Download Document

Triangle Congruence by SSS and SAS
GEOMETRY LESSON 4-2
1. In VGB, which sides include B? BG and BV
2. In STN, which angle is included between NS and TN? N
3. Which triangles can you prove congruent?
Tell whether you would use the SSS or SAS Postulate.
APB
XPY; SAS
4. What other information do you need to prove
DWO
DWG?
If you know DO DG, the triangles are by SSS;
if you know DWO DWG, they are by SAS.
5. Can you prove SED
BUT from the information given?
Explain.
No; corresponding angles are not between
corresponding sides.
4-2
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
(For help, go to Lesson 4-2.)
In
JHK, which side is included between the given pair of angles?
1.  J and  H
2.  H and  K
HK
JH
In
NLM, which angle is included between the given pair of sides?
3. LN and LM
4. NM and LN
L
N
Give a reason to justify each statement.
5. PR PR
6.  A
By the Reflexive
Property of Congruence,
a segment is congruent
to itself
D
Third Angles Theorem
Check Skills You’ll Need
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
You can use the Third Angles Theorem to prove
another congruence relationship based on ASA. This
theorem is Angle-Angle-Side (AAS).
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
Using ASA
Suppose that F is congruent to C and I is not congruent to C. Name
the triangles that are congruent by the ASA Postulate.
The diagram shows N
If F
C, then F
Therefore,
FNI
A
C
CAT
D and FN
CA
GD.
G
GDO by ASA.
Quick Check
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
Writing a proof using ASA
Write a paragraph proof.
Given: A
Prove:
B, AP
APX
It is given that A
APX
BP
BPY
B and AP
BP.
BPY by the Vertical Angles Theorem.
Because two pairs of corresponding angles and
their included sides are congruent, APX
BPY
by ASA.
Quick Check
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
Planning a Proof using AAS
Write a Plan for Proof that uses AAS.
Given: B
Prove:
D, AB || CD
ABC
CDA
Because AB || CD, BAC
Interior Angles Theorem.
DCA by the Alternate
Then ABC
CDA if a pair of corresponding
sides are congruent.
By the Reflexive Property, AC
ABC
CDA by AAS.
AC so
Quick Check
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
Writing a proof using AAS
Write a two-column proof that uses AAS.
Given: B D, AB || CD
Prove: ABC
CDA
Statements
Reasons
1. B
1. Given
D, AB || CD
2. BAC & DCA are AIA 2. Definition of Alternate Interior Angle.
3. BAC DCA
3. Alternate Interior Angle Theorem .
4. AC
5.
CA
ABC
4. Reflexive Property of Congruence
CDA
5. AAS Theorem
Quick Check
4-3
Triangle Congruence by ASA and AAS
GEOMETRY LESSON 4-3
1. Which side is included between R and F in FTR?
2. Which angles in STU include US? S and U
RF
Tell whether you can prove the triangles congruent by ASA or AAS. If you
can, state a triangle congruence and the postulate or theorem you used. If
not, write not possible.
3.
4.
GHI
AAS
PQR
5.
not possible
4-3
ABX
AAS
ACX