Geom. Drill SAT/PSAT Prep

•Find the sum of x + y, if: 3x + 5y = 11 5x + 3y = 7

• A) 1/8 B) 9/4 C) 17/8• D)17 E) 18

Geom. Drill Cont.•Find the measure of

A

B D

C

2x-57X-2E

AEB

Objective• Students will discover the

properties of angles formed by parallel lines and a transversal in order to solve problems involving those angles.

Key Terms• Transversal• Alternate Interior Angles• Same Side Interior Angles• Corresponding Angles• Alternate Exterior Angles

1 2

3 4

5 6

8 7

m

n

Geometry is all around US!• Despite the messy interior of my wife’s car,

she was looking at her brand new GPS and wanted to find the location that corresponded to her destination. She knew she was on a road parallel to her desired street. She heard a voice from the GPS say “turn right at the next light and your destination is on your right.” This meant it was on the same side of the street as her car. Can you draw a picture that represents this information?

Transversal•A line that intersects two or more lines.

Alternate Interior Angles

•Two angles on opposites of a transversal between the two lines.

Same Side Interior Angles

•Two angles on the same side of the transversal between the two lines.

Corresponding Angles

•Two angles which if the intersecting lines where place on top of each other they would be in the same position.

Alternate Exterior Angles

•Two angles on opposites of a transversal outside the two lines.

Investigation

Corresponding Angles Postulate

• If two lines cut by a transversal are parallel, then corresponding angles are congruent.

1 234

5 6

7 8

Alternate Interior Angles Theorem

• If two lines cut by a transversal are parallel, then alternate interior angles are congruent.

1 234

5 6

7 8

Same Side Interior Angles• If two lines cut by a

transversal are parallel, then Same Side interior angles are supplementary.

1 234

5 6

7 8

Conclusions:• Given two parallel lines cut by a

transversal:

• 1) Alternate Interior Angles are…

• 2) Same Side Interior Angles are…

• 3) Corresponding Angles are…

State the postulate or theorem that justifies each statement.

t k

l

p

1 2

3

5 67 8

4

54.676.3

84.563.2

18064.451.1

mm

mm

mm

What angles must be congruent to angle 2?

t k

l

p

1 2

5

9 10

13 14

6

3 47

11 12

15 16

8

What angles must be congruent to angle 2, if line t //line k and line l //line p?

t k

l

p

1 2

5

9 10

13 14

6

3 47

11 12

15 16

8