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? A: 692 yards

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 A: 692 yards

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. A: 692 yards

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)

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

The Distance Formula 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) c a b

Practice Find the length of the hypotenuse of a right triangle with leg lengths of 9 ft and 12 ft. c 9 ft 12 ft

Distance

Two Points

Two Points The Distance Formula

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Yes Simplest Radical Form?

Using the Distance Formula Find the lengths of the segments. Tell whether any of the segments have the same length. EF = rad17, FG = 2rad5, GH = rad10; none of these 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? A: 5x340 + 3x480 = 1700 + 1440 = 3140 feet B: AB = rad (1020-(-680))^2 + (960 – (-480))^2 = rad 1700^2 + 1440^2 = rad 4,963,600 = approx. 2228 feet So the diagonal distance is 912 feet less than the walking distance.

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.