Transcript Triangle Congruence Tests 4.4 Proving Congruence – SSS, SAS 4.5

Advanced Geometry
Triangle Congruence
Lesson 2
Proving Triangles
Congruent
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.
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.
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.
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.
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.
These are the
tests that work:
These tests
DO NOT work:
SSS
AAA
SAS
SSA
ASA
AAS
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
ASA
Congruence
Postulate
not
possible
AAS
Congruence
Theorem
Examples: Determine whetherEFG  MNP
given the coordinates of the vertices. Explain.
E  4, 3 , F  2,1 , G  2, 3 , M  4, 3 , N  2,1 , P  2, 3
Write a two-column proof.
If AD  DC and B is the midpoint of AC ,
then ABD  CBD.
Write a two-column proof.
If K  M and JK  NM ,
then J  N.
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.