Midsegment of triangles

Midsegment of triangles

• 1.
  Using the Midsegment Theorem
• 2.
  Section 5.4 Midsegment Theorem A 8 ft. 8 ft. C B Point C is the midpoint of line segment AB Because segment AC = 8 and segment CB = 8, then these two segments are equal.
• 3.
  Now if wehave two segments. Midpoint of AD Midpoint of BD D S T A Midsegment B because it connects the two midpoints
• 4.
  The midpoints divideeach side Midpoint of AD Midpoint of BD D S T A Midsegment B because it connects the two midpoints
• 5.
  Now form aTriangle by connecting points A and B D S T A B  ABD
• 6.
  Lets look atthis with some numbers. 7 5 D T 7 5 S A B  ABD
• 7.
  Moving onto theMidsegment Theorem 5 D 7  ABD T 7 5 S A B The theorem states that ST is parallel to AB
• 8.
  Moving On… 7  ABD 5 D T 7 5 S A B 1 If AB  ST Then ST AB 2
• 9.
  Using some numbers 7 5 D 8 T 7 5 S A 16 B 1 So, ST = 8 and AB = 16 ST AB Better way to say this 2 theorem is that AB is twice the length of ST
• 10.
  A little easytrick… D S x T 2x If you let the midsegment be x, then the length is 2x
• 11.
  Going Back Words… D S ½x T x Looking at from a different perspective, If the side of a is x, then the midsegment is half (½) the length of the side
• 12.
  Example 1 D S x T 22 x = ½ of 22 x = 11
• 13.
  Example 2 D S 4 T x x = 2(4) = 8 because x is twice the length of the midsegment ST
• 14.
  We can havemidsegment parallel to each side of the triangle. Midsegment Midsegment Midsegment
• 15.
  Watch as eachside is related to each midsegment. Midsegment Midsegment Midsegment
• 16.
  Solve the equation forx. 3x + 7 7x+6 7x + 6 = 2(3x + 7) 7x + 6 = 2(3x + 7) 7x + 6 = 6x + 14 Midsegment relating x +6 = 14 Side of triangle to side of triangle x=8
• 17.
  For an AnimatedLook at this Theorem Click Here Points of Interest: Watch how the length of 1. Move Point A the side BC and it’s midsegments change. 2. Move Point B 3. Move Point C Is the midsegment always half side BC?
• 18.
  Citation Page Triangles aredrawn using PowerPoint Lines (drawn by David Curlette) On Slide Number 8: Formula is from http://hotmath.com/hotmath_help/topics/triangle-midsegment-theorem.html On Slide Number 17: Animation website is ttp://www.mathopenref.com/trianglemidsegment.html