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1-2Use Segments and Congruence

1-2Use Segments and Congruence. Hubarth Geometry. The point on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B is written as AB.

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1-2Use Segments and Congruence

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  1. 1-2Use Segments and Congruence Hubarth Geometry

  2. The point on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B is written as AB. AB is also called the length. AB is the absolute value of the difference of the Coordinates of A and B Names of points A B . . x1 x2 Coordinates of points AB . B . A x1 x2

  3. 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 Ex 1 Measure the Segment SOLUTION

  4. Segment Addition Postulate Words and Symbols If B is between A and C, Then AC = AB +BC If AC= AB +BC, Then B is Between A and C AB BC . . . A B C AC

  5. 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 Ex 2 Apply 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

  6. Use the diagram to find GH. FH = FG+ GH 36 21+GH = 15 GH = Ex 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.

  7. Congruent Segments Line segment that have the same length are called congruent segments. In the diagrams Below, you can say “ the length of AB is equal to the length of CD”, or you can say “AB is Congruent to CD”. The symbol means “ is congruent to”. Lengths are equal Segments are Congruent . A . B AB = CD AB D . . is equal to is congruent to C D

  8. 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 Ex 4 Compare Segments for Congruence SOLUTION LM Segment JK LM

  9. 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. 1. Use the diagram to find WX. 1 8 3. ANSWER No. ANSWER 107 ANSWER 5 1 in. 8 2. Practice Use a ruler to measure the length of the segment to the nearest inch.

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