2.5 Proving Angles Congruent
September 21, 2009
Sep 22­6:28 AM
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2.5 Proving Angles Congruent
September 21, 2009
2­5 Proving Angles Congruent
Objective:
Prove and apply theorems about angles.
Sep 22­6:28 AM
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2.5 Proving Angles Congruent
September 21, 2009
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
September 21, 2009
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
September 21, 2009
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
September 21, 2009
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
September 21, 2009
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
September 21, 2009
HOMEWORK
Practice 2­4/2­5
Show all your work!
Sep 22­6:29 PM
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Attachments
Vertical Angles.gsp