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1.3 Segments and Their Measures
Learning Targets:I can use segment postulates.I can use the Distance Formula to measure distances.
Postulates vs. Theorems
Postulates – rules accepted without proof Theorems – rules that are proven
Find the distance between two points.
How would you measure the length to the nearest millimeter of the following segment:
G____________________________H
Postulate 1 : Ruler Postulate The points on a line can be matched one-to-one
with the real numbers. The real number that corresponds to a point is the coordinate of the point.
The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B.
AB is also called the length of segment AB.
Postulate 1 in simple terms…
Basically, you can find the length or distance of a line segment by measuring it.
Postulate 2:Segment Addition Postulate
Two friends leave their homes and walk in a straight line toward the other’s home. When they meet one has walked 425 yards and the other has walked 267 yards. How far apart are their homes?
Postulate 2:Segment Addition Postulate
If B is between A and C, then AB + BC = AC
If AB + BC = AC, then B is between A and C
Postulate 2 in simple terms…
Basically, you can add the length of one segment to the length of another segment, to find the total length of the segments put together.
Guided Practice
Two cars leave work and head towards each other. When the two cars meet, the first car has traveled 4.3 miles and the second car has traveled 7.1 miles. How far apart were the cars to begin with?
Using Postulate 2…
A, B, C, and D are collinear points. Find BC if AC = 2x + 4, BC = x, BD = 3x + 1, and AD = 17.
Guided Practice
W, X, Y, and Z are collinear points. Find YZ if WX = 3x – 1, XY = 2x + 3, YZ = 5x, and WZ = 42.
Sage and Scribe
Page. 21-22 #16 – 28 (Even Nos. Only)
#31-33 (ALL)
Work on this for 15 minutes
Answers to Sage and Scribe p 21-22
16. 2.7 cm 31. 4; 20, 3, 23
18. 3.4 cm 32. 13; 100, 43, 143
20. GH + HJ = GJ 33. 1; 2.5, 4.5, 7
22. QR + RS = QS
24. RS = 3
26. ST = 11
28. RT = 14
Objective:
• I can use the distance formula to find the distance between two points.
The Distance Formula
The Distance Formula is a formula for computing the distance between two points in a coordinate plane.
The formula is:d =
Pythagorean Theorem Review
The sum of the squares of the two legs of a triangle is equal to the square of the hypotenuse (right triangles only)
a
b
c2 2 2a b c
Practice
Find the length of the hypotenuse of a right triangle with leg lengths of 9 ft and 12 ft.
9 ft
12 ft
c
x
y
1 1,x y
2 2,x y
x
y
1 1,x y
2 2,x y
d
x
y
1 1,x y
2 2,x y
2x
d
x
y
1 1,x y
2 2,x y
2x
1x
d
x
y
1 1,x y
2 2,x y
2x
1x
d
2 1x x
x
y
1 1,x y
2 2,x y
d
2 1x x
x
y
1 1,x y
2 2,x y
d
2 1x x 2y
x
y
1 1,x y
2 2,x y
d
2 1x x 2y
1y
x
y
1 1,x y
2 2,x y
d
2 1x x 2y
1y
2 1y y
x
y
1 1,x y
2 2,x y
d
2 1x x
2 1y y
x
y
1 1,x y
2 2,x y
d
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
x
y
1 1,x y
2 2,x y
d
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
x
y
1 1,x y
2 2,x y
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
a
d
x
y
1 1,x y
2 2,x y
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
a
d
x
y
1 1,x y
2 2,x y
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
ab
d
x
y
1 1,x y
2 2,x y
2 1x x
2 1y y
2 2 2c a b 2
1
2
12 22d x x y y
ab
d
2
1
2
12 22d x x y y
2
2 1 2
2
1d x x y y
2
1
2
12 22d x x y y
2
2 1 2
2
1d x x y y
1 21 2, ,x xy y
2
2 1 2
2
1d x x y y
2
2 1 2
2
1d x x y y
1 21 2, ,x xy y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2 231d
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2 231d
2
2 1 2
2
1d x x y y
3, 1 2 ,4
2 212 3 4d
1x 1y 2x 2y
2 231d
2 231d
1 9d
1 9d
2 231d
1 9d
2 231d
1 9d
2 231d
1 9d
2 231d
10d
Using the Distance Formula Find the lengths of the segments. Tell
whether any of the segments have the same length.
Find distances on a city map
To walk from A to B you can walk five blocks east and three blocks north. So…
What would the distance be if a diagonal street existed between the two points?
Sage and Scribe
Work on page 22 :
#34 to 40 Even nos only
Homework
Work on #42 and #43 of page 22 of Geometry book.