2.5 Proving Angles Congruent 2011
September 28, 2011
Warm­up:
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2.5 Proving Angles Congruent 2011
September 28, 2011
2­5 Proving Angles Congruent
Objective:
Prove and apply theorems about angles.
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2.5 Proving Angles Congruent 2011
September 28, 2011
Vertical Angles Theorem
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3
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Open Attachments
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Vertical Angles are CONGRUENT.
m 1 ≅ m 2
m 3 ≅ m 4
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2.5 Proving Angles Congruent 2011
September 28, 2011
Using the Vertical Angles Theorem
Find the value of x.
(4x)o
(3x + 35)o
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2.5 Proving Angles Congruent 2011
September 28, 2011
More Angle Theorems
Congruent Supplements Theorem
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
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2
3
Angles 1 and 2 are supplements.
Angles 2 and 3 are supplements.
Since Angle 1 and 3 have angle 2 as a supplement, then angles 1 and 3 are equal.
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2.5 Proving Angles Congruent 2011
September 28, 2011
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2.5 Proving Angles Congruent 2011
September 28, 2011
Congruent Complements Theorem
If two angles are complements of the same angle (or congruent angles), then the two angles are congruent.
1 + 2 = 90 and 2 + 3 = 90
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2
Therefore: 1 + 2 = 2 + 3
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Subtract Angle 2 from each side.
What do you have?
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2.5 Proving Angles Congruent 2011
September 28, 2011
Angle A is twice as big as it's supplement Angle B. How big is each angle?
Step 1: Draw a picture.
Step 2: Define your variables.
Let the smallest angle be x.
The larger angle would be 2x.
Step 3: Set up an equation and solve.
x + 2x = 180
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2.5 Proving Angles Congruent 2011
September 28, 2011
HOMEWORK
Practice 2­4/2­5
Show all your work!
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Attachments
Vertical Angles.gsp