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Transcript
4-4 Proving Triangles
Congruent SSS, SAS
You proved triangles congruent using
the definition of congruence.
• Use the SSS Postulate to test for triangle
congruence.
• Use the SAS Postulate to test for triangle
congruence.
Congruent Triangles
Do you really need six pairs of
corresponding congruent parts to prove
triangles congruent?
Look at the triangle.
What angle is opposite side ST?
What angle is included between RS and ST?
T
R
S
Side-Side-Side
Congruence
Postulate (SSS)
If each of the three sides of one triangle
are congruent to the side of another
triangle, then the two triangles are
congruent.
Page 264
Side-Angle-Side
Congruence Postulate
(SAS)
If two sides and the included angle of one
triangle are congruent to two sides and
the included angle of another triangle,
then the two triangles are congruent.
Angle-Side-Angle
Congruence Postulate
(ASA)
If two angles and the included side
of one triangle are congruent to
two angles and the included side
of another triangle, then the two
triangles are congruent.
Use SSS to Prove Triangles
Congruent
Given:
Prove:
___ ___ ___ ___
QU  AD, QD  AU
ΔQUD  ΔADU
1. Given
2. Given
3. Reflexive
4. SSS
Which___
information
is missing
___
from the flowproof?
Given: AC  AB
D is the midpoint of BC.
Prove: ΔADC  ΔADB
___
___
A. AC  AC
___ ___
B. AB  AB
___ ___
C. AD  AD
___
___
D. CB  BC
Side-Angle-Side
Congruence Postulate
(SAA)
If two angles and a side opposite one
of them in one triangle are
congruent to the corresponding
parts of another triangle, then the
two triangles are congruent.
Use SAS to Prove Triangles
are Congruent
ENTOMOLOGY The wings
of one type of moth form
two triangles. Write a twocolumn proof to prove that
ΔFEG  ΔHIG if EI  FH,
and G is the midpoint of
both EI and FH.
Given: EI  FH; G is the
midpoint of both EI and FH.
Prove:
ΔFEG  ΔHIG
Statements
1.
EI  FH; G is the
midpoint ofEI; G is the
midpoint of FH.
Reasons
1. Given
2.
2. Midpoint Theorem
3. FGE  HGI
3. Vertical Angles
4. SAS
4. ΔFEG  ΔHIG
What are two short
cuts to prove triangles
congruent?
• Side-Side-Side (SSS)
• Side-Angle-Side (SAS)
4-4 Assignment
Page 269, 5, 6, 12, 13, 16-19
• Do all proof problems in two
columns.
• Write out the Given and Prove.
• Draw the figure.