HW #3 B,
Part III
Solutions
M 333L
FALL
2010
Theorem 3.2.3 (Restated for clarity)
Prove parts (2) and (4).
( 1 ) Supplements of congruent angles are congruent.
( 2 ) Complements of congruent angles are congruent.
( 3 ) Supplements of the same angle are congruent.
( 4 ) Complements of the same angle are congruent.
Proof of (2):
Let
,
,
ABC
DEF
PQR and
XYZ
be any four angles such that
ABC
is a
complement of
PQR
and
DEF
is a complement of
XYZ
and
PQR
XYZ
.
[ We need to prove that
ABC
DEF
. ]
By definition of “complement,”
m
ABC
+
m
PQR
=
90° ,
so
m
ABC
=
90°
–
m
PQR
,
and
m
DEF
+
m
XYZ
=
90° ,
so
m
DEF
=
90°
–
m
XYZ
.
By definition of “congruent,”
m
PQR
=
m
XYZ
.
By substitution,
m
ABC
=
90°
–
m
XYZ
.
m
ABC
=
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 Spring '10
 Shirley
 Angles, 90°, def, PQR, 333L

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