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1.5 Measuring Segments 1.6 Distance Formula

1.5 Measuring Segments 1.6 Distance Formula. Agenda. Homework Check ( Page 30 #16-23, 27, 28 and Page 38 #10-12 ) [10 min] Warm Up [10 min ] Pretest scores [15 min] Measuring Line Segments [35 min] Distance Formula [15 min]. Objectives. To find the lengths of segments.

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1.5 Measuring Segments 1.6 Distance Formula

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  1. 1.5 Measuring Segments1.6 Distance Formula

  2. Agenda • Homework Check (Page 30 #16-23, 27, 28 and Page 38 #10-12) [10 min] • Warm Up [10 min] • Pretest scores [15 min] • Measuring Line Segments [35 min] • Distance Formula [15 min]

  3. Objectives • To find the lengths of segments. • To find the distance between two points in the coordinate plane.

  4. Homework • Page 30 #12,14, 29-32, 47, 48 • Page 46 #2-16 EVEN • Quiz next Monday (1.4-1.6)

  5. Warm Up Given:m AOC = 140, m AOB = (2x – 6) and m BOC = (6x + 10) 1. What is the value of x? ________________________. 2. What is the _________________________. 3. can be classified as a(n) ___________________ angle. 4. and are what type of angles? ________________________? (vertical, adjacent, complementary, supplementary)

  6. Ruler Postulate • Two segments with the same length are congruent () segments. • In other words, if then . You can use these statements interchangeably.

  7. Midpoint A midpoint of a segment is a point that divides a segment into two congruent segments. A midpoint, or any line, ray, or segment through a midpoint, is said to bisect the segment. M is the midpoint of .

  8. Let’s Practice! What is the length of _____________ Name a segment congruent to . ____________ What is the midpoint of _____________

  9. Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then

  10. Example #1 –Segment Addition Postulate Given: If , find the value of . Then find AN and NB. A N B

  11. Example #2- Finding Lengths Given: M is the midpoint of Find , , and . R M T

  12. Example #3 - Finding the Length of a Segment Strategy: Draw a picture to help answer each question. If and , and then , , Is G the midpoint of

  13. Practice! • Working with a partner, you will have 20 minutes to complete this sheet.

  14. Finding Distance on the Coordinate Plane Given two points, what is the distance between the two points? Let’s try to discover the formula. • For each of the triangles A, B, C and D complete the following: • (i) using the scale, write the coordinates of each of the three vertices (ii) calculate the vertical distance (iii) calculate the horizontal distance • (iv) calculate the length of the hypotenuse to two significant figures

  15. The Distance Formula**The distance formula is just an extension of the Pythagorean Theorem!** • The distance between two points and B is

  16. Example #4- Finding Distance Find the distance between and to the nearest tenth.

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