Math Problem Statement

Find the lengths of segments EG, JL, and FG based on the given segment addition problems.

Solution

Let's analyze and solve each of the three problems presented in the image:


Problem 10: Find EGEG

We are given the following distances on the segment EGEG:

  • EF=22EF = 22
  • FG=93FG = 93

To find the length of EGEG, we add the given distances: EG=EF+FG=22+93=115EG = EF + FG = 22 + 93 = 115

Answer: EG=115EG = 115


Problem 11: Find JLJL

We are given the following distances on the segment JLJL:

  • JK=15JK = 15
  • KL=67KL = 67

To find the length of JLJL, we add the given distances: JL=JK+KL=15+67=82JL = JK + KL = 15 + 67 = 82

Answer: JL=82JL = 82


Problem 12: Find FGFG

We are given the following distances on the segment FHFH:

  • FGFG is unknown.
  • GH=22GH = 22
  • FH=61FH = 61

Since FHFH is the total length and FG+GH=FHFG + GH = FH, we can solve for FGFG as follows: FG=FHGH=6122=39FG = FH - GH = 61 - 22 = 39

Answer: FG=39FG = 39


Summary of Answers:

  • EG=115EG = 115
  • JL=82JL = 82
  • FG=39FG = 39

Would you like any further explanations or details?

Here are 5 related questions to expand your understanding:

  1. If EGEG is 115 and we move 25 units from point EE, where would we be on the line?
  2. How would you find the missing segment if only the total length and one segment are known?
  3. How could you use similar methods to solve for unknowns on a triangle or polygon?
  4. What is the general formula for finding a total length from two segments on a line?
  5. How can you check your answers to problems like these?

Tip: When dealing with segment addition problems, always confirm the units and ensure all parts of the segment sum to the total.

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Math Problem Analysis

Mathematical Concepts

Segment Addition
Basic Geometry
Addition of Distances

Formulas

Segment Addition Formula: Total Length = Segment 1 + Segment 2

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 6-8