2.5 Proving Angles Congruent 2010
September 20, 2010
Sep 22­6:28 AM
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2.5 Proving Angles Congruent 2010
September 20, 2010
2­5 Proving Angles Congruent
Objective:
Prove and apply theorems about angles.
Sep 22­6:28 AM
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2.5 Proving Angles Congruent 2010
September 20, 2010
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
Sep 22­6:34 AM
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2.5 Proving Angles Congruent 2010
September 20, 2010
Using the Vertical Angles Theorem
Find the value of x.
(4x)o
(3x + 35)o
Sep 22­6:52 AM
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2.5 Proving Angles Congruent 2010
September 20, 2010
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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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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3
Sep 22­4:21 PM
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2.5 Proving Angles Congruent 2010
September 20, 2010
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?
Sep 22­6:03 PM
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2.5 Proving Angles Congruent 2010
September 20, 2010
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
Sep 22­6:14 PM
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2.5 Proving Angles Congruent 2010
September 20, 2010
HOMEWORK
Practice 2­4/2­5
Show all your work!
Sep 22­6:29 PM
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2.5 Proving Angles Congruent 2010
September 20, 2010
Sep 20­8:16 AM
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Attachments
Vertical Angles.gsp