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NAME ______________________________________________ DATE
4-4
____________ PERIOD _____
Lesson Reading Guide
Proving Congruence—SSS, SAS
Get Ready for the Lesson
Read the introduction to Lesson 4-4 in your textbook.
Why do you think that land surveyors would use congruent right triangles rather
than other congruent triangles to check a measurement?
Read the Lesson
1. Refer to the figure.
N
a. Name the sides of 䉭LMN for which ⬔L is the included angle.
M
b. Name the sides of 䉭LMN for which ⬔N is the included angle.
L
c. Name the sides of 䉭LMN for which ⬔M is the included angle.
2. Determine whether you have enough information to prove that the two triangles in each
figure are congruent. If so, write a congruence statement and name the congruence
postulate that you would use. If not, write not possible.
b.
B
E
D
D
C
G
c. E
苶H
苶 and 苶
DG
苶 bisect each other.
d.
R
G
E
U
F
D
F
S
T
H
Remember What You Learned
3. Find three words that explain what it means to say that two triangles are congruent and
that can help you recall the meaning of the SSS Postulate.
Chapter 4
28
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
a. A
NAME ______________________________________________ DATE
4-4
____________ PERIOD _____
Study Guide and Intervention
Proving Congruence—SSS, SAS
SSS Postulate
You know that two triangles are congruent if corresponding sides are
congruent and corresponding angles are congruent. The Side-Side-Side (SSS) Postulate lets
you show that two triangles are congruent if you know only that the sides of one triangle
are congruent to the sides of the second triangle.
If the sides of one triangle are congruent to the sides of a second triangle,
then the triangles are congruent.
SSS Postulate
Example
Write a two-column proof.
Given: A
苶B
苶⬵苶
DB
苶 and C is the midpoint of A
苶D
苶.
Prove: 䉭ABC ⬵ 䉭DBC
B
C
Statements
Reasons
苶B
苶⬵苶
DB
苶
1. A
1. Given
苶D
苶.
2. C is the midpoint of A
2. Given
苶⬵苶
DC
苶
3. 苶
AC
3. Midpoint Theorem
苶⬵苶
BC
苶
4. 苶
BC
4. Reflexive Property of ⬵
5. 䉭ABC ⬵ 䉭DBC
5. SSS Postulate
D
Exercises
Write a two-column proof.
1.
B
A
C
2.
Y
Z
X
T
R
U
S
苶⬵苶
XY
苶, A
苶C
苶⬵苶
XZ
苶, B
苶C
苶⬵苶
YZ
苶
Given: 苶
AB
Prove: 䉭ABC ⬵ 䉭XYZ
苶⬵苶
UT
苶, R
苶T
苶⬵苶
US
苶
Given: 苶
RS
Prove: 䉭RST ⬵ 䉭UTS
Statements
Statements
Chapter 4
Reasons
29
Reasons
Glencoe Geometry
Lesson 4-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A
NAME ______________________________________________ DATE
4-4
Study Guide and Intervention
____________ PERIOD _____
(continued)
Proving Congruence—SSS, SAS
SAS Postulate Another way to show that two triangles are congruent is to use the
Side-Angle-Side (SAS) Postulate.
SAS Postulate
If two sides and the included angle of one triangle are congruent to two sides
and the included angle of another triangle, then the triangles are congruent.
Example
For each diagram, determine which pairs of triangles can be
proved congruent by the SAS Postulate.
a. A
b. D
X
B
C
Y
Z
E
F
In 䉭ABC, the angle is not
“included” by the sides 苶
AB
苶
and 苶
AC
苶. So the triangles
cannot be proved congruent
by the SAS Postulate.
H
G
J
The right angles are
congruent and they are the
included angles for the
congruent sides.
䉭DEF ⬵ 䉭JGH by the
SAS Postulate.
c.
P
Q
1
2
S
R
The included angles, ⬔1
and ⬔2, are congruent
because they are
alternate interior angles
for two parallel lines.
䉭PSR ⬵ 䉭RQP by the
SAS Postulate.
Exercises
For each figure, determine which pairs of triangles can be proved congruent by
the SAS Postulate.
2.
P
T
4.
Q
N
U
R
V
3. N
X
Y
M
Z
W
5. A
W
B
P
L
M
6. F
G
K
M
Chapter 4
T
D
C
30
J
H
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.