Angle-Side-Angle (ASA) Congruence Postulate

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Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one
triangle are congruent to two angles and the
included side of a second triangle, then the two
triangles are congruent.
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Theorem 4.13 Angle-Angle-Side (AAS) Congruence
Theorem
If two angles and a non-included side of one
triangle are congruent to two angles and the
corresponding non-included side of a second
triangle, then the two triangles are congruent.
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Theorem 4.14 Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal,
then the pair of alternate interior angles are
_________.
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congruent
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4
Identify congruent triangles
Example 1
Can the triangles be proven congruent with the
information given in the diagram? If so, state
the postulate or theorem you would use.
a.

1. There is not enough information to prove the
   triangles congruent, because no _______ are known
   to be the congruent.

sides
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Identify congruent triangles
Example 1
Can the triangles be proven congruent with the
information given in the diagram? If so, state
the postulate or theorem you would use.
b.
non-included

1. Two pairs of angles and a ______________ pair of
   sides are congruent. The triangles are congruent
   by the _____________________________.

AAS Congruence Theorem
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Identify congruent triangles
Example 1
Can the triangles be proven congruent with the
information given in the diagram? If so, state
the postulate or theorem you would use.
c.

1. The vertical angles are congruent,

so two pairs of angles and their _______________
are congruent. The triangles are congruent by the
____________________________.
included sides
ASA Congruence Postulate
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Checkpoint. Complete the following exercises.
you have two pairs of angles and a non-included
pair of sides.
The triangles are congruent by the
AAS Congruence Theorem
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Write a flow proof
Example 2
Given
Prove
supplements
supplements
Given
Given
supplementary
Reflexive Prop.
AAS Congruence Theorem
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Checkpoint. Complete the following exercises.
Given
Prove
Given
Given
Reflexive Prop.
ASA Congruence Postulate
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Pg. 267, 4.10 1-20