle
  triangles are the only
  ones that have an
  hypotenuse.
 Why do we use the Pythagorean
          Theorem?


• TO FIND AN UNKNOWN SIDE
  IN A RIGHT ANGLE
  TRIANGLE, GIVEN THE
  OTHER TWO SIDES.
The Pythagorean Theorem
        c2=a2+b2
              • The hypotenuse ( c ) is always
                directly across from the right angle.

   THE
            • The right angle points to the
   HYPOTENUSE
                 hypotenuse.

              • The hypotenuse is always the longest
                side.

              • WE ALWAYS USE « c > TO
                IDENTIFY THE HYPOTENUSE.
              c2=a2+b2

• “In all right angle triangles, the square
  constructed on the hypotenuse is equal to
  the some of the area of the squares on the
  other two sides.”
          c2=a2+b2

• To find the   • To find a
  hypotenuse:     side:

• c2=a2+b2      • a2=c2-b2
• c=√a 2+b2     • a=√c 2-b2
Practice finding the unknown side:
Practice finding the unknown side:
       Finding missing angles…
•   1. The sum of the angles of a triangle. (180)
•   2. Complementary Angles. (add to 90)
•   3. Supplementary angles. (add to 180)
•   4. Opposite angles. (X)
•   And with parallel lines:
•   5. Co-interior Angles. (C)
•   6. Corresponding Angles. (F)
•   7. Alternate Interior Angles. (Z)
              Let’s Review
• 1. Sum of the angles   • 2. Complementary
  of a triangle.           Angles.
• 3. Supplementary   • 4. Opposite Angles.
  Angles.
          Parallel lines

• Parallel lines   • _________________

  are lines that
  are always the   • _________________
  same distance
  apart and will   • We use > and >> on
                     lines to show that they
  never meet.        are parallel.
       5. Co-Interior Angles
• ________________
                     • Make a C.

• _______________
                     • Add up to
                       180 degrees.
     6. Corresponding Angles
• ________________
                     • Make an F.

• _______________
                     • Are equal.
  7. Alternate (Interior) Angles
• ________________
                     • Make a Z.
• _______________

                     • Are equal.

				
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posted:9/12/2012
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