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Unformatted text preview: 1.3 Segments & their Measures Measures
p. 17 Postulates Postulates
• Rules that are accepted as Rules true with having to be proven. proven. • Sometimes they are called Sometimes axioms. axioms. Postulate 1: Ruler post. Postulate
• The points on a line can be The matched with those on the real # line. line. • The real # that corresponds to a The point is the coordinate of the coordinate point. point. • If you find the difference between If difference the coordinates of 2 points, then take the absolute value, you will absolute you have the distance between the distance points. points. Ruler post. (continued) Ruler
A x1 B x2 • The length of AB can be found by x2-x1 • **The symbol for the length of AB is AB. Example: Find AB. Example
A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5 Is Alex between Ty and Josh? between
Ty Alex Josh How about now? No, but No, why not? why In order for a point to be between 2 others, all 3 points MUST BE collinear!! Post. 2: Segment Addition Post. Post.
• If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C.
A B C Ex: if DE=2, EF=5, and Ex if DE=FG, find FG, DF, DG, & EG. EG.
D E F G FG=2 DF=7 DG=9 EG=7 Reminders: Reminders:
• Pythagorean Theorem – a2+b2=c2 a & b are the lengths of the legs of a are right triangle and c is the length of the hypotenuse. hypotenuse. • Distance formula – ( x2 − x1 ) 2 + ( y2 − y1 ) 2 (x1,y1) & (x2,y2) are the 2 points. (x Congruent ( ≅ ) Segments Congruent
• Segments that have the same length. If AB & XY have the same length, Then AB=XY, but AB ≅ Y X
Symbol for congruent Assignment Assignment ...
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- Spring '08