1-3 Segments, Rays, and Distance A) Terms: 1) Line segment - is part of a line that has end points. - symbol: AB or BA Ex.

2) Ray - is part of a line that consists of one endpoint and extends to one of the directions. Ex. A B symbol: AB A B symbol: BA * In a ray, the endpoint starts the symbol then extends to the other point on the line showing direction.

a) Opposite rays -are found on the same line, but heading in opposite directions. Ex opposite rays: EB and EF

1) Draw 3 collinear points A, B, and C A B C Draw D which is not collinear to A, B, and C. Draw AB and BD and CD 2) Name two pairs of opposite rays in the figure below. A B C D

2) Draw four points J, K, L, and M, no three of which are collinear 2) Draw four points J, K, L, and M, no three of which are collinear. Then sketch JK, KL, LM and MJ. [This is one diagram] 3) Draw five points, P, Q, R, S, and T no three of which are collinear. Then sketch PQ, RS, QR, ST, and TP. [This is one diagram]

3) Postulates or Axioms - statements that are accepted without proof. 4) Congruent - two objects that have the same size or shape. symbol: a) congruent segments – are segments that have equal lengths.

B) Postulate 1: Ruler Postulate 1) each point on a line can be matched one to one with real numbers. - the real numbers that correspond to a point are called coordinates. 2) The distance between the points is the absolute value of the difference between the coordinates of the points. 3) AB is also called the length of AB Ex. A Points B -3 Coordinates 1 Distance of AB is | 1 - -3 | =

In the diagram of the collinear points, PT = 20, QS = 6, PQ = QR = RS In the diagram of the collinear points, PT = 20, QS = 6, PQ = QR = RS. Find each length. 1) RS 2) PQ 3) ST 4) RT 5) QT

Postulate 2: Segment Addition Postulate 1) If B is between A and C, then AB + BC = AC 2) If AB + BC = AC, then B is between A and C. | AC | A B C | AB | BC | Ex. Suppose M is between L and N. Find the lengths of LM and MN. LM = 11, MN = 4c, and LN = 83 LM = 4n + 3, MN = 2n - 7, and LN = 22

Student practice. Suppose M is between L and N. Find the lengths LM and MN 1) LM = 3x + 8, MN = 2x – 5, and LN = 23 Suppose Y is between X and Z. Find the value of a. 2) XY = 3a, YZ = 14, and XZ = 5a - 4

Suppose M is between L and N. Find LM and MN. 3) LM = 7y + 9 , MN = 3y + 4, LN = 143 Suppose Y is between X and Z. Find the value of d. 4) XY = 11d, YZ = 9d – 2, and XZ = 5d + 28

5) Midpoint of a segment - is the point that divides the segment into 2 equal lengths. ex. B is the midpoint of AC ex.2 If B is the midpoint of AC and AB = x + 7 and BC = 3x – 11. Find x

6) Bisector of a segment - can be a line, segment, ray, or plane that intersects the segment at its midpoint. Bisector Ex. Midpoint

Examples: Q is the midpoint of PR, solve for y. 1) PQ = 9y – 2 QR = 14 + 5y 2) PQ = 3x – 4 QR = 5x – 26 3) PQ = 3x – 4 QR = 5x – 26 4) PQ = 7x – 15 QR = 33