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Understanding Segment Properties in Geometry: Reflexive, Symmetric, and Transitive

Discover the essential properties of segments in geometry, including reflexive, symmetric, and transitive properties. This guide explains how these properties apply to segments with practical examples, such as measuring lengths and finding missing distances. Learn how to apply addition, subtraction, multiplication, and division properties to solve segment-related problems effectively. Whether calculating distances between points or determining the middle point among collinear segments, you'll gain a deeper understanding of geometry basics.

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Understanding Segment Properties in Geometry: Reflexive, Symmetric, and Transitive

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  1. Geometry 2.2Segments

  2. Silly Properties • Reflexive Property • For any number a: a=a • Symmetric Property • For any a and b: if a=b then b=a • Transitive Property • For any a, b, and c: if a=b and b=c then a=c

  3. Silly Properties • Addition and Subtraction Property • For numbers a, b, c: if a=b then a+c=b+c • Multiplication and Division Property • For numbers a, b, c: if a=b then axc=bxc • Substitution Property • For numbers a, b: if a=b then a can go anywhere that b is.

  4. Line Segment Stuff • If AB = 7 and BC= 12.. • Find AC • AB + BC = AC • 7 + 12 = A B C 19

  5. Line Segment Stuff • If PQ = 18 and QR = 15... • Find PR • PQ + QR = PR • 18 + 15 = P Q R 33

  6. Line Segment Stuff • If LM = 22 and LN = 41... • Find MN • LM + MN = LN • 22 + MN = 41 • MN = 41 – 22 = L M N 19

  7. What is in the middle? • If three points are collinear and ... • AD = 2 ED = 5 AE = 7 • What point is in the middle?

  8. What is in the middle? • If three points are collinear and ... RS = 45 TS = 25 RT = 20 • What point is in the middle?

  9. Easy way to do this... • The two short measures add up to the long one. • Look at the two shorties • The letter they have in common is in the middle !!!

  10. Let’s try • XY = 15 • XZ = 7 • YZ = 22 • THE SMALL ONES ARE XY AND XZ • THEY BOTH HAVE X • SO X IS IN THE MIDDLE

  11. Let’s try • DR = 45 • GR = 19 • Dg = 26 • THE SMALL ONES ARE GR AND DG • THEY BOTH HAVE G • SO G IS IN THE MIDDLE

  12. Let’s try • Roy to Layton is 8 miles • Layton to Salt Lake is 25 miles • Roy to Salt Lake is 33 miles • Which city is in the middle?

  13. 2.24-7, 10-22

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