Download Exploring Angle Pairs

Proving Angles Congruent
Angle Pairs
Vertical angles – two angles whose sides are
opposite rays
• Adjacent angles – two coplanar angles with a
common side, a common vertex, no common
interior points
Complementary angles – two angles, the sum of
whose measure is 90

m  1 + m  2 = 90 º
• Supplementary angles – two angles, the sum of
whose measure is 180
1
2
m  1 + m  2 = 180º
• Linear pair :
The sum of a linear pair is also equal 180º
A convincing argument that uses
deductive reasoning is called a proof. A
conjecture that is proven is a theorem.
Theorem 2-1 – Vertical Angles Theorem
Vertical angles are congruent.
1  3 and
2  4
Theorem 2-2 - Congruent
Supplements Theorem
If two angles are supplements of
congruent angles (or of the same angle),
then the two angles are congruent.
1
2
3
Theorem 2-3 Congruent
Complements Theorem
If two angles are complements of
congruent angles (or of the same angle),
then the two angles are congruent.
Theorem 2-4
All right angles are congruent.
Theorem 2-5
If two angles are congruent and
supplementary, then each is a right angle.
What can you conclude
about the diagram?
Find the measure
of each angle:
Find x and justify each
step.
Statements
Reasons
Homework:
p. 100
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