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1-4 Measuring Segments

We learn by doing. If we do nothing, we learn nothing. The more we do, the more we learn. 1-4 Measuring Segments. OBJECTIVE: Find the distance between two points RELEVANCE: Useful for discovering properties of other geometric figures. Segment.

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1-4 Measuring Segments

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  1. We learn by doing. If we do nothing, we learn nothing. The more we do, the more we learn. 1-4 Measuring Segments OBJECTIVE: Find the distance between two points RELEVANCE: Useful for discovering properties of other geometric figures

  2. Segment • Part of a line that consists of two points, called endpoints, and all the points between them. EX: A B Segment AB or AB

  3. Segment Addition Postulate • If Q is between P and R, then PQ+QR=PR.

  4. Example • Find LM if L is between N and M, NL=6x-5, LM=2x+3, and NM=30. N M L

  5. PRACTICE If B is between A and C, find BC. • AB = 3x – 1, BC = x + 7, AC = 38 • AB = x + 12, BC = 2x – 3, AC = 5x - 17

  6. A-B Pair-Share Instructions • Person “A” works the 1st problem while Person “B” observes and provides assistance when needed. • When “A” has finished, “A” and “B” switch rolls and repeat the process with the second problem. • DO NOT work at the same time!!!

  7. A-B Pair-Share If U is between T and B, find the value of x and the measure of segment TU. 1. TU = 2x, UB = 3x + 1, TB = 21 2. TU = 4x – 1, UB = 2x – 1, TB = 5x

  8. Questions???

  9. Exit Ticket • If W is between R and S, RS = 7n + 8, RW = 4n – 3, and WS = 6n + 2, find the value of n and WS.

  10. Pythagorean Theorem • In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. • (leg)² + (leg)² = (hypotenuse)²

  11. Example • Find the distance from A(1, 2) to B(6, 14) using the Pythagorean Theorem.

  12. Practice: • Find the distance between R(7, 11) and S(-1, 5) using the Pythagorean Theorem.

  13. Distance Formula • The distance d between any two points with coordinates (x1, y1) and (x2, y2) is given by the formula

  14. Example • Find PQ for P(-3, -5) and Q(4, -6) using the distance formula.

  15. Practice: • Find LM for L(-3, 5) and M(12, -2) using the distance formula.

  16. A-B Pair-Share Use either the Pythagorean Theorem or the distance formula to find the distance between the given points. • E(-1, 1), F(3, 4) • H(3, -1), K(5, -4)

  17. Exit Ticket – Show Your Work!! Use either the Pythagorean Theorem or the distance formula to find the distance between W(9, -5) and X(-6, 12).

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