Download Find the measures of the angles or sides in each triangle. 1. The

Chapter 7
Find the measures of the angles or sides in
each triangle.
1. The ratios of the measures of the three angles is 4 :
5 : 11.
No; sample answer: The measures of the angles of
ABC are 37, 53, and 90. The measures of the
angles of DEF are 41, 49, and 90. Since the
corresponding angles of the figures are not
congruent, the figures are not similar.
5. ANSWER: 36, 45, 99
2. The ratio of the three sides is 5 : 3 : 6 and the
perimeter is 98 centimeters.
ANSWER: 35 cm, 21 cm, 42 cm
3. FAMILY Shawn surveyed his homeroom class to
find out how many of his classmates have at least 1
sibling. Of the 32 people in his homeroom, 25 have at
least one sibling.
a. If there are 470 students in Shawn’s school, write
a proportion that could be used to predict the number
of students in the school who have at least one
sibling.
b. What is the number of students in Shawn’s school
with at least one sibling?
ANSWER: ANSWER: Yes; sample answer:
with a
scale factor of
Each pair of polygons is similar. Find the value
of x.
6. ANSWER: 5
7. a.
b.
Determine whether each pair of figures is
similar. If so, write the similarity statement and
scale factor. If not, explain your reasoning.
4. ANSWER: 8.8
Determine whether the triangles are similar. If
so, write a similarity statement. Explain your
reasoning.
8. ANSWER: No; sample answer: The measures of the angles of
ABC are 37, 53, and 90. The measures of the
angles of DEF are 41, 49, and 90. Since the
corresponding angles of the figures are not
congruent, the figures are not similar.
5. eSolutions Manual - Powered by Cognero
ANSWER: Not similar; sample answer: We know that the Page 1
vertical angles are congruent, so we would need to
show that the sides that include the angle are
foot long. If Rachel is 5 feet 6 inches tall, how tall is
her cousin?
ANSWER: Chapter
7
8.8
ANSWER: 2 ft 9 in.
Determine whether the triangles are similar. If
so, write a similarity statement. Explain your
reasoning.
8. Refer to the figure shown. 11. If PN = 4, NM = 1, and PQ = 5, find PR.
ANSWER: 6.25
ANSWER: Not similar; sample answer: We know that the
vertical angles are congruent, so we would need to
show that the sides that include the angle are
proportional. Since
similar.
≠ , the triangles are not
9. 12. If PR = 13, PQ = 9, and NM = 3, find PN.
ANSWER: 6.75
,
, and
are midsegments of ABC .
Find the value of x.
13. ANSWER: 51
ANSWER: Similar; sample answer: MNP ~ XYZ; XYZ is
equilateral. Equilateral triangles are also equiangular.
So XYZ is equiangular. MNP is also equiangular.
All three angles in equiangular triangles measure 60.
Therefore, m∠N = m∠P = m∠Y = m∠Z = 60, which
means ∠N
∠Y and ∠P
∠Z. So MNP ~ XYZ by AA Similarity.
10. When Rachel stands next to her cousin, Rachel’s
shadow is 2 feet long and her cousin’s shadow is 1
foot long. If Rachel is 5 feet 6 inches tall, how tall is
her cousin?
14. ANSWER: 12
Find x.
15. ANSWER: 2 ft 9 in.
Refer to the figure shown. ANSWER: 16. eSolutions Manual - Powered by Cognero
11. If PN = 4, NM = 1, and PQ = 5, find PR.
ANSWER: Page 2
ANSWER: Chapter 7
16. ANSWER: eSolutions Manual - Powered by Cognero
Page 3