Download Glencoe Geometry

LESSON 3–1
Parallel Lines and
Transversals
Five-Minute Check (over Chapter 2)
TEKS
Then/Now
New Vocabulary
Key Concepts: Parallel and Skew
Example 1: Real-World Example: Identify Parallel and Skew
Relationships
Key Concepts: Transversal Angle Pair Relationships
Example 2: Classify Angle Pair Relationships
Example 3: Identify Transversals and Classify Angle Pairs
Over Chapter 2
Make a conjecture about the next number in the
sequence, 5, 20, 80, 320.
A. 380
B. 395
C. 1280
D. 1580
Over Chapter 2
Write the contrapositive of this statement. If you
live in Boston, then you live in Massachusetts.
A. If you do not live in
Massachusetts, then you do
not live in Boston.
B. If you live in Massachusetts,
then you do not live in Boston.
C. If you do not live in
Massachusetts, then you live
in Boston.
D. You might live in
Massachusetts or Boston.
Over Chapter 2
Use the Law of Detachment or the Law of Syllogism
to determine whether a valid conclusion can be
reached from the following set of statements. If two
angles form a linear pair and are congruent, they
are both right angles. A and B are both right
angles.
A. Yes, A and B are a linear
pair.
B. no conclusion
Over Chapter 2
Name the property that justifies the statement.
If m1 + m2 = 75 and m2 = m3, then
m1 + m3 = 75.
A. Substitution Property
B. Reflexive Property
C. Addition Property
D. Symmetric Property
Over Chapter 2
Find m1 and m2 if m1 = 8x + 18 and
m2 = 16x – 6 and m1 and m2 are
supplementary.
A. m1 = 106, m2 = 74
B. m1 = 74, m2 = 106
C. m1 = 56, m2 = 124
D. m1 = 14, m2 = 166
Targeted TEKS
G.5(A) Investigate patterns to make conjectures about
geometric relationships, including angles formed by parallel
lines cut by a transversal, criteria required for triangle
congruence, special segments of triangles, diagonals of
quadrilaterals, interior and exterior angles of polygons, and
special segments and angles of circles choosing from a
variety of tools.
Mathematical Processes
G.1(E), G.1(F)
You used angle and line segment relationships
to prove theorems.
• Identify relationships between two lines or
two planes.
• Name angle pairs formed by parallel lines
and transversals.
• parallel lines
• skew lines
• parallel planes
• transversal
• interior angles
• exterior angles
• consecutive
interior angles
• alternate interior
angles
• alternate exterior
angles
• corresponding
angles
Identify Parallel and Skew
Relationships
A. Name all segments parallel to BC.
Answer: AD, EH, FG
Identify Parallel and Skew
Relationships
B. Name a segment skew to EH.
Answer: AB, CD, BG, or CF
Identify Parallel and Skew
Relationships
C. Name a plane parallel to plane ABG.
Answer: plane CDE
A. Name a plane that is
parallel to plane RST.
A. plane WTZ
B. plane SYZ
C. plane WXY
D. plane QRX
B. Name a segment that
intersects YZ.
A. XY
B. WX
C. QW
D. RS
C. Name a segment that
is parallel to RX.
A. ZW
B. TZ
C. QR
D. ST
Transversal
– a line that
intersects two or more lines in a
plane at different points.
1)
Fold a third of a piece of copy paper down.
Use a ruler, protractor, or straightedge
to draw a straight line across the crease.
2)
Draw this figure in the top third portion of the paper
1
3
5 6
7 8
2
4
Write the following information in the bottom section
of your paper…
Consecutive – same side of the transversal
Alternate – opposite sides of the transversal
Interior – in between the intersecting lines
Exterior – outside of the intersecting lines
Write the following information in the bottom section
of your paper…
Consecutive – same side of the transversal
Alternate – opposite sides of the transversal
Interior – in between the intersecting lines
(Angles 3, 4, 5, and 6 are interior.)
Exterior – outside of the intersecting lines
(Angles 1, 2, 7, and 8 are exterior.)
Write the following information in the bottom
section of your paper…
Corresponding – same side of the
transversal and same side of the
intersecting lines
(could say same “corner” in the diagram)
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Corresponding Angles
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Corresponding Angles
1 and 5
2 and 6
3 and 7
4 and 8
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Vertical Angles (congruent)
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Vertical Angles (congruent)
1 and 4
2 and 3
5 and 8
6 and 7
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Alternate Exterior Angles
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Alternate Exterior Angles
1 and 8
2 and 7
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Alternate Interior Angles
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Alternate Interior Angles
3 and 6
4 and 5
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Consecutive Exterior Angles
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Consecutive Exterior Angles
1 and 7
2 and 8
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Consecutive Interior Angles
Write the following information in the
bottom section of your paper…
SPECIAL ANGLE RELATIONSHIPS
Consecutive Interior Angles
3 and 5
4 and 6
Classify Angle Pair Relationships
A. Classify the relationship between 2 and 6 as
alternate interior, alternate exterior, corresponding,
or consecutive interior angles.
Answer: corresponding
Classify Angle Pair Relationships
B. Classify the relationship between 1 and 7 as
alternate interior, alternate exterior, corresponding,
or consecutive interior angles.
Answer: alternate exterior
Classify Angle Pair Relationships
C. Classify the relationship between 3 and 8 as
alternate interior, alternate exterior, corresponding,
or consecutive interior angles.
Answer: consecutive interior
Classify Angle Pair Relationships
D. Classify the relationship between 3 and 5 as
alternate interior, alternate exterior, corresponding,
or consecutive interior angles.
Answer: alternate interior
A. Classify the relationship
between 4 and 5.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
B. Classify the relationship
between 7 and 9.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
C. Classify the relationship
between 4 and 7.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
D. Classify the relationship
between 2 and 11.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Identify Transversals and Classify Angle Pairs
A. BUS STATION The driveways at a bus station are
shown. Identify the transversal connecting 1 and
2. Then classify the relationship between the pair
of angles.
Answer: The transversal connecting 1 and 2 is
line v. These are corresponding angles.
Identify Transversals and Classify Angle Pairs
B. BUS STATION The driveways at a bus station are
shown. Identify the transversal connecting 2 and
3. Then classify the relationship between the pair
of angles.
Answer: The transversal connecting 2 and 3 is
line v. These are alternate interior angles.
Identify Transversals and Classify Angle Pairs
C. BUS STATION The driveways at a bus station are
shown. Identify the transversal connecting 4 and
5. Then classify the relationship between the pair
of angles.
Answer: The transversal connecting 4 and 5 is
line y. These are consecutive interior
angles.
A. HIKING A group of nature
trails is shown. Identify the sets
of lines to which line a is a
transversal.
A. lines c, f
B. lines c, d, e
C. lines c, d, f
D. lines c, d, e, f
B. HIKING A group of nature
trails is shown. Identify the sets
of lines to which line b is a
transversal.
A. no lines
B. lines c, f
C. lines c, d, e, f
D. lines a, c, d, e, f
C. HIKING A group of nature
trails is shown. Identify the sets
of lines to which line c is a
transversal.
A. no lines
B. lines a, b, d, e, f
C. lines a, d, f
D. lines a, b, e
LESSON 3–1
Parallel Lines and
Transversals
CW – Transversals
Pg. 176; #13-36