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Lesson 4-4
Proving Congruence:
SSS and SAS
5-Minute Check on Lesson 4-3
Transparency 4-4
Refer to the figure.
1. Identify the congruent triangles.
2. Name the corresponding congruent
angles for the congruent triangles.
3. Name the corresponding congruent sides for the congruent triangles.
Refer to the figure.
4. Find x.
5. Find mA.
6.
Find mP if OPQ  WXY and
mW = 80, mX = 70, mY = 30.
Standardized Test Practice:
A
30
B
70
C
80
D
100
5-Minute Check on Lesson 4-3
Transparency 4-4
Refer to the figure.
1. Identify the congruent triangles.
LMN  RTS
2. Name the corresponding congruent
angles for the congruent triangles.
L  R, N  S, M  T
3. Name the corresponding congruent sides for the congruent triangles.
LM  RT, LN  RS, NM  ST
Refer to the figure.
4. Find x.
3
5. Find mA.
6.
63
Find mP if OPQ  WXY and
mW = 80, mX = 70, mY = 30.
Standardized Test Practice:
A
30
B
70
C
80
D
100
Objectives
• Use the SSS Postulate to test for triangle
congruence
• Use the SAS Postulate to test for triangle
congruence
Vocabulary
• Included angle – the angle formed by two
sides sharing a common end point (or
vertex)
Postulates
• Side-Side-Side (SSS) Postulate: If the
sides of one triangle are congruent to the
sides of a second triangle, then the
triangles are congruent.
• Side-Angle-Side (SAS) Postulate: If two
sides and the included angle of one triangle
are congruent to two sides and the included
angle of a second triangle, then the
triangles are congruent.
Side – Angle – Side (SAS)
Given: AC = CD
BC = CE
Prove:
ABC =
DEC
Statements
Reasons
AC = CD
Given in problem
BC = CE
Given
ACB  DCE (included angle)
ABC 
DEC
Vertical Angles Theorem
SAS Postulate
ENTOMOLOGY The wings of a moth form two triangles. Write
a two-column proof to prove that FEG  HIG
if EI  FH, FE  HI, and G is the midpoint of both EI and FH.
Given: EI  FH; FE  HI; G is the midpoint
of both EI and FH.
Prove: FEG  HIG
Proof:
Statements
Reasons
1.
1. Given
2.
2. Midpoint Theorem
3. FEG
HIG
3. SSS
Write a two-column proof to prove that ABC
Proof:
Statements
Reasons
1.
2.
3. ABC GBC
1. Given
2. Reflexive
3. SSS
GBC if
COORDINATE GEOMETRY Determine whether
WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4),
L(1, –5), P(2, –1), and M(4, –7). Explain.
Use the Distance
Formula to show that
the corresponding
sides are congruent.
Answer:
By
definition of congruent segments, all
corresponding segments are congruent.
Therefore, WDV MLP by SSS.
Determine whether ABC DEF for A(5, 5), B(0, 3),
C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.
Answer:
By definition
of congruent segments, all corresponding
segments are congruent. Therefore,
ABC DEF by SSS.
Write a flow proof.
Given:
Prove: QRT
Answer:
STR
Write a flow proof.
Given:
Prove: ABC ADC
Proof:
Determine which postulate can be used to prove that
the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
Two sides and the
included angle of one
triangle are congruent
to two sides and the
included angle of the
other triangle. The
triangles are
congruent by SAS.
Answer: SAS
Determine which postulate can be used to prove that
the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
Each pair of corresponding
sides are congruent. Two
are given and the third is
congruent by Reflexive
Property. So the triangles
are congruent by SSS.
Answer: SSS
Determine which postulate can be used to prove that
the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
a.
Answer: SAS
b.
Answer: not possible
Summary & Homework
• Summary:
– If all of the corresponding sides of two triangles
are congruent, then the triangles are congruent
(SSS).
– If two corresponding sides of two triangles and
the included angle are congruent, then the
triangles are congruent (SAS).
• Homework:
– Pg 266-8: 4, 16-19, 24, 25