geometry section 3-1 1112

CHAPTER 3

Parallel and Perpendicular Lines

Tuesday, December 13, 2011

SECTION 3-1Parallel Lines and Transversals


ESSENTIAL QUESTIONS

How do you identify the relationships between two lines or two planes?

How do you name angle pairs formed by parallel lines and transversals?


VOCABULARY

1. Parallel Lines:

2. Skew Lines:

3. Parallel Planes:

4. Transversal:


VOCABULARY

1. Parallel Lines: Two or more lines in the same plane that do not

intersect

2. Skew Lines:

3. Parallel Planes:

4. Transversal:


VOCABULARY


intersect

2. Skew Lines: Two or more lines that are in different planes and

do not intersect

3. Parallel Planes:

4. Transversal:


VOCABULARY


intersect


do not intersect

3. Parallel Planes: Two or more planes that do not intersect

4. Transversal:


VOCABULARY


intersect


do not intersect

3. Parallel Planes: Two or more planes that do not intersect

4. Transversal: A line that intersects two other coplanar lines at

two different points


VOCABULARY

5. Interior Angles:

6. Exterior Angles:

7. Consecutive Interior Angles:

8. Alternate Interior Angles:


VOCABULARY

5. Interior Angles: Angles that are formed in the region between

two lines being intersected by a transversal

6. Exterior Angles:




VOCABULARY



6. Exterior Angles:



Angles that are formed in the region outside of

the two lines being intersected by a transversal


VOCABULARY



6. Exterior Angles:





Interior angles that are on the

same side of the transversal, thus being “next” to each other


VOCABULARY



6. Exterior Angles:


8. Alternate Interior Angles: Nonadjacent interior angles that are

on opposite sides of the transversal



Interior angles that are on the

same side of the transversal, thus being “next” to each other


VOCABULARY

9. Alternate Exterior Angles:

10. Corresponding Angles:


VOCABULARY

9. Alternate Exterior Angles: Nonadjacent exterior angles that are


10. Corresponding Angles:


VOCABULARY

9. Alternate Exterior Angles: Nonadjacent exterior angles that are


10. Corresponding Angles: Angles that are on the same side of the

transversal and on the same side of the lines being intersected

by the transversal; these angles have the same position


EXAMPLE 1

Identify each of the following using the box.

a. All segments parallel to BC

b. A segment that is skew to EH

c. A plane that is parallel to plane ABG


EXAMPLE 1



FG, AD, EH




EXAMPLE 1



FG, AD, EH


DC, CF, AB, or BG



EXAMPLE 1



FG, AD, EH


DC, CF, AB, or BG


Plane DEC


EXAMPLE 2Refer to the figure below. Classify the relationship between

each pair of angles as alternate interior, alternate exterior,

corresponding, or consecutive interior angles.

a. ∠2 and ∠6 b. ∠1 and ∠7





a. ∠2 and ∠6 b. ∠1 and ∠7

Corresponding Angles





a. ∠2 and ∠6 b. ∠1 and ∠7

Corresponding Angles Alternate Exterior Angles





c. ∠3 and ∠8 d. ∠3 and ∠5





c. ∠3 and ∠8 d. ∠3 and ∠5

Consecutive Interior Angles





c. ∠3 and ∠8 d. ∠3 and ∠5

Consecutive Interior Angles Alternate Interior Angles


EXAMPLE 3The driveways at a bus station are shown. Identify the

transversal connecting each pair of angles in the figure. Then

classify the relationship between each pair of angles.

a. ∠1 and ∠2 b. ∠2 and ∠3





a. ∠1 and ∠2 b. ∠2 and ∠3

v; Corresponding





a. ∠1 and ∠2 b. ∠2 and ∠3

v; Corresponding v; Alternate Interior





c. ∠4 and ∠5





c. ∠4 and ∠5

y; Consecutive Interior


CHECK YOUR UNDERSTANDING

Check out the problems on p. 173 #1-12.


PROBLEM SET


PROBLEM SET

p. 174 #13-45 odd

“It has long been an axiom of mine that the little things are

infinitely the most important.” - Sir Arthur Conan Doyle


geometry section 3-1 1112

Education