Unit 4 HW 8
p. 213 # 1, 2, 5 – 10
McCaleb
1.
Either BC = DC or BC ≠ DC. Assume BC = DC. The given information tells
us that AB = AD; AC is congruent to itself by the reflexive property. This makes
ΔABC = ΔADC by SSS, and by CPCTC <BAC = <DAC. This contradicts the given
information.
Therefore BC cannot be congruent to DC
2.
Either JP bisects <HJK, or it does not. Assume that JP bisects <HJK; this
would make <HJP = <KJP (def bisect). The given information tells us that HJ =
JK, and the reflexive property says that JP is congruent to itself. This information
taken together makes ΔHJP = ΔKJP by SAS. HP = PK by CPCTC, so P must be
the midpoint of segment HK. This contradicts the given information, so it is not
possible for ray JP to bisect <HJK.
5.
Either OB bisects <AOC or it does not. Assume OB bisects <AOC. The
definition of bisect tells us that <AOB = <COB. O is the center of the circle, so OA
= OC, as both are radii of the same circle. OB must be congruent to itself by the
reflexive property, the ΔAOB = ΔCOB by SAS. CPCTC makes <OBA = <OBC;
these angles are also a linear pair, and therefore supplementary. If 2 angles are
both supplementary and congruent, then they are right angles, so <OBA & <OBC
are right angles. The definition of an altitude tells us that OB is an altitude if it
forms right angles with the side of the triangle to which it is drawn; however this
contradicts the given information that OB is not an altitude.
Therefore, ray OB cannot bisect <AOC
6.
a)
b)
c)
d)
E(2a, 2a) F(0, 2a)
(2a)2 = 4a2
(a, a)
(a, a)
7.
a) C(2a, 2b)
b) yes
8. C(7, 0) D(0, -11)
m = -11 – 0
0–7
= -11/-1 = 11/7
9.
a) corresponding <s
b) alt int <s
10.
Either AB = AC or AB ≠ AC. Assume AB = AC. The given information that
PA is perpendicular to both AB and AC tells us that both <PAB & <PAC are right
angles, and therefore congruent (by the right angle thm). PA has to be congruent
to itself (by the reflexive property), so ΔPAB = ΔPAC by SSS. By CPCTC <B =
<C, but this contradicts the given information.
Therefore, AB cannot be congruent to AC