Proving Triangles Congruent

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Lesson 4-5

• Proving Triangles Congruent

(SSS, SAS, ASA, AAS)
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Postulates
If the sides of one triangle are congruent to the
sides of a second triangle, then the triangles
are congruent.
SSS
Included Angle
In a triangle, the angle formed by two sides is
the included angle for the two sides.
Included Side
The side of a triangle that forms a side of two
given angles.
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Included Angles Sides
Included Angle



Included Side
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Postulates
If two angles and the included side of one
triangle are congruent to the two angles and the
included side of another triangle, then the
triangles are congruent.
ASA
If two sides and the included angle of one
triangle are congruent to the two sides and the
included angle of another triangle, then the
triangles are congruent.
SAS
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Postulates
If two angles and a non included side of one
triangle are congruent to the corresponding two
angles and side of a second triangle, then the
two triangles are congruent.
AAS
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Steps for Proving Triangles Congruent

• Mark the Given.
• Mark Reflexive Sides / Vertical Angles
• Choose a Method. (SSS , SAS, ASA, AAS)
• List the Parts in the order of the method.
• Fill in the Reasons why you marked the parts.
• Is there more?

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Problem 1 ?
Step 1 Mark the Given
Step 2 Mark reflexive sides
SSS
Step 3 Choose a Method (SSS /SAS/ASA/AAS )
Step 4 List the Parts in the order of the method
Step 5 Fill in the reasons
Step 6 Is there more?
Given
Given
Reflexive Property
SSS Postulate
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Problem 2 ?
Step 1 Mark the Given
Step 2 Mark vertical angles
SAS
Step 3 Choose a Method (SSS /SAS/ASA/AAS)
Step 4 List the Parts in the order of the method
Step 5 Fill in the reasons
Step 6 Is there more?
Given
Vertical Angles.
Given
SAS Postulate
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Problem 3
Step 1 Mark the Given
Step 2 Mark reflexive sides
ASA
Step 3 Choose a Method (SSS /SAS/ASA/AAS)
Step 4 List the Parts in the order of the method
Step 5 Fill in the reasons
Step 6 Is there more?
Given
Reflexive Postulate
Given
ASA Postulate
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Problem 4 ?
Step 1 Mark the Given
Step 2 Mark vertical angles
AAS
Step 3 Choose a Method (SSS /SAS/ASA/AAS)
Step 4 List the Parts in the order of the method
Step 5 Fill in the reasons
Step 6 Is there more?
Given
Vertical Angle Thm
Given
AAS Postulate
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Homework
Page 238/1, 3, 4, 6, 9 You can choose to do a
2-column proof for all proofs.