Lesson 1-1 Point, Line, Plane 1

Grade 63.01 Identify intersections in a

plane

Point, Line, Plane

AAB

Lesson 1-1 Point, Line, Plane 2

Points Points do not have actual size.

How to Sketch:

Using dots

How to label:

Use capital letters

Never name two points with the same letter (in the same sketch).

A

B AC

Lesson 1-1 Point, Line, Plane 3

Lines Lines extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends.

How to name: 2 ways(1) small script letter – line n(2) any two points on the line -

Never name a line using three points - , , , , ,AB BC AC BA CA CB

������������������������������������������������������������������������������������������������������������������������������������������������ �����������

nA

BC

ABC�������������� �

Lesson 1-1 Point, Line, Plane 4

Collinear Points Collinear points are points that lie on the same line. (The line does

not have to be visible.) A point lies on the line if the coordinates of the point satisfy the

equation of the line.Ex: To find if A (1, 0) is collinear with

the points on the line y = -3x + 3.

Substitute x = 1 and y = 0 in the equation.

0 = -3 (1) + 3

0 = -3 + 3

0 = 0

The point A satisfies the equation, therefore the point is collinear

with the points on the line.

A B C

AB

C

Collinear

Non collinear

Lesson 1-1 Point, Line, Plane 5

Planes

A plane is a flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 2 ways

(1) Capital script letter – Plane M(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC /

BCA / CAB / CBA

A

BC

Horizontal Plane

M

Vertical Plane Other

Lesson 1-1 Point, Line, Plane 6

Different planes in a figure:A B

CD

EF

GH

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

Lesson 1-1 Point, Line, Plane 7

Other planes in the same figure:

Any three non collinear points determine a plane!

H

E

G

DC

BA

F

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

Lesson 1-1 Point, Line, Plane 8

Coplanar Objects

Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.

H

E

G

DC

BA

F

Are the following points coplanar?

A, B, C ?A, B, C, F ?H, G, F, E ?E, H, C, B ?A, G, F ?C, B, F, H ?

YesNo

YesYesYesNo

Lesson 1-1 Point, Line, Plane 9

Intersection of Figures

The intersection of two figures is the set of points that are common in both figures.

The intersection of two lines is a point.

m

n

P

Continued…….

Line m and line n intersect at point P.

Lesson 1-1 Point, Line, Plane 10

3 Possibilities of Intersection of a Line and a Plane

(1) Line passes through plane – intersection is a point.

(2) Line lies on the plane - intersection is a line.

(3) Line is parallel to the plane - no common points.

Lesson 1-1 Point, Line, Plane 11

Intersection of Two Planes is a Line.

P

R

A

B

Plane P and Plane R intersect at the line AB�������������� �

Draw a pictureIntersections in the plane

A line and a triangle are in the same plane. The line intersects the triangle at exactly one point, P. Which

statement is true?

A) P is a vertex of the triangle.

B) P is a midpoint of a side of the triangle.

C) P is in the interior of the triangle.

D) P is in the exterior of the triangle.

Lesson 1-1 Point, Line, Plane 12

Draw a pictureIntersections in the plane

What is the maximum possible number of points of intersection between an equilateral triangle and a circle in the same plane?

A 3 B 4 C 6 D 7

Lesson 1-1 Point, Line, Plane 13

Explain

Radius FH is 7 cm.

H

What is the length of the longest chord

of circle H?

A) 7 cm C) 14 cm

B) 9 cm D) 21 cm

Lesson 1-1 Point, Line, Plane 14

F

Which statement below must be trueabout circle Q?

A) The distance from U to W is the same as the distance from R to T.

B) The distance from U to W is the same as the distance from Q to J.

C) The distance from R to T is half the distance from Q to R.

D) The distance from R to T is twice U w

the distance from Q to J. Q\

T R

Lesson 1-1 Point, Line, Plane 15

Q

J

Remember C =πd 2r=d

The radius of a circle is 45 in. Which is a true statement about the circumference (c)?

A) c > 6,000 in. and c < 6,500 in.

B) c > 250 in. and c < 300 in.

C) c > 100 in. and c < 150 in.

D) c > 50 in. and c < 100 in.

Lesson 1-1 Point, Line, Plane 16

r = 45 in.