Download Geometry A Unit 3 Day 1 Warm-Up 3.1 Transversals and Angles I

Geometry A Unit 3 Day 1 Warm-Up
3.1 Transversals and Angles
I. Look at the picture below.
M
A. What do the curves placed on
MNP and
MNL mean?
____________________________________
B. Are
MNP and
LNM (circle answer below)
A LINEAR PAIR or VERTICAL ANGLES?
P
C. What do you think is the measure of angles
MNP and
D. Given:
Prove:
LNM ? _______________
MNP = LNM
MNP = 90o
Statement
Reason
1. ___________________________
1. ____________________________
2. ____________________________
2. ____________________________
3.
MNP +
MNP = 180o
3. Substitution
4. _____________________________ 4. Simplify
5. _____________________________
5. ____________________________
L
N
G
F
II. Definitions
A
B
H
E
C
D
A. PARALLEL LINES - Lines that do not cross AND ARE ON THE SAME
PLANE.
B. SKEW LINES – Lines that do not cross AND ARE NOT ON THE SAME
PLANE.
Ex: In the picture above, AB is parallel to _______, _______ and _____
In the picture above, AB is skew to _____, _____, _____ and ______
C. TRANSVERSAL – ONE LINE THAT INTERSECTS TWO OR MORE
OTHER LINES.
R
Q
V
12
3 4
5 6
7 8
S
R
2 3
1 4
S
T
Q
U
T
5 7
6
8
U
V
In each diagram above, line ___________ is a transversal.
D. INTERIOR – region between two intersected lines
E. EXTERIOR – region outside two intersected lines
Which angles are INTERIOR ANGLES in each picture above? ____, ____, ___ and ____
Which angles are EXTERIOR ANGLES in each picture above? ___, ____, ___ and ____
III. Pairs of Angles Created by Transversals
A definition and an example of 4 types of angles are given. Give all other pairs
of each type of angle.
R
S
Q
T
12
R
24
3 4
S
1 3
6
8
5 6
5
T
7
V
7 8
Q
U
V
A. CORRESPONDING ANGLES – angles formed by a transversal that
are in the same position in their group on angles.
Ex:
5 are corresponding angles in both pictures (each is the top left angle in
1 and
a group of 4)
The other three pairs of corresponding angles are _____ and _____;
_____ and ______
_______ and _______
B. ALTERNATE INTERIOR ANGLES – angles that are both on the interior
of a diagram, but are on different sides of a transversal. LINEAR PAIRS
ARE NOT ALTERNATE INTERIOR ANGLES.
3 and
6 are alternate interior angles, so are _______ and _________
C. ALTERNATE EXTERIOR ANGLES – angles that are both on the exterior
of a diagram, but are on different sides of a transversal. LINEAR PAIRS
ARE NOT ALTERNATE EXTERIOR ANGLES.
7 and
2 are alternate exterior angles, so are ________ and ________
D. CONSECUTIVE INTERIOR ANGLES – angles that are both on the
interior of a diagram, and are on the same side of the transversal.
3 and
5 are consecutive interior angles, so are ______ and __________
U