Objective: to measure segments and add segment lengths

1. DO NOW: EVALUATE. Plot each point on a coordinate plane. TAKE OUT YOUR RULERS I WILL BE COMING AROUND TO CHECK THAT YOU HAVE THEM. THIS WILL COUNT AS CLASS PARTICIPATION!!! I-15I I7I I10-34I I-12-(-2)I A (2, -5) B (-3, 6) C (4, 4) D (-1, -6) Objective: to measure segments and add segment lengths Homework: 1.5 Practice A

2. DO NOW B • 15 • 7 • 24 • 10 C A D

3. HOMEWORK CHECK- 1.4 Practice A Point Line Point D Point C Line q Line r False True True False False False True next slide next slide next slide next slide Point B Point C Main Street & Park Street Park Street & Penn Street

4. Homework Checkcontinued… 14. 15. 16. 17.

5. Important Vocabulary: • Coordinate: The real number that corresponds to a point is the coordinate of the point (x, y) (-3, 5) • Distance: The distance between points A and B, written as AB is the ABSOLUTE VALUE of the difference of the coordinates of A and B I -4 - - 1I = I -4 +1I = I -3I = I 3 I • Length: The distance between A and B is also called the length of AB e.g. AB = length • Between: When three points lie on a line, one of them in between the other two. e.g. • Congruent Segments: Congruent segments are segments that have the same length AB = BC -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 A B C ~

6. POSTULATE 5 SEGMENT ADDITION POSTULATE FOLLOW UP • If B is between A and C then, AC = B + C. If AC = AB + BC, then B is between A and C. • What is the relationship between the two parts of Postulate 5? They are converses. • Converses: “if, then statements” • Statement (if): If it snows… • Converse (then): there will be no school. • You can also reverse it…There will be no school if it snows! I AC I A B C I AB I BC I

7. Example 1 Measure the lengths of AC and BC to the nearest millimeter Find distance between two points A B C

8. Solution • Point A lines up with 0. Point C lines up with 87. • AC = I 87 – 0 I = 87 mm • Point B lines up with 66. Point C lines up with 87. • BC = I 87 – 66 I = 21 mm

9. Example 2 Use the map to find the distance from Athens to Albany. Find distance on a map A Athens 80 miles M Macon 90 miles B Albany

10. Solution • Because the three cities lie on a line, you can use the Segment Addition Postulate. • AM = 80 miles • MB = 90 miles • AB = AM + MB = 80 + 90 = 170 miles • The distance from Athens to Albany is 170 miles.

11. Example 3 Use the diagram to find EF. Find a distance by subtracting 16 10 D E F

12. Solution • DF = DE + EF (Use the SEGMENT ADDITION POSTULATE,) • 16= 10 + EF (Substitute values for DF and DE.) • 6 = EF (Solve for EF.)

13. Example 4 Are the segments shown in the coordinate plane congruent? Decide whether segments are congruent D (-3, 3) E (1, 3) F (-2, 1) G (-2, -3)

14. Solution • For a horizontal segment, subtract the x-coordinates. • DE = I 1 – (-3)I = I 4 I = 4 • For a vertical segment, subtract the y-coordinates • FG = I -3 – 1 I = I -4 I = 4 • Answer DE = FG so DE = FG • (remember: LINE SEGMENTS ARE CONGRUENT HENCE THE SYMBOL!!! ALSO, WE LABEL LINE SEGMENTS WITH THE LINE SEGMENT SYMBOL) ~

15. CHECK POINT • Solutions • AB = 3 3/8 in. • CD = 1 7/8 in. • PQ = 39 mm • ST = 116 mm • AC = 20 • ST = 8 • Yes • no