Section1.3a
- 1. Segments, Rays, & Distance Section 1-3
- 2. And Now, for Some New Definitions Segment – two points on a line and all the points between them B C Segment BC, or… BC B and C are the endpoints of BC. In geometry, between means “on the line connecting.”
- 3. More New Definitions Ray – one point on a line and all the points extending in one direction only C K Ray CK, or… CK (not KC!!!) C is the endpoint of CK.
- 4. More New Definitions Opposite rays – rays that extend in opposite directions along the same line from a common endpoint X Y Z YX and YZ are opposite rays.
- 5. More New Definitions Length – the distance from one point to another X W Y Z • • • • -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 The length of XY is denoted XY. To find lengths on a number line, take the absolute value of the difference of the coordinates of the endpts.: XY = 3−(−5) =8 OR XY = −5−3 =8 Distance must be positive.
- 6. More New Definitions Postulates – statements accepted without proof; also called axioms Congruent – having the same size and shape congruence symbol:
- 7. More New Definitions Congruent Segments – segments of equal length •N 10 cm P• 10 cm •M L• To show congruence in the diagram The segments have Which means that they equal lengths: are congruent: LN = MP LN = MP
- 8. More New Definitions Midpoint of a Segment – point that divides a segment into two congruent segments • • • A B C If AB = BC, then B is the midpoint of AC.
- 9. One More Definition Segment Bisector – a line, segment, ray, or plane that intersects a segment at its midpoint
- 10. Let’s Practice!!! Look to your textbooks, page 14, #1-14