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Triangle Inequalities (PowerPoint)

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  • pg 1
									    Inequalities in One
         Triangle
Objectives:
 Use triangle measurements to decide which side
is longest or which angle is largest
 Apply the Triangle Inequality
Which side is larger, AC or BC?
 B
             5       BC > AC

         A             C
                 3
Which angle is larger B or A?
B               A > B
            5



        A            C
                3
Theorem: Side Angle
   one side of a triangle is
 If
 longer than another side,
 then the angle opposite the
 longer side is larger than
 the angle opposite the
 shorter side.
Which angle is larger, D or F?
D          F > D
     24

                40
        E              F
Which side is larger, DE or EF?
D                 DE > EF
      24

                40
         E             F
Ex. 1 Write the angles in order from least to
greatest.

  A                     C, A, B
                52
12
   B                               C
              43
Theorem: Angle Side
   one angle of a triangle is
 If
 larger than another angle,
 then the side opposite the
 larger angle is longer than
 the side opposite the
 smaller angle.
Ex. 2 Write sides in order from greatest to
least.
               Y
                          XZ, XY, YZ
              128º
     22º               30º      Z
X
      81


54         45
Theorem: Exterior Angle Inequality
   The measure of an
   exterior angle of a   1
   triangle is greater
   than the measure
   of either of the
   two nonadjacent
   interior angles.
                     2            3
Which angle is larger 2 or 3? 2  3
Which angle is larger 1 or 3? 1  3
Constructing a
  Triangle
  Not every group of 3
segments can be used to
    form a triangle.
 How can you tell if it is possible
for three sides to form a triangle?

The 2 smaller sides must add up to be
   MORE THAN the largest side.
Triangle Inequality Theorem
          The sum of the
          lengths of the two
    C     smaller sides must be
          greater than the
       B
          length of the 3rd side.
A
Determine if the three numbers can be measures of
the sides of a triangle. If no, explain.
a. 13, 28, 19                    ?
                  13  19  28         Yes

b. 8, 4 2 , 4 2                   ?
                4 2  4 2  8 Yes
c. 28, 96, 124
                             ?
                  28  96 124 NO
Finding Possible Side Lengths
If two sides of a triangle have the
following measures, find the range of
possible measures of the third side.
  a. 10, 7             b. 18 , 11


  3 < x < 17           7 < x < 29
  Practice

p. 287 #1 – 23 odd
  (12 problems)

								
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