Geometry Segment Addition Postulate Worksheet

Overview

• Completing segments addition postulate worksheet using CUDA software.
• Focus on numbers 15-20.

Number 15: Finding Length C E

• Given: C E = x + 26
• Required: Solve for x
• Use the equation: BC + C E = B E
• Known values:
  • B C = 3x + 47
  • B E = BD + DE
  • BD = 27, DE = 10

Steps to Solve:

1. Set up the equation:
   BC + C E = BD + DE
   (3x + 47) + (x + 26) = 27 + 10
2. Combine like terms:
   4x + 73 = 37
3. Isolate x:
   • Subtract 73 from both sides:
     4x = -36
   • Divide by 4:
     x = -12
4. Calculate C E:
   C E = -12 + 26 = 14

Number 16: Finding Length B D

• Given: B D = 2x - 4
• Total length of B E = 3x - 1

Steps to Solve:

1. Set up the equation:
   B C + C E = B E
   (BC) + (2x - 3) = (3x - 1)
2. Solve for B C:
   B C = 3x - 1 - (2x - 3)
   B C = x + 2
3. Set up the equation for BD:
   B C + CD = B D
   (x + 2) + 2 = 2x - 4
4. Solve:
   x + 4 = 2x - 4
   • Subtract x from both sides:
     4 + 4 = x
     x = 8
5. Calculate B D:
   B D = 2(8) - 4 = 12

Number 17: Finding Length D E

• Given: D E = 3x - 28
• Total length: D G = 33

Steps to Solve:

1. Set up:
   D E + E F + F G = D G
   (3x - 28) + (3x - 30) + x = 33
2. Combine like terms:
   7x - 58 = 33
3. Solve for x:
   7x = 91
   x = 13
4. Calculate D E:
   D E = 3(13) - 28 = 11

Number 18: Finding Length E G

• Given: E G = x + 23
• Total length: E F + F H = 26 + x

Steps to Solve:

1. Set up:
   E F + 12 = 26 + x
   E F = 14 + x
2. Set equation for E G:
   (14 + x) + (14 + x) = (x + 23)
3. Combine and solve:
   28 + 2x = x + 23
   x = -5
4. Calculate E G:
   E G = -5 + 23 = 18

Critical Thinking Questions

Number 19: Finding Length A C

• Given: A E = x + 50, C E = x + 32
• Set up:
  A C + C E = A E
• Solve:
  A C = (x + 50) - (x + 32)
  A C = 18

Number 20: Segment Addition Problem

• Example problem: A B + B C = A C
  • Set A B = 50, B C = x, A C = 70
  • Solving gives x = 20

Conclusion

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