1.3 segs & their meas. ppt 1
- 1. 1.3 Segments & their Measures p. 17
- 2. Postulates • Rules that are accepted as true with having to be proven. • Sometimes they are called axioms.
- 3. Postulate 1: Ruler post. • The points on a line can be matched with those on the real # line. • The real # that corresponds to a point is the coordinate of the point. • If you find the difference between the coordinates of 2 points, then take the absolute value, you will have the distance between the points.
- 4. Ruler post. (continued) A B x1 x2 • The length of AB can be found by x2-x1 • **The symbol for the length of AB is AB.
- 5. Example: Find AB. A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5
- 6. Is Alex between Ty and Josh? Yes! Ty Alex Josh No, but How about now? why not? In order for a point to be between 2 others, all 3 points MUST BE collinear!!
- 7. Post. 2: Segment Addition Post. • If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C. C B A
- 8. Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7
- 9. Reminders: • Pythagorean Theorem – a2+b2=c2 a & b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. • Distance formula – ( x2 − x1 ) 2 + ( y2 − y1 ) 2 (x1,y1) & (x2,y2) are the 2 points.
- 10. Congruent ( ≅ ) Segments • Segments that have the same length. If AB & XY have the same length, Then AB=XY, but AB ≅ XY Symbol for congruent
- 11. Assignment