Geo_Book_Answers

Answers to Exercises
LESSON 11.7
1. 5 cm 2. 33 1
3
cm
3. 45 cm 4. 21 cm
5. 28 cm 6. no
7. José’s method is correct. Possible explanation:
Alex’s first ratio compares only part of a side of the
larger triangle to the entire corresponding side of the
smaller triangle, while the second ratio compares
entire corresponding sides of the triangles.
8. yes
9. 6 cm; 4.5 cm
10. 13.3 cm; 21.6 cm
11. yes; no; no
12. yes; yes; yes
13. 32 cm; 62 cm
14.
15.
E
16. Extended Parallel/Proportionality Conjecture
17. You should connect the two 75-marks. By the
Extended Parallel/Proportionality Conjecture,
drawing a segment between the 75-marks will
75
form a similar segment that has length
100
of the original.
18. 2064 cm3 6484 cm3 19. possible proof:
a b
c d
I J
ad cb
ad ab cb ab
a(d b) b(c a)
a(d b)
ab
b(c a)
ab
d b c a
b
a
132 ANSWERS TO EXERCISES
F
, or 75%,
So two pairs of corresponding sides of XYZ and
XAB are proportional. X X, so
XYZ XAB by the SAS Similarity Conjecture.
Because XYZ XAB, XAB XYZ.
Hence, AB YZ by the Converse of the Parallel
Lines Conjecture.
20. Set the screw so that the shorter lengths of the
styluses are three-fourths as long as the longer
lengths.
21. x 4.6 cm, y 3.4 cm
22. x 45 ft, y 40 ft, z 35 ft
23. 343
729
24. She is incorrect. She can make only nine 8 cm
diameter spheres.
25. 6x2 ;24x2 ;54x2 26. 1
3 r
27a. Possible construction method: Use the
triangle-and-circle construction from Lesson 11.3,
Exercise 18, to locate the golden cut, X, of AB.
Then use perpendicular lines and circles to create a
rectangle with length AB and width AX.
27b. Possible construction method: Construct
golden rectangle ABCD following the method from
27a. For square AEFD, locate EF by constructing
circle A and circle D each with radius AD. Repeat
the process of cutting off squares as often as
desired. For the golden spiral from point D to point
E, construct circle F with radius EF; select point D,
point E, and circle F and choose Arc On Circle from
the Construct menu.
28. possible answer:
A
S
P
D
B
R
Q
C
Given: Circumscribed quadrilateral ABCD, with
points of tangency P, Q , R, and S
Show: AB DC AD BC