1.2 Points, Line and Planes1.3 Measuring Segments

Point Line Plane Model:

Description: A location

Straight path that extends in two opposite directions without end and has no thickness.

A flat surface that extends without end and has no thickness.

Named by: A capital letter

The letters representing two points on the line or a lowercase script letter

The letters representing three non-collinear points or a capital script letter

1. A collinear points are points all in one line.

2. Coplanar points are points all in one plane. 3. Space is the set of all points in three dimensions

4. Segment is part of a line with two endpoints and all the points between.

5. Ray is part of a line with one endpoint and all the points of the line on one side of the endpoint.

6. Opposite Rays are two rays that share the same endpoint and form a line.

7. Postulate is an accepted statement or fact.

8. Intersection is the set of points the figures have in common

B. Postulates:

1. Through any two points there is exactly one line.

2. Through any three noncollinear points there is exactly one plane.

3. If two lines intersect, then they intersect in exactly one point.

4. If two planes intersect, then their intersection is a line.

Construction – Intersecting Planes

• Label one index card as Q and another as R.

• Hold the two index cards together and cut a slit halfway through both cards.

• Hold the cards so that the slits meet and insert one card into the slit of the other. Use tape to hold together.

• Where the two cards meet models a line. Draw the line and label two points, C and D, on the line.

Analyze

1. Draw a point F on your model so that it lies in Q but not in R. Can F lie on DC?

2. Draw a point G so that it lies in R, but not in Q. Can G lie on DC?

3. If point H lies in both Q and R, where would it lie? Draw point H on your model.

4. Draw a sketch of your model on paper. Label all points, lines, and planes appropriately.

Examples: 1 – 7 True or False? 1. P is in plane M _______________ 2. line b is in plane M _______________ 3. YX contains P ___________ 4. Plane M is in YX ________________ 5. A is on line b _____________ 6. A and P are in plane M ___________ 7. Plane N contains P ______________ 8. Name a line that contains point A _____________

X

Y

N

A M

b

P

Refer to the figure. 11. How many planes are shown in the figure? 12. Name three points that are collinear. 13. Are points A, C, and D coplanar? Explain.

B A

F H

C

D

G

E

K

J

Q : Is the following statement true?

“Through any line and a noncollinear point, there is exactly one plane.” Explain.

9. Congruent ( ) Segments – segments that have the same length.

11. Segment Bisector is a line, segment, ray, or plane

that intersects the segment at its midpoint.

10. Midpoint is the point that divides the segment into two congruent segments.

B. Distance Formula:

1. Number Line PQ = ba

a b

C. Midpoint Formula:

1. Number Line: 2

ba

Examples: Find the distance between two points and the midpoint between the two points. 14. –1, 4 15. –2, -6

Find the measure of each segment. Assume that each figure is not drawn to scale. 16. EG 17. XY

E

F

G

2.4 cm

1.3 cm

3 in

X Y Z 18

5 in

Find the value of the variable and LM if L is between N and M. 18. NL = 5x, LM = 3x, 19. NL = 6x – 5 , LM = 2x + 3, and NL = 15 and NM = 30

Find the value for x if B is the midpoint AC . 20. AB = 3x and BC = 12 21. AB = 2x – 9 and BC = 3x – 27

22. What is the measure of PR if Q is the midpoint of PR?

14x + 2

6 – 3x

P

Q

R

Homework

• Pg 16 # 9 – 25 odd, 27 – 64, 65 – 68

• Pg 24 # 9 – 21 odd, 23 – 43, 44 – 47

• Draw all pictures for credit!!!