Geometry Section 3-1 1112
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CHAPTER 3
Parallel and Perpendicular Lines
Tuesday, December 13, 2011
SECTION 3-1Parallel Lines and Transversals
Tuesday, December 13, 2011
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?
Tuesday, December 13, 2011
VOCABULARY
1. Parallel Lines:
2. Skew Lines:
3. Parallel Planes:
4. Transversal:
Tuesday, December 13, 2011
VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines:
3. Parallel Planes:
4. Transversal:
Tuesday, December 13, 2011
VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
do not intersect
3. Parallel Planes:
4. Transversal:
Tuesday, December 13, 2011
VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
do not intersect
3. Parallel Planes: Two or more planes that do not intersect
4. Transversal:
Tuesday, December 13, 2011
VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
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
Tuesday, December 13, 2011
VOCABULARY
5. Interior Angles:
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
Tuesday, December 13, 2011
VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
Tuesday, December 13, 2011
VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
Angles that are formed in the region outside of
the two lines being intersected by a transversal
Tuesday, December 13, 2011
VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
Angles that are formed in the region outside of
the two lines being intersected by a transversal
Interior angles that are on the
same side of the transversal, thus being “next” to each other
Tuesday, December 13, 2011
VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles: Nonadjacent interior angles that are
on opposite sides of the transversal
Angles that are formed in the region outside of
the two lines being intersected by a transversal
Interior angles that are on the
same side of the transversal, thus being “next” to each other
Tuesday, December 13, 2011
VOCABULARY
9. Alternate Exterior Angles:
10. Corresponding Angles:
Tuesday, December 13, 2011
VOCABULARY
9. Alternate Exterior Angles: Nonadjacent exterior angles that are
on opposite sides of the transversal
10. Corresponding Angles:
Tuesday, December 13, 2011
VOCABULARY
9. Alternate Exterior Angles: Nonadjacent exterior angles that are
on opposite sides of the transversal
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
Tuesday, December 13, 2011
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
Tuesday, December 13, 2011
EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
c. A plane that is parallel to plane ABG
Tuesday, December 13, 2011
EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
DC, CF, AB, or BG
c. A plane that is parallel to plane ABG
Tuesday, December 13, 2011
EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
DC, CF, AB, or BG
c. A plane that is parallel to plane ABG
Plane DEC
Tuesday, December 13, 2011
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
Tuesday, December 13, 2011
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
Corresponding Angles
Tuesday, December 13, 2011
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
Corresponding Angles Alternate Exterior Angles
Tuesday, December 13, 2011
EXAMPLE 2Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
Tuesday, December 13, 2011
EXAMPLE 2Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
Consecutive Interior Angles
Tuesday, December 13, 2011
EXAMPLE 2Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
Consecutive Interior Angles Alternate Interior Angles
Tuesday, December 13, 2011
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
Tuesday, December 13, 2011
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
v; Corresponding
Tuesday, December 13, 2011
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
v; Corresponding v; Alternate Interior
Tuesday, December 13, 2011
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.
c. ∠4 and ∠5
Tuesday, December 13, 2011
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.
c. ∠4 and ∠5
y; Consecutive Interior
Tuesday, December 13, 2011
CHECK YOUR UNDERSTANDING
Check out the problems on p. 173 #1-12.
Tuesday, December 13, 2011
PROBLEM SET
Tuesday, December 13, 2011
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
Tuesday, December 13, 2011
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