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a. Find the length of the midsegment of an equilateral triangle with side lengths of 12.5 cm.

b. Given that UT is the perpendicular bisector of line segment AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.

c. Given angle EFG has angle bisector FH, where EF = GF, find the value of y if EH = 5y + 10 and HG = 28 - y.

Respuesta :

mhanifa

Answer:

  • a. 6.25
  • b. AT = 33
  • c. y = 3

Step-by-step explanation:

a. Midsegment is half the length of the parallel side:

  • 12.5/2 = 6.25

b. Segment addition postulate:

  • AB = AT + TB = 3x + 6 + 42 - x = 2x + 48

Perpendicular bisector of segment divides the segment in two equal halves:

  • AT = TB
  • 3x + 6 = 42 - x
  • 4x = 36
  • x = 9

AT is:

  • AT = 3*9 + 6
  •      = 33

c) The point on the angle bisector H is equidistant from the point E and G:

  • EH = HG
  • 5y + 10 = 28 - y
  • 5y + y = 28 - 10
  • 6y = 18
  • y = 3

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