Math Problem Statement

Worksheet on measuring segments, congruent segments, and the segment addition postulate. It includes questions such as finding segment lengths and solving for unknown variables using algebraic expressions.

Solution

Let's go through the worksheet you uploaded.

Measuring Segments:

  1. The distance between two points AA and BB is written as ABAB, or d(A,B)d(A, B).

Congruent Segments:

  1. If two segments have the same length, then the segments are congruent. This is written as ABCD\overline{AB} \cong \overline{CD}.

Segment Addition Postulate:

  1. If points AA, BB, and CC are collinear and BB is between AA and CC, then AB+BC=ACAB + BC = AC.

Now, let's solve the specific problems:

1. If PQ=9PQ = 9 and QR=28QR = 28, find PRPR.

  • PR=PQ+QR=9+28=37PR = PQ + QR = 9 + 28 = 37.

2. If QR=17QR = 17 and PR=21PR = 21, find PQPQ.

  • Using the segment addition postulate: PR=PQ+QRPR = PQ + QR. Therefore, PQ=PRQR=2117=4PQ = PR - QR = 21 - 17 = 4.

3. If EG=71EG = 71, find the value of xx. Given: 8x178x - 17 and 5x35x - 3.

  • Since EG=EF+FGEG = EF + FG: (8x17)+(5x3)=71(8x - 17) + (5x - 3) = 71 Simplifying: 13x20=7113x=91x=9113=713x - 20 = 71 \quad \Rightarrow \quad 13x = 91 \quad \Rightarrow \quad x = \frac{91}{13} = 7

4. If TV=14x8TV = 14x - 8, find TUTU. Given: TU=9x+2TU = 9x + 2 and UV=5UV = 5.

  • Since TV=TU+UVTV = TU + UV: (9x+2)+5=14x8(9x + 2) + 5 = 14x - 8 Simplifying: 9x+7=14x87+8=14x9x15=5xx=39x + 7 = 14x - 8 \quad \Rightarrow \quad 7 + 8 = 14x - 9x \quad \Rightarrow \quad 15 = 5x \quad \Rightarrow \quad x = 3 Substituting x=3x = 3 into TUTU: TU=9(3)+2=27+2=29TU = 9(3) + 2 = 27 + 2 = 29

5. If JL=5x+2JL = 5x + 2, find JLJL. Given JK=27JK = 27 and KL=3x1KL = 3x - 1.

  • Since JL=JK+KLJL = JK + KL: 27+(3x1)=5x+227 + (3x - 1) = 5x + 2 Simplifying: 26+3x=5x+2262=5x3x24=2xx=1226 + 3x = 5x + 2 \quad \Rightarrow \quad 26 - 2 = 5x - 3x \quad \Rightarrow \quad 24 = 2x \quad \Rightarrow \quad x = 12 Substituting x=12x = 12 into JLJL: JL=5(12)+2=60+2=62JL = 5(12) + 2 = 60 + 2 = 62

6. If CE=7x+4CE = 7x + 4, find the value of xx. Given CD=x+3CD = x + 3 and DE=8x9DE = 8x - 9.

  • Since CE=CD+DECE = CD + DE: (x+3)+(8x9)=7x+4(x + 3) + (8x - 9) = 7x + 4 Simplifying: 9x6=7x+49x7x=4+62x=10x=59x - 6 = 7x + 4 \quad \Rightarrow \quad 9x - 7x = 4 + 6 \quad \Rightarrow \quad 2x = 10 \quad \Rightarrow \quad x = 5

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Related Questions:

  1. How would you apply the segment addition postulate to three-dimensional geometry?
  2. Can two non-collinear points form a congruent segment?
  3. How would these rules change in non-Euclidean geometry?
  4. What is the importance of congruence in determining shapes' properties?
  5. Can you think of a real-life application of measuring and adding segments?

Tip:

Always double-check your algebra when solving for variables, especially when combining multiple terms or distributing values!

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Congruent Segments
Segment Addition Postulate

Formulas

AB = d(A, B) (distance between two points)
Congruent segments: \( \overline{AB} \cong \overline{CD} \)
Segment Addition Postulate: AB + BC = AC

Theorems

Segment Addition Postulate

Suitable Grade Level

Grade 7-9