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1.2 Key Concepts

1.2 Key Concepts. Postulate. A rule that is accepted without proof. Sometimes called an Axiom. Theorem. A rule that can be proved. Congruent Segments. Line Segments that have equal lengths. Ruler Postulate. The points on a line can be matched one to one with real numbers.

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1.2 Key Concepts

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  1. 1.2 Key Concepts

  2. Postulate A rule that is accepted without proof. Sometimes called an Axiom.

  3. Theorem A rule that can be proved.

  4. Congruent Segments Line Segments that have equal lengths

  5. Ruler Postulate The points on a line can be matched one to one with real numbers. The number that corresponds to a point is the COORDINATE of that point.

  6. Ruler Postulate The DISTANCE between points is the absolute value of the difference of the coordinates. Example

  7. Measure the length of STto the nearest tenth of a centimeter. Align one mark of a metric ruler with S. Then estimate the coordinate of T. For example, if you align Swith 2, T appears to align with 5.4. ST=5.4 – 2 = 3.4 The length of STis about 3.4 centimeters. ANSWER EXAMPLE 1 Apply the Ruler Postulate SOLUTION Use Ruler Postulate.

  8. Maps The cities shown on the map lie approximately in a straight line. Use the given distances to find the distance from Lubbock, Texas, to St. Louis, Missouri. The distance from Lubbock to St. Louis is about 740 miles. ANSWER EXAMPLE 2 Apply the the Segment Addition Postulate SOLUTION Because Tulsa, Oklahoma, lies between Lubbock and St. Louis, you can apply the Segment Addition Postulate. LS = LT + TS = 380 + 360 = 740

  9. 1 8 1. 2. for Examples 1 and 2 GUIDED PRACTICE Use a ruler to measure the length of the segment to the nearest inch.

  10. In Exercises 3 and 4, use the diagram shown. In the diagram, WY = 30. Can you use the Segment Addition Postulate to find the distance between points Wand Z? Explain your reasoning. 4. 3. Use the Segment Addition Postulate to find XZ. ANSWER 73 ANSWER No; W is not between X and Z. for Examples 1 and 2 GUIDED PRACTICE

  11. Use the diagram to find GH. FH = FG+ GH 36 21+GH = 15 GH = EXAMPLE 3 Find a length SOLUTION Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. Segment Addition Postulate. Substitute 36 for FHand 21 for FG. Subtract 21 from each side.

  12. Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate plane. Then determine whether JKand LMare congruent. To find the length of a horizontal segment, find the absolute value of the difference of the x-coordinates of the endpoints. JK = 2 – (– 3) = 5 EXAMPLE 4 Compare segments for congruence SOLUTION Use Ruler Postulate.

  13. LM = – 2 – 3 = 5 ~ JKand LMhave the same length. So, JK LM. = ANSWER EXAMPLE 4 Compare segments for congruence To find the length of a vertical segment, find the absolute value of the difference of the y-coordinates of the endpoints. Use Ruler Postulate.

  14. Plot the points A(– 2, 4),B(3, 4), C(0, 2), and D(0, – 2) in a coordinate plane. Then determine whether ABand CDare congruent. Use the diagram to find WX. ANSWER No. ANSWER 107 6. for Examples 3 and 4 GUIDED PRACTICE 5.

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