Transcript No Slide Title

4.10 Prove Triangles Cong. by ASA and AAS
Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle
are congruent to two angles and the included side
of a second triangle, then the two triangles are
E
B
congruent.
A
C D
F
If Angle A  _____,
D Side AC  _____,
DF and
Angle C  _____
F
then ABC  ______
DEF
4.10 Prove Triangles Cong. by ASA and AAS
Theorem 4.13: Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a non-included side of one
triangle are congruent to two angles and the
corresponding non-included side of a second
triangle, then the two triangles are congruent.
E
B
A
C
D
F
If Angle A  _____,
F and
D Angle C  _____,
then ABC  ______
DEF
Side BC  _____,
EF
4.10 Prove Triangles Cong. by ASA and AAS
Theorem 4.14: Alternate Interior Angles Theorem
If two parallel lines are
cut by a transversal, then
the pair of alternate
interior angles are
congruent
_________.
t
p
4
5
q
4  5
4.10 Prove Triangles Cong. by ASA and AAS
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.
a.
a. There is not enough information to prove the triangles
congruent, because no _______
sides are known to be the
congruent.
4.10 Prove Triangles Cong. by ASA and AAS
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.
b.
b. Two pairs of angles and a ______________
non-included pair of sides
are congruent. The triangles are congruent by the
_____________________________.
AAS Congruence Theorem
4.10 Prove Triangles Cong. by ASA and AAS
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.
c.
c. The vertical angles are congruent,
so two pairs of angles and their
included sides are congruent.
_______________
The triangles are congruent by the
____________________________.
ASA Congruence Postulate
4.10 Prove Triangles Cong. by ASA and AAS
Checkpoint. Complete the following exercises.
1. Can STW and VWT be proven congruent
with the information given in the diagram? If so,
state the postulate or theorem you would use.
S
V
60
o
U
60 o
T
W
Since TW  WT,
you have two pairs of angles and a non-included pair of sides.
The triangles are congruent by the
AAS Congruence Theorem
4.10 Prove Triangles Cong. by ASA and AAS
C
Example 2 Write a flow proof
In the diagram, 1  4 and CF
bisects ACE. Write a flow
proof to show CBF  CDF. A
Given: 1  4, CF bisects ACE.
Prove: ΔCBF  ΔCDF
1  4,
Given
3 D
4
B 2
1
E
F
supplements
1 and 2 are _________
supplements
3 and 4 are _________
CF bisects
ACE.
supplementary angles
Def. of _______________
Given
2  ___
3
CF  CF
Cong. Supps. Thm.
Reflexive Prop.
ΔCBF  ΔCDF
ECF
ACF  
_____
Def. of bisector
AAS
Congruence Theorem
_________________________
4.10 Prove Triangles Cong. by ASA and AAS
Checkpoint. Complete the following exercises. C
2. In the diagram, CF bisects ACE
and  BFD. Write a flow proof to B 2
1
show CBF  CDF.
A
3 D
4
F
Given: CF bisects ACE, CF bisects BFD.
Prove: ΔCBF  ΔCDF
CF bisects BFD
CF bisects ACE
Given
Given
ACF  ECF
Def. of  bisector
CF  CF
Reflexive Prop.
BFC  DFC
Def. of  bisector
ΔCBF  ΔCDF
ASA Congruence Postulate
E
4.10 Prove Triangles Cong. by ASA and AAS
Pg. 267, 4.10 #1-20