1.3 segments and their measures geometry. postulates rules that are accepted as true without proof ...
TRANSCRIPT
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1.3 Segments and Their MeasuresGeometry
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PostulatesRules that are accepted as true without
proofSometimes they are called axioms.
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Postulate 1: Ruler Postulate
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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
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Example 2Find the measure of PRAns: |3-(-4)|=|3+4|=7Would it matter if I asked for
the distance from R to P ?
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Between
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Postulate 2: Segment Addition Postulate
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Example 3: DE=2, EF=5, and DE=FG. Find FG, DF, DG, & EG.
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Example 4: Find the length of JT.
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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
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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.
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Pythagorean Theorem222 )()()( hypotenuselegleg
222 cba
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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
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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).
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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
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Example 8: Observe the map to answer the following questions:
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The Distance Formula
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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
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Example 10: Use the distance formula
Find the length of the green segment
Ans: 109 or approximately 10.44
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Example 11: Find the lengths of all the segments. Tell whether any of the segments have the same length.
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Congruent Segments