2.2 Segment and Angle Addition Postulates (Structure of Geometry) · 2016. 9. 9. · Segment...
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2.2 Segment and Angle Addition Postulates (Structure of Geometry) 1 September 09, 2016 Sep 510:08 AM warm up X Z Y W The figure shows three angles whose vertex is X. 1. Write two names for each angle. 2. Which two angles are adjacent. 3. Is Y in the interior or exterior of ? Sep 510:12 AM 2.2 the structure of geometry Learning Targets 1. I can use postulates and theorems relating points, lines, and planes to justify statements.
Transcript of 2.2 Segment and Angle Addition Postulates (Structure of Geometry) · 2016. 9. 9. · Segment...
2.2 Segment and Angle Addition Postulates (Structure of Geometry)
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September 09, 2016
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warm up
X
Z
Y
W
The figure shows three angles whose vertex is X.
1. Write two names for each angle.
2. Which two angles are adjacent.
3. Is Y in the interior or exterior of ?
Sep 510:12 AM
2.2 the structure of geometry
Learning Targets
1. I can use postulates and theorems relating points, lines, and planes to justify statements.
2.2 Segment and Angle Addition Postulates (Structure of Geometry)
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Postulates (axioms):
Basic assumptions or statements that are accepted without proof
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The Ruler Postulate:
The points on a line can be matched, onetoone with a set of real numbers (coordinates).
OR
The distance between two points on a number line can be found by taking the absolute value of the difference of their coordinates.
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Segment Addition Postulate:On if B is between A and C, then AB + BC = AC
Example 1:
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Example 2: Given that SG = 20, find the following:
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Example 3:
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If C and D are in plane P, then the measure of is equal to the absolute value of the difference between the real numbers for
and
Example 4: find
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Angle Addition Postulate:If C is in the interior of then
Also:
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The Protractor Postulate:On in a given plane, P, choose any point O between A and B.
Consider and (opposite rays) and all the rays that can be drawn from O on the same side of
These rays can be paired with real numbers from 0 to 180 inclusive
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Example 5:
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Example 6:
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classworkWork with a partner or small group to complete
the following problems in the textbook:
Page 6769 #1122 all, #3742 all
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recap1. The ________ ___________ says that points on a line can be matched onetoone with the real numbers.
2. ___________ are basic assumptions that are accepted without proof.
3. AC = x + (x+6) is an example of the
________ ___________ __________
4. The _________ __________ says that rays extending from a common vertex on the same side of a line containing the vertex can be paired with real numbers from 0 to 180.
Segment Addition Postulate
Protractor Postulate
Ruler Postulate
Postulates
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exit ticket1. Explain how you think the Segment Addition Postulate could be used in real life.
2. Sketch and label the following objects:
a. A point exterior to an obtuse angle
b. The midpoint of the segment joining (0,2) and (4,6)
