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Bellwork

Explore the concepts of segment addition and midpoints in geometry through segment PQ and QR. Learn how to apply the Segment Addition Postulate, which states that if point B lies between points A and C, then the lengths of segments AB and BC sum to the length of segment AC. This foundational principle aids in calculating unknown segment lengths and verifying collinearity. Gain insights into identifying congruent segments and midpoints while practicing with various examples to solidify your understanding of these geometric concepts.

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Bellwork

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  1. Bellwork 4) Suppose you know PQ and QR. Can you use the segment addition postulate to find PR? Explain.

  2. 1-3 Measuring Segments and Angles

  3. Postulate 1: Ruler post. • The points on a line can be matched with those on the real # line. • The real # that corresponds to a point is the coordinate of the point. • If you find the difference between the coordinates of 2 points, then take the absolute value, you will have the distance between the points.

  4. Ruler post. (continued) • The length of AB can be found by x2-x1 • **The symbol for the length of AB is AB. A B x1 x2

  5. Example: Find AB. A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5

  6. Is Alex between Ty and Josh? Yes! In order for a point to be between 2 others, all 3 points MUST BE collinear!! Ty Alex Josh No, but why not? How about now?

  7. Post. 1-6: Segment Addition Post. • If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C. C B A

  8. EX. • If EG= 59, what are EF and FG? 8x-14 F G 4x+1 E

  9. OYO. • If EG= 120, what are EF and FG? 4x+6 F G 7x+15 E

  10. Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7

  11. Congruent ( ) Segments • Segments that have the same length. If AB & XY have the same length, Then AB=XY, but AB XY Symbol for congruent

  12. Midpoint- a point that divides the segment into two congruent segments • Segment Bisector- a point, line, or ray that intersects a segment at its midpoint

  13. Ex.. • Q is the midpoint of PR. What are PQ,QR, and PR? 6x-7 5x +1 Q R P

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