Oct 1.notebook
Objectives
October 01, 2015
October 1
Planner: pg 44 #16­21, 23,24
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OMG
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Postulate
statements that are accepted as true without proof Oct 1.notebook
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pg 39
In geometry, axioms, or postulates, are statements that are accepted as true without proof in order to provide a starting point for deductive reasoning.
Like point, line, and plane, distance along a line is an undefined term in geometry used to define other geometric terms. For example, the length of a line segment is the distance between its endpoints.
If two points are no more than 1 foot apart, you can find the distance between them by using an ordinary ruler. (The inch rulers below have been reduced to fit on the page.)
Oct 1.notebook
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In the figure, the distance between point A and point B is 5 inches. Of course, there is no need to place the zero of the ruler on point A. In the figure below, the 2­inch mark is on point A. In this case, AB, measured in inches, is |7 − 2| = |2 − 7| = 5, as before. The number obtained as a measure of distance depends on the unit of length. For example, the distance between two points in inches will be a different number than the distance between the two points in centimeters. Oct 1.notebook
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pg 40
Attend to precision. Determine the length of each segment in centimeters (to the nearest tenth).
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3. Using your results from Items 1 and 2, describe any patterns that you notice.
4. Given that N is a point between endpoints M and P of line segment MP, describe how to determine the length of MP, without measuring, if you are given the lengths of MN and NP.
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5. Use the Segment Addition Postulate and the given information to complete each statement.
a. If B is between C and D, BC = 10 in., and BD = 3 in., then CD = .
b. If Q is between R and T, RT = 24 cm, and QR = 6 cm, then QT = .
c. If P is between L and A, PL = x + 4, PA = 2x − 1, and
LA = 5x − 3, then x = and LA = .
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The midpoint of a segment is the point on the segment that divides it into two congruent segments.
For example, if B is the midpoint of pg 41
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7. Points D and E are aligned with a ruler. Point D is at the mark for 4.5 cm, and the distance between points D and E is 3.4 cm. At which two marks on the ruler could point E be located?
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9. Reason abstractly. Does a ray have a midpoint? Explain. 10. Give an example that illustrates the Segment Addition Postulate. Include a sketch with your example.
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You can also use a number line to find the distance between two points.
11. What is LM?
The midpoint of a segment is halfway between its endpoints. So, if you know the coordinates of the endpoints, you can average them to find the coordinate of the midpoint.
12.What is the coordinate of the midpoint M of PQ?
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When you bisect a geometric figure, you divide it into two equal or congruent parts.
14. Reason abstractly. Line segment WZ bisects XY at point Z. What are two conclusions you can draw from this information?
Oct 1.notebook
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