Geom 1point3
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The document discusses key concepts in geometry including segments, measures of segments, and the Pythagorean theorem. It defines segments and their measures using the ruler postulate and distance formula. It also explains how to use the distance formula, segment addition postulate, and Pythagorean theorem to measure and relate segments on a coordinate plane. Students are assigned example problems and a homework assignment involving these geometric concepts.
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Geom 1point3
- 1. Segments and Their Measures Objectives: - Use segment postulates - Use the Distance Formula to measure distances
- 2. Postulates Rules that are accepted without proof Also called axioms
- 3. 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 AB x 1 x 2 l A B AB = |x 2 - x 1 |
- 4. Example Look at the example on the bottom of page 17. How long is segment AB? Does it matter how you place the ruler? When 3 points lie on a line, you can say that one of them is between the other two.
- 5. 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 Reading a map is an example of this postulate
- 6. Pythagorean Theorem A 2 + B 2 = C 2
- 7. The Distance Formula If A(x 1 , y 1 ) and B(x 2 , y 2 ) are points in a coordinate plane, then the distance between A and B is AB = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2
- 8. Do Example 3 From the bottom of page 19
- 9. Congruent Segments Segments that have the same length are called congruent segments For example, in Example 3, AB and AD are congruent There is a special symbol for congruence: AB ~= AD “is congruent to”
- 10. Do Example 4 P. 20
- 11. Do p. 21 1-12 together Homework: Do 20-70, evens Quiz Tomorrow Fun Game: nlvm.usu.edu Virtual Library Pythagorean