ENGAGE! • Please complete the discovery worksheet on pairs of lines...
Transcript of ENGAGE! • Please complete the discovery worksheet on pairs of lines...
ENGAGE! • Please complete the discovery worksheet on pairs of lines and angles – please get patty paper, straight edge and a protractor
Tell me about parallel lines
• Where do you see them?
• What use do they serve?
• What about perpendicular lines?
• Perpendicular lines ⊥ • lines that form right angles • ⊥ lines opposite reciprocal slopes
(product = -1)
• Oblique lines - intersecting lines that are not ⊥ • Skew lines - noncoplanar, nonparallel lines
that don’t intersect.
13
31 −and
45
54 and−
Intersecting lines
• lines with different slopes • lines that have a single common point
C
A
E
D
F
H
G
B
AD & EH are _______________. AD & FG are _______________. AD & AE are _______________. AD & HG are _______________.
parallel
parallel
perpendicular
skew
Know your angles!!!
1 2 3 4
5 6 7 8
Vertical angles Linear Pairs
Supplementary angles
Interior angles
Exterior angles 9 10 11 12
3.1 Identify Pairs of Lines and Angles
3.1-3.3 Parallel Lines and their Transversals
Transversal – a line that intersects two or
more coplanar lines at different points.
t
Corresponding Angles (C) – have corresponding
positions. For example: label ∠2 and ∠ 6
t
2
6
Corresponding Angles (C)
What shape do corresponding angles make?
t
2
6 F
Alternate Interior Angles (AI) – lie on alternate
(opposite) sides of the transversal on the interior (inside/between) the two lines. For example: label ∠ 4 and ∠5
t
4
5
Alternate Interior Angles (AI)
What shape do alternate interior angles make?
t
4
5
Z
Alternate Exterior Angles (AE) – lie on alternate
(opposite) sides of the transversal and on the exterior (outside) of the two lines. For example: label ∠1 and ∠8
t
1
8
Alternate Exterior Angles (AE)
Do alternate exterior angles have a shape?
t
1
8
Not really
Same Side Interior Angles (SSI) – lie on the same
side of the transversal and on the (inside) of the two lines. For example: label ∠3 and ∠ 5
t
3
5
Same Side Interior Angles (SSI)
What shape do Same Side Interior angles make?
t
3
5
C
Don’t forget!!!
Vertical Angles (V) Linear Pair (LP)
1 2 3 4
X shape Slanty T shape
Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.
1. ∠4 and ∠7 1 2 3 4 5 6
7 8 9 10 11 12 13 14
Same-Side Interior
Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.
2. ∠6 and ∠9 1 2 3 4 5 6
7 8 9 10 11 12 13 14
Alternate Interior
Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.
3. ∠6 and ∠14 1 2 3 4 5 6
7 8 9 10 11 12 13 14
Corresponding
Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.
4. ∠9 and ∠10 1 2 3 4 5 6
7 8 9 10 11 12 13 14
Linear Pair
Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.
5. ∠3 and ∠7 1 2 3 4 5 6
7 8 9 10 11 12 13 14
No Relationship
How does angle 9 relate to the other angles?
4 1 3 2 10 9
11 12
8
7 5
6
In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.
2x + 5 = 65
x = 30
m<3 = 65
m<4 = 115
What angle relationships can you use?
In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.
m<1 = 50 m<2 = 60
m<3 = 60
m<4 = 70
In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.
2x = 60 x = 30
5y + 2 = 60
y = 11.6 60
In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.
x + y = 30 x - y = 150
2x = 180 x = 90
x + y=30 90 +y = 30
Y = -60
150
In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.
x = 60
y = 130
z = 60
In-Class Practice What two lines, if any, are parallel if the given information is true: a. m<1 = m<4 b. m<6 = m<4 c. m<2 + m<3 = m<5 d. m<2 + m<3 + m<5 = 180º f. <5 and <6 are supplementary e. <6 ≅ <8 g. <5 is supplementary to <8
t and r
m and n
t and r
none
t and r
m and n
none
Got it?
• Elaborate ws
Practice Evaluate WS