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4.4 SSS and SAS 2017 ink.notebook
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November 07, 2017
page 154
4.4 SSS and SAS
page 155 page 156
Lesson Objectives Standards Lesson Notes
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4.4 SSS and SAS
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully use SSS and SAS to prove triangles are congruent.
4.4 SSS and SAS 2017 ink.notebook
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Lesson Objectives Standards Lesson Notes
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.10 Prove theorems about triangles.
You know that two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent. The following postulates lets you show that two triangles are congruent if you know only about congruent sides and angles in a specific order.
CONGRUENCE POSTULATE
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
SIDESIDESIDE (SSS)
AB
C S
R T
4.4 SSS and SAS 2017 ink.notebook
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Decide whether the congruence statement is true. Explain your reasoning.
MK
J
L9
8
9
8 S
RW
T V
b) ∆RST § ∆TVW a) ∆JKL § ∆MKL
Statements Reasons
Prove: ∆ABC § ∆DBC Given: AB § DB and C is the midpoint of ADc) Finish the twocolumn proof
A
B
C D
1.
2.
3. Defn of _____________
4.
5.
1. AB § DB
2. C is the midpoint of AD
3. AC § DC
4. BC § BC
5. ∆ABC § ∆DBC
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S
R TU
V
W
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 two triangles are congruent.
CONGRUENCE POSTULATESIDEANGLESIDE (SAS)
f)
The included angles, ⁄1 and ⁄2, are congruent because _________________________________.
For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate.d) e)
Ë______ § Ë _____ by the _____ Postulate.
Ë______ § Ë _____ by the _____ Postulate.
Ë______ § Ë _____ by the _____ Postulate.
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In ΔABC, the angle is not "included" by the sides So the triangles cannot be proved congruent by the SAS Postulate. THERE IS NO “DONKEY” (AS–S or SSA) Theorem!
D
E F
A
B C
Statements Reasons1.
2.3.
1. JN § ____
2. ⁄1 § ⁄23. ∆JKN § ∆LMN
KN § ____
Prove: ∆JKN § ∆LMNGiven: JN § LN, KN § MN
g) Finish the twocolumn proof
K
JN
L
M
1 2
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On the Worksheet
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, write not possible.
1. 2.
3.
Determine whether ΔABC § ΔKLM. Explain.4. A(–3, 3), B(–1, 3), C(–3, 1), K(1, 4), L(3, 4), M(1, 6)
x
y
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K(0, –2), L(0, 1), M(4, 1) 5. A(–4, –2), B(–4, 1), C(–1, –1),
Determine whether ΔABC § ΔKLM. Explain.
x
y
6. INDIRECT MEASUREMENT To measure the width of a sinkhole on his property, Harmon marked off congruent triangles as shown in the diagram. How does he know that the lengths A′B′ and AB are equal?
Practice
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Answers:
Answers page 2: 1. SSS 3. None 5. SSS 7. SAS 9. SSS 11. SASAnswers page 3: first proof: Given, SAS
BOOKWORK
In the book, do page 267 – 269, problems: 8, 9, 16 – 19, 35
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x
y
