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Understanding Line, Segment, Ray, and Angle Properties: Naming, Labeling, and Problem Solving

This chapter provides comprehensive methods for naming and labeling geometric figures, including lines, segments, rays, and angles. It covers practical problem-solving techniques through illustrative examples, such as finding segments using given lengths and algebraic expressions. Topics include the “Between” problem for measuring segments, solving for unknown variables in vertical angles, and interpreting diagrams to extract critical information about angles and segments. This guide is ideal for students seeking to enhance their understanding of basic geometry concepts.

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Understanding Line, Segment, Ray, and Angle Properties: Naming, Labeling, and Problem Solving

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  1. Chapter 1 Review

  2. Naming and Labeling Name each using the proper symbol and draw and label. • Line HI • Segment OP • Ray ST • Angle JKL

  3. Naming and Labeling • Line HI HI H I • Segment OP OP O P • Ray ST ST S T • Angle JKL < JKL KJ L

  4. “Between” Problem • S is between R and T on a line. If RT= 52, RS=2x+9 and ST=6x-5. Draw and label the diagram and solve for RS and ST.

  5. “Between” Problem • S is between R and T on a line. If RT= 52, RS=2x+9 and ST=6x-5. Draw and label the diagram and solve for RS and ST. • RT= RS + ST • 52= 2x + 9 + 6x – 5 • 52 = 8x + 4 • 48 = 8x • x = 6, RS = 21, ST = 31

  6. Segment Problem • Using the diagram and the following information, find AB. • AD = 17 BC = 9 AB = CD

  7. Segment Problem • Using the diagram and the following information, find AB • AD = 17 BC = 9 AB = CD • AD = AB + BC + DC • 17 = x + 9 + x • 17 = 2x + 9 • 8 = 2x • x = 4, AB = 4

  8. Vertical Angles Problem • Based on the diagram, solve for x and determine the measure of <1, 2, 3, and 4.

  9. Vertical Angles Problem • Based on the diagram, solve for x and determine the measure of <1, 2, 3, and 4. • Vertical angles are equal, therefore < 1 = < 3 and < 2 = < 4. • Supplementary angles add to equal 180o. • 5x – 4 = 3x + 16 • 2x = 20 • x = 10 • < 2 = < 4 = 46o < 1 = < 3 = 134 o

  10. Getting Information from a diagram Segment AD forms a right angle with segment FB. Segment GE forms a right angle with segment GC. Segment GD bisects angle EGC. Mark the diagram to the left and answer the following questions. Angle AGC is a ______ angle. What is the measure of angle CGB? Name a straight angle. Name three terms to describe angle EGD and angle CGD.

  11. Getting Information from a diagram Segment AD is perpendicular to segment FB. Segment GE is perpendicular to segment GC. Segment GD bisects angle EGC. Mark the diagram to the left and answer the following questions. Angle AGB is a ______ angle. Ans. right What is the measure of angle CGB? Ans. 45o Name a straight angle. Ans. AGD, FGB Name three terms to describe angle EGD and angle CGD. Ans. Congruent, complementary, adjacent

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