Copy and complete the statement.
10.
If
—
QP
≅
—
QR
, then
∠
__
≅
∠
__.
11.
If
∠
TRV
≅
∠
TVR
, then ___
≅
___.
12.
If
—
RQ
≅
—
RS
, then
∠
__
≅
∠
__.
13.
If
∠
SRV
≅
∠
SVR
, then ___
≅
___.
14.
Find the values of
x
and
y
in the diagram.
N
M
L
T
V
S
Q
P
R
5
y
+
1
8
x
°
26
Proving Triangle Congruence by SAS
(pp. 245–250)
5.3
Write a proof.
Given
—
AC
≅
—
EC
,
—
BC
≅
—
DC
Prove
ABC
≅
EDC
STATEMENTS
REASONS
1.
—
AC
≅
—
EC
1.
Given
2.
—
BC
≅
—
DC
2.
Given
3.
∠
ACB
≅
∠
ECD
3.
Vertical Angles Congruence Theorem (Theorem 2.6)
4.
ABC
≅
EDC
4.
SAS Congruence Theorem (Theorem 5.5)
Decide whether enough information is given to prove that
WXZ
≅
YZX
using the
SAS Congruence Theorem (Theorem 5.5)
.
If so, write a proof. If not, explain why.
8.
Y
Z
X
W
9.
Y
Z
X
W
E
C
D
B
A

292
Chapter 5
Congruent Triangles
Proving Triangle Congruence by SSS
(pp. 261–268)
5.5
Write a proof.
Given
—
AD
≅
—
CB
,
—
AB
≅
—
CD
Prove
ABD
≅
CDB
STATEMENTS
REASONS
1.
—
AD
≅
—
CB
1.
Given
2.
—
AB
≅
—
CD
2.
Given
3.
—
BD
≅
—
DB
3.
Re exive Property of Congruence (Theorem 2.1)
4.
ABD
≅
CDB
4.
SSS Congruence Theorem (Theorem 5.8)
15.
Decide whether enough information is given to prove that
LMP
≅
NPM
using the
SSS Congruence Theorem
(Thm. 5.8).
If so, write a proof. If not, explain why.
P
N
M
L
16.
Decide whether enough information is given to prove that
WXZ
≅
YZX
using the
HL Congruence Theorem (Thm. 5.9)
.
If so, write a proof. If not, explain why.
Y
X
W
Z
Proving Triangle Congruence by ASA and AAS
(pp. 269–276)
5.6
Write a proof.
Given
—
AB
≅
—
DE
,
∠
ABC
≅
∠
DEC
Prove
ABC
≅
DEC
STATEMENTS
REASONS
1.
—
AB
≅
—
DE
1.
Given
2.
∠
ABC
≅
∠
DEC
2.
Given
3.
∠
ACB
≅
∠
DCE
3.
Vertical Angles Congruence Theorem (Thm. 2.6)
4.
ABC
≅
DEC
4.
AAS Congruence Theorem (Thm. 5.11)
B
C
D
A
B
A
C
D
E

Chapter 5
Chapter Review
293
Decide whether enough information is given to prove that the triangles are congruent
using the AAS Congruence Theorem (Thm. 5.11)
.
If so, write a proof. If not, explain why.
17.
EFG
,
HJK
18.
TUV
,
QRS
E
G
H
K
F
J
T
V
U
Q
S
R
Decide whether enough information is given to prove that the triangles are congruent
using the ASA Congruence Theorem (Thm. 5.10)
.
If so, write a proof. If not, explain why.
19.
LPN
,
LMN
20.
WXZ
,
YZX
P
N
M
L
X
Y
Z
W
Using Congruent Triangles
(pp. 277–282)
5.7
Explain how you can prove that
∠
A
≅
∠
D
.
If you can show that
ABC
≅
DCB,
then you will know that
∠
A
≅
∠
D.
You are given
—
AC
≅
—
DB
and
∠
ACB
≅
∠
DBC.
You
know that
—
BC
≅
—
CB
by the Re exive Property of Congruence
(Thm. 2.1). Two pairs of sides and their included angles are
congruent, so by the SAS Congruence Theorem (Thm. 5.5),
ABC
≅
DCB
.
Because corresponding parts of congruent triangles are congruent,
∠
A
≅
∠
D
.
21.
Explain how to prove that
∠
K
≅
∠
N
.
J
K
H
M
L
N
22.

#### You've reached the end of your free preview.

Want to read all 62 pages?

- Fall '19