1. Chapter 9 Geometry
Homework Answers

2. Sec 9.1 12 cm 19.2 cm 5.3 cm 10 cm 26 cm 8.5 cm 24 cm 3.6 cm 40 cm
127 ft
512 m²
11.3 cm
3, 4, 5
28 m

3. Sec 9.2 yes no No, the given lengths are not a Pythagorean triple.
y = 25 cm
y = 24 units
y = 17.3 m
6, 8, 10
60 cm²
14.1 ft
17.9 cm²
102 m
a cm²
b cm
Sample answer: The numbers given satisfy the Pythagorean Theorem, so the triangle is a right triangle; but the right angle should be inscribed in an arc of 180°. Thus the triangle is not a right triangle.
Sample answer: BD² = 6² - 3² = 27; BC² = BD² +9² = 108; then AB² + BC² = AC² ( = 144), so ΔABC is a right triangle by the Converse of the Pythagorean Theorem.

4. Sec 9.3 72√2 cm 13 cm 10 cm. 5√3 cm 10√3 cm. 10 cm 34 cm, 17 cm 72 cm
(1/√2, 1/√2)
A 30°-60°-90° triangle must have sides whose lengths are multiples of 1, 2, √3. The triangle shown does not reflect this rule.
a. ΔCDA, ΔAEC, ΔAEB, ΔBFA, ΔBFC
b. ΔMDB, ΔMEB, ΔMEC, ΔMFC, ΔMFA

5. Sec 9.4 10 m No. The space diagonal of the box is 30.1 in. 50 km/hr
area: 60 m²; cost: $7200
surface area of prism = (27√ ) cm² ≈ cm²; surface area of cylinder = 78π cm² ≈ cm²
36/√3 cm
12 units
18√2 cm
Draw radii CD and CB. ‹ABC = ‹ADC = 90°. For quadrilateral ABCD 54° + 90° + m‹C + 90° = 360°, so m‹C = 126°. Radii BD = 126° but 126° +226° ≠ 360°.

6. Sec 9.5 5 units 45 units 34 units 354 m 52.4 units isosceles
x² + y² = 16
(x – 2)² +y² = 25
center is (2, -5), r = 6
center is (0,1), r = 9
(x – 3)² + (y + 1)² = 18
a. √14 units
b. √176 = 4√11 units
c. AB = √ (x1 – x2)² + (y1 – y2)² + (z1 – z2)²
(-√3/2,½)
k = √2, m = √6
x = 6/√3, y = 12/√3
96 cm

7. Sec 9.6 456π cm² (32π - 32√3) cm² (64√3 - 64π/3) cm²⅚
Inscribed circle: 3π cm². Circumscribed circle: 12π cm². The area of the circumscribed circle is four times as great as the area of the inscribed circle.
Inscribed circle: π cm². Circumscribed circle: 4π cm². The area of the circumscribed circle is four times as great as the area on the inscribed circle.
√77 cm
(-1/√2, 1/√2)
(-√3/2, -1/√2)
(x – 3)² + (y – 3)² = 36
center = (1,0), r = 10

8. Ch 9 Review 20 cm 10 cm obtuse 26 cm (√3/2, 1/√2) (-1/√2, -1/√2)
d = 12√2 cm
246 cm²
72π in.²
24π cm²
(2π – 4) cm²
222.8 cm²
isosceles right
No. The closest she can come to the camp is 10 km.
No. 15 cm is the longer diagonal.
1.4 km; 8½ min
yes
29 ft

9. Ch 9 Review cont’d 707 m² 6√3 and 18 12 m 42
4; 0; 10. The rule is n/2 if n is even, but 0 if n is odd.
4π, or approximately 12.6 in./sec
true
False. The hypotenuse is of length x√2.
AB =
False. A glide reflection is a combination of a translation and a reflection.
False. Equilateral triangles, squares, and regular hexagons can be used to create monohedral tessellations. D B A C

10. Ch 9 Review cont’d C D see diagram 34 cm²; 22 + 4√2 ≈ 27.7 cm
about 55.9 m
about 61.5 cm²
48 cm
322 ft²