Download 4.4 SSS and SAS notes

4.4 SSS and SAS2 ink.notebook
November 08, 2016
page 158
page 157
page 156
4.4 SSS and SAS
Lesson Objectives
Standards
Lesson Notes
page 159
4.4 SSS and SAS
Press the tabs to view details.
1
4.4 SSS and SAS2 ink.notebook
Lesson Objectives
Standards
November 08, 2016
Lesson Notes
Standards
Lesson Objectives
After this lesson, you should be able to successfully use SSS and SAS to prove triangles are congruent. 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.
Press the tabs to view details.
G.CO.10 Prove theorems about triangles.
SIDE­SIDE­SIDE (SSS) CONGRUENCE POSTULATE
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.
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
C
B
A
S
R
T
2
4.4 SSS and SAS2 ink.notebook
November 08, 2016
Decide whether the congruence statement is true. Explain your reasoning.
a) ÆJKL ¤ ÆMKL L
9
9
8
8
J
K
b) ÆRST ¤ ÆTVW W
R
M
S
T
V
3
4.4 SSS and SAS2 ink.notebook
November 08, 2016
B
c) Finish the two­column proof
Given: AB ¤ DB and C is the midpoint of AD
Prove: ÆABC ¤ ÆDBC A
Statements
C
D
Reasons
1. AB ¤ DB
1.
2. C is the midpoint of AD 2.
3. AC ¤ DC
3. Defn of _____________
4. BC ¤ BC
4.
5. ÆABC ¤ ÆDBC
5.
SIDE­ANGLE­SIDE (SAS) CONGRUENCE 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 two triangles are congruent.
S
R
V
T
U
W
4
4.4 SSS and SAS2 ink.notebook
November 08, 2016
For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate.
e)
d)
è______ ¤ è _____ è______ ¤ è _____ by the _____ Postulate.
by the _____ Postulate.
f)
The included angles, Ú1 and Ú2, are congruent because
_________________________________.
è______ ¤ è _____ by the _____ Postulate.
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!
A
B
D
C
E
F
5
4.4 SSS and SAS2 ink.notebook
November 08, 2016
g) Finish the two­column proof
L
J
1
Given: JN ¤ LN, KN ¤ MN Prove: ÆJKN ¤ ÆLMN
N
2
M
K
Statements
1. JN ¤ ____
Reasons
1.
KN ¤ ____
2. Ú1 ¤ Ú2
3. ÆJKN ¤ ÆLMN
2.
3.
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, write not possible.
On the
Worksheet
1.
2.
3.
6
4.4 SSS and SAS2 ink.notebook
November 08, 2016
Determine whether ΔABC ¤ ΔKLM. Explain.
Determine whether ΔABC ¤ ΔKLM. Explain.
5. A( 4, 2), B(–4, 1), C(–1, –1), K(0, –2), L(0, 1), M(4, 1) –
4. A(–3, 3), B(–1, 3), C(–3, 1),
K(1, 4), L(3, 4), M(1, 6)
y
–
y
x
x
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
7
4.4 SSS and SAS2 ink.notebook
November 08, 2016
8
4.4 SSS and SAS2 ink.notebook
November 08, 2016
9
4.4 SSS and SAS2 ink.notebook
November 08, 2016
Answers:
BOOKWORK
Answers page 2: 1. SSS 3. None 5. SSS 7. SAS 9. SSS 11. SAS
Answers page 3: first proof: Given, SAS
In the book, do page 267 – 269, problems: 8, 9, 16 – 19, 35
10
4.4 SSS and SAS2 ink.notebook
November 08, 2016
y
x
11