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Understanding Segments and Distance Calculation: A Hands-On Approach

This lesson emphasizes the learning-by-doing approach in geometry, focusing on measuring segments and calculating distances between points. Students will explore the concept of segments, endpoint definition, and the Segment Addition Postulate. They will engage in pair-share activities to solve segment problems collaboratively, utilizing the Pythagorean Theorem and Distance Formula. By the end of the session, students will be skilled in finding the distance between two points on a coordinate plane and will understand the relevance of these concepts in exploring geometric properties.

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Understanding Segments and Distance Calculation: A Hands-On Approach

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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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