Other methods of Proving Triangles Congruent (AAS), (HL)

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Other methods of Proving Triangles Congruent
(AAS), (HL)

• 4-5

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EXAMPLE 2
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
Write a proof.
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for Examples 1 and 2
GUIDED PRACTICE

SOLUTION
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for Examples 1 and 2
GUIDED PRACTICE
ANSWER
Therefore are
congruent because vertical angles are congruent
so two pairs of angles and a pair of non included
side are congruent. The triangle are congruent by
AAS Congruence Theorem.
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for Examples 1 and 2
GUIDED PRACTICE
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EXAMPLE 3
Write a flow proof
In the diagram, CE BD and ? CAB
CAD.
ABE ADE
Write a flow proof to show
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EXAMPLE 4
Standardized Test Practice
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EXAMPLE 4
Standardized Test Practice
By the ASA Congruence Postulate, all triangles
with these measures are congruent. So, the
triangle formed is unique and the fire location
is given by the third vertex. Two lookouts are
needed to locate the fire.
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EXAMPLE 4
Standardized Test Practice
ANSWER
The correct answer is B.
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for Examples 3 and 4
GUIDED PRACTICE

In Example 3, suppose ABE ADE is
also given. What theorem or postulate besides ASA
can you use to prove that
ABE ADE?
SOLUTION
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for Examples 3 and 4
GUIDED PRACTICE
SOLUTION
Proved by ASA congruence
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for Examples 3 and 4
GUIDED PRACTICE
By the ASA Congruence Postulate, all triangles
with these measures are congruent. No triangle
is formed by the location of the fire and tower,
so the fire could be anywhere between tower B and
C.