Download ANSWERS FOR 9.3 2. acute: right: obtuse: 8. right 10. not right 12

ANSWERS
FOR
9.3
For use with pages 545–549
9.3 Guided Practice
26. The quadrilateral has two
2. acute: c2 < 242 182
c < 30
right: c2 242 182
c 30
obtuse: c2 > 242 182
c > 30
4. D
6. A
9.3 Practice and Applications
8. right
10. not right
12. not right
14. right
16. obtuse
18. acute
20. right
22. acute
24. acute
pairs of congruent opposite
sides. The triangle formed
by the diagonal is a right
triangle because
142 82 265 2;
260 260.Therefore, the
quadrilateral has four right
angles. The quadrilateral is a
rectangle.
28. Rhombus; the diagonals
bisect each other so the
quadrilateral is a parallelogram. 32 42 52, so the
diagonals intersect at right
angles to form perpendicular
lines so the parallelogram is
a rhombus.
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30. distance from B to C 3 02 7 32
5
distance from B to A 3 42 7 62
52
distance from A to C 4 02 6 32
52 52 52 2
5
25 25 50; therefore ABC is a right triangle.
145
ANSWERS
FOR
9.3 (CONT.)
For use with pages 545–549
32. right
34. Since x2 32 < 42, ABC is
obtuse and ABC is obtuse.
1 and ABC are a linear
pair and are therefore supplementary. By the definition of
supplementary angles,
mABC m1 180.
Since ABC is obtuse,
mABC > 90. Therefore,
m 1 < 90. 1 is an acute
angle by definition of an
acute angle.
Geometry Answer Transparencies
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36. If a, b, and c are a
Pythagorean triple, then
a2 b2 c2. Let k represent
a positive integer.
Multiplying a, b, and c by k
gives the equation
k2a2 k2b2 k2c2. Dividing
both sides of the equation by
k2 yields a2 b2 c2. By
the Converse of the
Pythagorean Theorem,
ABC is a right triangle and
a, b, and c represent the side
lengths of ABC.
38. parallelogram, rectangle,
rhombus, square
40. 509,796 < 521,210
Cincinnati is not directly
north of Tallahassee. It is
northeast of Tallahassee.
42. Given:
In ABC, c2 > a2 b2
Prove:
ABC is an obtuse triangle.
Plan for Proof: Draw right
triangle PQR with side
lengths a, b, and x. Compare
lengths c and x.
x2 a2 b2
Pythagorean Theorem
c2 > a2 b2
Given
c2 > x2
Substitution prop. of equality
c>x
A property of square roots
m C > m P
Converse of Hinge Thm.
C is an obtuse angle
Given, def. of rt. angle, def.
of obtuse angle, sub. prop. of
equality
146
ANSWERS
FOR
9.0 (CONT.)
For use with pages xxx–xxx
42. CONTINUED
Quiz 1
ABC is an obtuse triangle
Def. of obtuse triangle (C
is the largest of ABC).
44. A
2. BD
4. 12
6. 65
8. No; the square of the longest
side is larger than the sum of
the squares of the smaller
sides.
46. NP is an altitude
Given
mNPM mNPQ 90
Def. of an altitude
t
r
t
s
Given
MQN is a right triangle
Theorem 9.2
9.3 Mixed Review
48. 43
Geometry Answer Transparencies
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52.
45
5
50. 310
54.
26
3
56. reduction with center C and
scale factor
3
5
147