Download PPT 2.5 Angle Relationships

Warm Up
1.
For #1-2 find the rule, then find the
next three terms in the sequence.
2 ,-4,-10, -16, -22…
-6; -28,-34,-40
2. -8, -4, 0, 4, 8…
4; 12,16,20
2.5 Angle Relationships
Geometry
HW: P. 135 #1, 2, 4, 6
Linear Pair Conjecture
Investigation
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Step 1) Draw PQ with point R between points P
and Q.
Step 2) Draw RS – Now you have a Linear Pair
Step 3) Label the angles <1 and <2.
Step 4) Use your protractor to measure <1 and
<2.
Step 5) Compare your results for your two angles
measures with your group or a classmate.
What do you notice about the two angles?
So…
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Linear Pair Conjecture – If two angles
form a linear pair, then the measures of the
angles add up to 180 degrees.
1
2
<1+<2=180 °
Vertical Angles Conjecture
Investigation
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Step 1) Draw two intersecting lines that are not
perpendicular onto patty paper. Label the
angles as shown:
1
Which angles are vertical?
4
2
3
Step 2) Fold the patty paper so that one pair of
vertical angles lie over each other.
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What do you notice about their measure?
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Vertical Angles Conjecture: If two angles are
vertical angles, then they are congruent.
<1=<3
1
4
3
2
<2=<4
Find the missing measures
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Ex 1)
a = 50°
b = 130°
c = 50°
a
b
130°
c
Find the missing measures
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Ex 2)
a = 90°
b = 90°
c = 25°
a
b
c
65°
Find the missing measures
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Ex 3)
a = 30°
b = 100°
c = 50°
d = 100°
a
b c
50° d
30°
Algebra with Angles – Ex 1
a)
b)
c)
d)
State the type of angles
State the relationship
Solve for x.
Then find measure of each angle.
3x-40
2x-10
m<1 = 50° m<2 = 50°
Now Try one on your own…
Find angle 1 and angle 2:
2x-60
x-10
m<1 = 40° m<2 = 40°
Algebra with Angles – Ex 2
a)
b)
c)
d)
State the type of angles
State the relationship
Solve for x
Find the measure of angle 1.
x
4x - 20
m<2 = 40°, m<1 = 140°
Now Try one on your own…
Find angle 1 and angle 2:
x + 10
X+80
m<1 = 55° m<2 = 125°