Proving Triangles Congruent

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Proving Triangles Congruent

• Advanced Geometry
• Triangle Congruence
• Lesson 2

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• For two triangles to be congruent
• 6 pairs of parts must be congruent.

The triangle congruence postulates and theorem
allow us to prove two triangles are congruent
using only 3 pairs of parts.
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Side-Side-Side Congruence Postulate
p. 226
If the sides of one triangle are congruent to
the sides of a second triangle, then the
triangles are congruent.
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Side-Angle-Side Congruence Postulate
p. 227
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
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Angle-Side-Angle Congruence Postulate
p. 235
If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the
triangles are congruent.
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Angle-Angle-Side Congruence Theorem
p. 236
If two angles and a nonincluded side of one
triangle are congruent to the corresponding two
angles and side of a second triangle, then the
two triangles are congruent.
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These are the tests that work SSS SAS ASA AAS
These tests DO NOT work
AAA
SSA
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Examples Determine which postulate or theorem
can be used to prove that the triangles are
congruent. If it is not possible to prove that
they are congruent, write not possible.
SAS Congruence Postulate
not possible
AAS Congruence Theorem
ASA Congruence Postulate
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Examples Determine whether
given the coordinates of the
vertices. Explain.
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Write a two-column proof. If
and B is the midpoint of then
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Write a two-column proof. If
and then
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Summary

• Prove 3 pairs of parts congruent.
• Use any reason we have learned.

• Prove the triangles congruent.
• Use a congruence test.

• If necessary, prove a pair of parts congruent.
• Use CPCTC.