EXAMPLE 3
NAMING CONGRUENT FIGURES Write a congruence statement for any figures
on p. 226
for Exs. 11–14
that can be proved congruent. Explain your reasoning.
11. X
12.
Y
W
13.
F
A
Z
B
B
14.
C
E
C
D
W
J
E
A
F
G
D
EXAMPLE 4
THIRD ANGLES THEOREM Find the value of x.
on p. 227
for Exs. 15–16
15. L
M
V
X
Z
Y
16.
Y
K
L
N
B
M
P
S
708
808
x8
N
X
Z
A
17. ERROR ANALYSIS A student says
C
R
M
that nMNP > nRSP because the
corresponding angles of the triangles
are congruent. Describe the error in
this statement.
18.
5x 8
458
N
R
S
nMNP > nRSP
P
TAKS REASONING Graph the triangle with vertices L(3, 1), M(8, 1),
and N(8, 8). Then graph a triangle congruent to nLMN.
ALGEBRA Find the values of x and y.
19.
20.
(17x 2 y)8
(6x 2 y)8
(4x 1 y)8
408
288
1308
(12x 1 4y)8
21.
TAKS REASONING Suppose n ABC > nEFD, nEFD > nGIH,
m∠ A 5 908, and m∠ F 5 208. What is m∠ H?
A 208
B 708
C 908
D Cannot be determined
22. CHALLENGE A hexagon is contained in a cube, as shown.
Each vertex of the hexagon lies on the midpoint of an
edge of the cube. This hexagon is equiangular. Explain
why it is also regular.
4.2 Apply Congruence and Triangles
229