PARALLEL LINES & TRANSVERSALS

COMMON CORE INVESTIGATION 4: GEOMETRY TOPICS

4 3 2 1 0In addition to level 3.0 and above and beyond what was taught in class, I may: Make connection

with real-world situations

Make connection with other concepts in math

Make connection with other content areas. 

I understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. understand the relationship

between the measure of an exterior angle and the other angles of a triangle

find and prove the measure of a missing angle of a triangle

explain the relationship of the angles formed when parallel lines are cut by a transversal

use vocabulary associated with parallel lines cut by a transversal

informally prove similarity of triangles

I understand congruency and similarity using physical models, transparencies or geometry software. construct

triangles find the

measure of a missing angle in triangle

find missing angles of parallel lines cut by a transversal

 

With help from theteacher, I have partial successwith the unit content.

Even with help, I have no success with the unit content.

Learning Goal 3(8.G.A.5):The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software.

DEFINITIONS:

Parallel Lines: Two lines that never intersect.

Transversal: A line that intersects two or more lines.

When parallel lines are intersected by a transversal, many angles are formed.

They can be acute, obtuse, or have a special relationships between pairs.

Tell your neighbor the difference between acute and obtuse angles.

THE SCENARIO

The Riverside students have been invited to purpose designs for a small park on a rectangular plot of land next to the school.

The plot has parallel paths crossing it.

A NEW PATH

Juan, Marsha, and Cora decide to include in their design a new path that connects different parts of the park.

The path will be diagonal and cross the existing two paths.

Here are some options they are considering:

Option #1

1 2

3 4

5 6

7 8

They numbered the angles in their design.

MORE OPTIONS:Option #1

1 2

3 4

5 6

7 8

Option #2

1 2

3 4

5 6

7 8

How does 1 change in relation to 2 as the new path moves?Name another pair of angles with the same relationship.

Option #3

1 2

3 4

5 6

7 8

When the path is moved, how does this affect the relationship between 1 and 4?Name another pair of angles with the same relationship.Describe the relationship between 1 and 8.Describe the relationship between 1 and 5.

YOUR TURN:

Supplies:

Activity Sheet: Parallel Lines & Transversals

Ruler

Protractor

Pencil