1 3 Segments Rays and Distance A Terms














- Slides: 14

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 • • • Ex. A symbol: BA B • * 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 D • • 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. 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. Find each length. • • • 1) 2) 3) 4) 5) RS PQ ST RT 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 = 4 c, and LN = 83 • LM = 4 n + 3, MN = 2 n - 7, and LN = 22

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

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

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

• Examples: • Q is the midpoint of PR, solve for y. • 1) PQ = 9 y – 2 QR = 14 + 5 y • 2) PQ = 3 x – 4 QR = 5 x – 26 • 3) PQ = 3 x – 4 QR = 5 x – 26 • 4) PQ = 7 x – 15 QR = 33
Ruler postulate definition
Postulates examples
Lesson 1-3 segments rays parallel lines and planes
Name all the rays
1-2 line segments and distance worksheet answers
Partitioning line segments formula
Like terms and unlike terms in polynomials
Like terms
How is distance different from displacement
The ratio of input distance to output distance
Shark class
Name two segments
Direct and indirect rays of the sun
Cosmic rays and clouds
Limitations of remote sensing