3-1 lines and angles geometry. lines and angles warm up 2) the soccer team scored 3 goals in each of...
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3-1 Lines and AnglesGeometry
LINES AND ANGLES
Warm Up
2) The soccer team scored 3 goals in each of their first two games, 7 goals in the next game, and 2 goals in each of the last four games. What was the average (mean) number of goals the team scored per game?
Warm Up
9 -1
====
=Solve the equation:
-0.8 -20
MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Formative
Essential Questions
How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?
PARALLEL LINES
Lines that do not intersect
• Notation: l || m AB || CD
lm A
B
C
D
Examples of Parallel Lines
• Opposite sides of windows, desks, etc.
• Parking spaces in parking lots
• Parallel Parking
• Streets in a city block
PERPENDICULAR LINES
Lines that intersect to form a right angle
• Notation: m n
• Key Fact: 4 right angles are formed.
m
n
Ex. of Perpendicular Lines
any angle less than 90ºAcute Angle –
a 90º angleRight Angle –
any angle larger than 90ºObtuse Angle -
angles that add up to 90ºComplementary Angles –
angles that add up to 180ºSupplementary Angles –
Adjacent Angles -angles that share a common vertex and ray…angles that are back to back.
*Vertex – the “corner” of the angle
*Ray – a line that has an endpoint on one end and goes on forever in the other direction.
Congruent Angles – Angles with equal measurement
A ≅ B denotes that A is congruent to B.
Transversal -
t
a line that intersects a set of parallel lines
Vertical Angles
Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles.
1 2
3 4
t
1 42 3
Vertical Angles
Find the measures of the missing angles
125
?
?
55
t
55
125
Two adjacent angles that form a line. They are supplementary. (angle sum = 180)
1 2
3 4
5 6
7 8
t
Linear Pair
5+6=1806+8=1808+7=1807+5=180
1+2=1802+4=1804+3=1803+1=180
Supplementary Angles/Linear Pair
Find the measures of the missing angles
? 72
?
t
108
108 180 - 72
Corresponding AnglesTwo angles that occupy corresponding positions when parallel lines are intersected by a transversal…same side of transversal AND same side of own parallel line. Corresponding angles are congruent angles.
Top Left
t
Top Left
Top Right
Top Right
Bottom Right
Bottom Right
Bottom Left
Bottom Left
1 52 63 74 8
1 2
3 4
5 6
7 8
Corresponding Angles
Find the measure of the missing angle
145
?
t
35
145
Alternate Interior Angles
Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent.
t
3 64 5
1 2
3 4
5 6
7 8
Alternate Interior Angles
Find the measure of the missing angle
82
?
t
98 82
Alternate Exterior Angles
Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent.
t
2 71 8
1 2
3 4
5 6
7 8
Alternate Exterior Angles
Find the measure of the missing angle
120
?
t
60 120
Same Side Interior AnglesTwo angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary.
t
3 +5 = 1804 +6 = 180
1 2
3 4
5 6
7 8
*Also known as Consecutive Interior Angles
Same Side Interior Angles
Find the measure of the missing angle
?
t
135
45
180 - 135
Same Side Exterior Angles
Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary.
t
1 + 7 = 1802 + 8 = 180
1 2
3 4
5 6
7 8
*Also known as Consecutive Exterior Angles
Same Side Exterior Angles
Find the measure of the missing angle
?
t
135
45
180 - 135
1,5 4,82,63,7
5,43,6
2,71,8
4,63,5
2,81,7
equivalent
equivalent
equivalent
supplementary
supplementary
112º
112º68º
112º68º
68º
68º
112º
Closing
What is a transversal?
Name the types of equivalent angles.
Name the types of supplementary angles.
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