+

Objective: to measure segments and add segment lengths

DO NOW: EVALUATE.

Plot each point on a coordinate plane.

1. I-15I2. I7I3. I10-34I4. 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

1.15

2.7

3.24

4.10A

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 Checkcontinued…14. 15.

16. 17.

+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

~

+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 = 80 + 90 = 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

5. AC = 20

6. ST = 8

7. Yes

8. no