4 7 Use Isosceles and Equilateral Triangles by 8npcq3Pa

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									4.7 Use Isosceles and
Equilateral Triangles
Notetaking Guide pages 108 – 110
5 4
Vocabulary
   The _______ of an isosceles triangle are the
           legs
    two congruent sides.
   The ____________ of an isosceles triangle is
          vertex angle
    the angle formed by the legs.
   The ______ of an isosceles triangle is the side
          base
    that is not the leg.
   The _____________ of an isosceles triangle
          base angles
    are the two angles adjacent to the base.
What does it look like?
<C
AC
Converse of The Isosceles Triangle
Theorem
   If two angles of a
    triangle are
    congruent, then
    the sides
    opposite those
    angles are
    congruent.
F   G
              equiangular




equilateral
Reminder
   Each angle of an equilateral triangle
    measures 60 degrees.

   The sum of the measures of the angles of a
    triangle is 180 .
Example 2 Find measures in a triangle



 equilateral

 equiangular
           180
           60
                          60
Example 3 Use isosceles and equilateral
triangles

             equiangular
          equilateral
           JL              8
                               <LJM
           LJ
                8
          JL
          8                    8
          4
Example 4 Solve a multi-step problem




                                    <DCA
         equiangular          Corollary to the
  Converse of Base Angles Theorem

                                 <ACB
                      AAS Congruence Theorem
Checkpoint

   H; J




   15
Use parts (a) and (b) in Example 4 to
show that m<BAD = 120
     DCA is equiangular
   m<ADC = m<DCA = m<CAD
   3(m<CAD) = 180       Triangle Sum Theorem
     m<CAD = 60          Division Property

   Because      DCA is equiangular and
      CBA =      ADC
   You know that m<BAC = 60

   m<BAD = m<BAC + m<CAD
        = 60 + 60
        = 120
Find the value of x.
      x


          62




          x = 56
Find the value of x.


                   x = 7.5



        10

               6


      2x - 5
Summary

								
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