1.3 Segments and Their MeasuresGeometry

PostulatesRules that are accepted as true without

proofSometimes they are called axioms.

Postulate 1: Ruler Postulate

Find the the measure measure of of AB.. AA BB

Point A is at 1.5 and B is at 5.

So, AB = 5 - 1 1.5 = 3.55 = 3.5

Example 1

Example 2Find the measure of PRAns: |3-(-4)|=|3+4|=7Would it matter if I asked for

the distance from R to P ?

Between

Postulate 2: Segment Addition Postulate

Example 3: DE=2, EF=5, and DE=FG. Find FG, DF, DG, & EG.

Example 4: Find the length of JT.

Ways to find the length of a segment on the coordinate plane

1) Pythagorean Theorem- Can be used on and off the coordinate plane

2) Distance Formula – only used on the coordinate plane

1) Pythagorean Theorem** Only can be used with Right TrianglesWhat are the parts to a RIGHT Triangle?1. Right angle2. 2 legs3. Hypotenuse

Right angle

LEG

Leg – Sides attached to the Right angle

Hypotenuse- Side across from the right angle. Always the longest side of a right triangle.

Pythagorean Theorem222 )()()( hypotenuselegleg

222 cba

Example 5: Find the missing length in the triangle. Find the missing segment- Identify the parts

of the triangle5 in

13 in

Ans: 5 2 + X 2 = 13 2

Leg 2 + Leg 2 = Hyp 2

hyp

Leg

Leg

25 + X 2 = 169

X 2 = 144

X = 12 in

Example 6: Find the distance of JT(Using the Pythagorean Theorem)

Make a right Triangle out of the segment

(either way)

Find the length of each leg of the right Triangle.

Then use the Pythagorean Theorem to find the Original segment JT (the hypotenuse).

10

88.12164

164

10064

108

2

2

222

DC

DC

DC

DC

We got 8 by | -4 – 4|

We got 10 by | 6 - - 4|

Example 7: Find the distance of CD

Example 8: Observe the map to answer the following questions:

The Distance Formula

Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values

(4-(-3))2 + (2-(5))2

(4+3)2 + (2-5)2

(7)2 +(-3)2

49+9 =58 ~ 7.6~

J (-3,5) T (4,2)

x1, y1 x2, y2

Example 9: Use the Distance Formula to find JT

Example 10: Use the distance formula

Find the length of the green segment

Ans: 109 or approximately 10.44

Example 11: Find the lengths of all the segments. Tell whether any of the segments have the same length.

Congruent Segments