+ Objective: to measure segments and add segment lengths DO NOW: EVALUATE. Plot each point on a coordinate plane. 1.I -15 I 2.I 7 I 3.I 10-34 I 4.I -12-(-2)

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Presentation transcript:

+ Objective: to measure segments and add segment lengths DO NOW: EVALUATE. Plot each point on a coordinate plane. 1.I -15 I 2.I 7 I 3.I I 4.I -12-(-2) I 1.A (2, -5) 2.B (-3, 6) 3.C (4, 4) 4.D (-1, -6) TAKE OUT YOUR RULERS I WILL BE COMING AROUND TO CHECK THAT YOU HAVE THEM. THIS WILL COUNT AS CLASS PARTICIPATION!!! Homework: 1.5 Practice A

+ DO NOW A B C D

+ HOMEWORK CHECK- 1.4 Practice A 1. Point 2. Line 3. Point D 4. Point C 5. Line q 6. Line r 7. False 8. True 9. True 10. False 11. False 12. False 13. True 14. next slide 15. next slide 16. next slide 17. next slide 18. Point B 19. Point C 20. Main Street & Park Street 21. Park Street & Penn Street

+ Homework Check continued…

+ 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 I = 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 A B C ~

+ POSTULATE 5 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! SEGMENT ADDITION POSTULATE FOLLOW UP A B C I AC I I AB I BC I

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

+ 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

+ 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

+ 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 = = 170 miles The distance from Athens to Albany is 170 miles.

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

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

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

+ 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) ~

+ CHECK POINT Solutions 1. AB = 3 3/8 in. 2. CD = 1 7/8 in. 3. PQ = 39 mm 4. ST = 116 mm 1. AC = ST = 8 3. Yes 4. no