GEOMETRY JOUR-NAL #3

BY: HYUNGUM KIM 9-4

Describe parallel lines and parallel planes. Include a discussion of skew lines. Give at least 3 examples.

Parallel lines are 2 lines that NEVER meet and they are in the same plane. Parallel planes are planes that never meet.(2)

Skew lines are lines that NEVER meet but they are not going in the same directions

12

Describe what a transversal is. Give at least 3 examples.

Transversal is a line that goes through 2 lines that form a parallel or a coplanar.

Describe the following angles: Corre-sponding, alternate exterior, alternate interior and consecutive interior angles. Give an example of each. CORRESTPONDING :

Those are angles that are on the same place of a transversal.

12

…..continued….

ALTERNATE EXTERIOR ANGLES: Those are angles that are on the outside

of a transversal and they are at the op-posite direction .

1 2

..continued…..

ALTERNATE INTERIOR ANGLES: Those are angles that are in the inside of

a transversal and they are opposite aswell.

1

2

…continued…

CONSECUTIVE INTERIOR ANGLES: Those are angles that are on the inside

of a transversal and they are on the same side.

1

2

Describe the corresponding angles postu-late and converse. Give at least 3 examples of each.

CONVERSE: It is that if the corresponding is formed then

there is a parallel. CORRESPONDING ANGLE POSTULATE:

The corresponding lines are congruent. They are congruent if a transversal is formed.

50° < 1 70°

Describe the alternate interior angles theo-rem and converse. Give at least 3 examples of each.

INTERIOR ANGLES THEOREM: When there is the transversal then the

interior angles are congruent. With the converse its that if alternate interior an-gles are congruent then it will be parallel as well.

40°

x =40 °

70°

x =70 °

80°

x =80 °

Describe the Same Side interior angles theorem and converse. Give at least 3 examples of each.

SAME SIDE INTERIOR ANGLES: If this is changed to a transversal it

would be supplementary, the converse would be that they would be parallel be-cause of the corresponding angles.

A B =180°

90° 90°=180° X Y=180°

Describe the alternate exterior angles theorem and converse. Give at least 3 examples of each. ALTERNATE EXTERIOR ANGLES

THEREM: When the transversal its formed then

this angle will be congruent. Later the converse would be that if they are con-gruent this (congruent) would be paral-lel.

60°X=x= 60°20°

X=x= 20°50°

X=x= 50°

Describe the perpendicular transversal theorems. Give at least 3 examples.

PERPENDICULAR TRANSVERSAL THEOREM: When you form a right angle that Is 90

degree. And you make them straight with a transversal form.A B

X

XㅗB

TD

V

VㅗD

Z H

G

GㅗZ

Describe how the transitive property also ap-plies to parallel and perpendicular lines. In-clude a discussion about the perpendicular line theorems. Give at least 2 examples of each. If a line is perpendicular to another

line, a last line is perpendicular to the same first line then the first and last lines are parallel (and the middle one will be too) And if many lines are parallel all will be parallel to each other too.

A B C

D G

J

Describe how to find the slope of a line. How is slope related to parallel and perpendicular lines. Give at least 3 ex-amples of each. Slope and parallel are related be-

cause they have equal slopes if they are parallel. And it is related to per-pendicular because of the recipro-cal.

You find slope by: Y1 - Y2 X1 - X2

EXAMPLES:

(8,5) (6,1) 5-1 = 4 8-6 = 2 (10,15) (7,11) 15-11 =4 10- 7 =3

(5,8) (2,6) 8-6 = 2 5-2 = 3

Describe how to write an equation of a line in slope/intercept form, and in Point/Slope form. Explain when you would want to use each form of a line. Give at least 3 examples of each. Slope intercept form is

Y =mx+b

Y= 4/2X+6 up 6 then up 4and 2 to the left

Y= 2/-2X+8 up 8 then up 2 and 2 to the left.

Y= 3/6X-9 down 9 then up 3 and 6 to the right.