geometry notes sections 3-1. what youll learn how to identify the relationships between two lines or...

Geometry Notes

Sections 3-1

What you’ll learn

How to identify the relationships between two lines or two planes

How to name angles formed by a pair of lines and a transversal

Vocabulary Parallel lines Parallel planes Skew lines Transversal Interior Angles Exterior Angles Consecutive (same – side ) Interior Angles Alternate Interior Angles Alternate Exterior Angles Corresponding Angles

RELATIONSHIPS BETWEEN LINES

2 Lines are either Coplanar Noncoplanar

Two noncoplanar lines that never intersect are called SKEW lines.

The lines intersect once(INTERSECTING LINES)

The lines never intersect(PARALLEL LINES)

The lines intersect at all pts(COINCIDENT LINES)

This is what we’ll study in

Chapter 3

Let’s start with any 2 coplanar lines Any line that

intersects two coplanar lines at two different points is called a transversaltransversal

8 angles are created by two lines and a transversal

12

34

5 6

7 8

4 Interior Angles 3, 4, 5, 6

4 Exterior Angles 1, 2, 7, 8

12

34

5 6

7 8

Consecutive Interior Angles We have two pairs

of interior angles on the same side of the transversal called Consecutive Interior Angles or same-side interior angles

The two pairs of consecutive (same-side) interior: 3 &5 and 4 & 6

Alternate

We have two pairs of interior angle on opposite sides of the transversal called Alternate Interior Angles

12

34

5 6

7 8

Alternate Interior Angles

InteriorAngles

The two pairs of alternate interior angles are: 3 &6 and 4 & 5

Alternate Exterior Angles

12

34

5 6

7 8

The two pairs of Alternate Exterior Angles 1 & 8 and 7 & 2

We have two pairs of exterior angles on opposite sides of the transversal called Alternate Exterior Angles

1

Corresponding Angles

2

34

5 6

7 8

There are four pairs of Corresponding Angles 1 & 5, 2 & 6, 3 & 7, and 4 & 8

Corresponding Angles are in the same relative position

Find an example of each term. Corresponding

angles Alternate exterior

angles Linear pair of

angles Alternate interior

angles Vertical angles

Now if the lines are parallel. . . All kinds of special things happen. . . The corresponding angles postulate (remember these are

true without question) says. . .

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

12

3 4

5 6

7 8

The four pairs of Corresponding Angles are

1 5 2 6 3 7 4 8

Tell whether each statement is always (A), sometimes (S), or never (N) true. 2 and 6 are

supplementary 1 3 m1 ≠ m6 3 8 7 and 8 are

supplementary m5 = m4

Find each angle measure.

Find each angle measure.

Find each angle measure.

Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

Have you learned .. . .

How to identify the relationships between two lines or two planes

How to name angles formed by a pair of lines and a transversal

Assignment: Worksheet 3.1