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EXAMPLE 1
Identify congruent triangles
Can the triangles be proven congruent with the
information given in the diagram? If so, state the
postulate or theorem you would use.
SOLUTION
a.
The vertical angles are congruent, so two pairs of
angles and a pair of non-included sides are
congruent. The triangles are congruent by the AAS
Congruence Theorem.
EXAMPLE 1
Identify congruent triangles
b.
There is not enough information to prove the
triangles are congruent, because no sides are
known to be congruent.
c.
Two pairs of angles and their included sides are
congruent. The triangles are congruent by the ASA
Congruence Postulate.
EXAMPLE 2
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
Write a proof.
GIVEN
PROVE
A
D,
ABC
C
DEF
F, BC
EF
GUIDED PRACTICE
1.
for Examples 1 and 2
In the diagram at the right, what
postulate or theorem can you use to
RST
VUT ? Explain.
prove that
SOLUTION
STATEMENTS
REASONS
S
U
Given
RS
UV
Given
RTS
UTV
The vertical angles
are congruent
GUIDED PRACTICE
for Examples 1 and 2
ANSWER
AAS;
RTS
UTV because they are vertical angles.
for Examples 1 and 2
GUIDED PRACTICE
Rewrite the proof of the Triangle Sum Theorem
on page 219 as a flow proof.
2.
ABC
GIVEN
PROVE m
1+m
2+m
3 = 180°
STATEMENTS
1. Draw BD parallel to AC .
2. m 4 + m 2 + m 5 = 180°
REASONS
1. Parallel Postulate
2. Angle Addition Postulate and
definition of straight angle
3.
1
4,
3
4. m
1= m
4,m
5. m
1+m
2+m
3. Alternate Interior Angles
5
3= m
5
3 = 180°
Theorem
4. Definition of congruent
angles
5. Substitution Property
of Equality