Download Pre-AP Geometry Review Chapter 7

Pre-AP Geometry Review Chapter 7
1. Determine which of the following isosceles
triangles are similar. Justify your answer.
P
A
8
4
55°
Q
3
6
70°
B
J
4.5
6
8
C
4
6. Find CE.
R
S
L
CE = __________
2
Identify the similar triangles, find x, and then find
the measures of the indicated sides.
T
1.5
70° 6
55°
1.5
K
U
___________________________
7.
Use the following information to find the measure.
Polygon
P
M
18
6
Q
N
S
80°
11
7.5
O 15
KM = ________
R
NM = ________
2. ratio of the perimeter of polygon PQRS to the
perimeter of polygon MNOS
8.
________
3. MN
_______
4. perimeter of quadrilateral MNOS
________
5. scale factor of quadrilateral PQRS to quadrilateral
MNOS
________
PQ = ________
QS = ________
13.
9.
D
A
3
9
F
8
x+ 2
B
D
C
4
E
A
24
C
CF = ________
30
27
CA = ________
10. Find PS if
medians,
and
are
and
P
A
B
A)
B)
C)
D)
No; sides are not proportional.
yes;
by SSS Similarity
yes;
by SSS Similarity
yes;
by SSS Similarity
S
D
B
F
10
6
C
Q
R
14. The ratio of measures of the three sides of a triangle
is 5:6:9. If the perimeter is 220 meter. Find the
measures of the sides of the triangle.
PS = ______________
Determine whether each pair of triangles is similar.
Justify your answer.
________, ________, _______
11.
15. Find DC.
________________________
12.
DC = _______
_____________________
16. Look at the figure shown below.
19. On a blueprint,
inch represents 16 feet. If
a driveway is 40 feet long, what is its length, in
inches, on the map?
If MKJ ~ MNL, which of the following
must be true?
A)
, because corresponding
angles of similar triangles are congruent.
B)
____________
20. A machine mints coins at the rate of one coin
per second. If it does this for 10 hours each
day, approximately how many days will it take
the machine to mint 360,000 coins?
, because the ratios of the
lengths of corresponding sides of similar
triangles are equal.
C)
, because the ratios of the
lengths of corresponding sides of similar
triangles are equal.
D)
, because corresponding
angles of similar triangles are congruent.
A)
B)
C)
D)
10
100
1000
10000
21. Find QR.
17. Find y.
QR = __________
22. Find CE.
y = __________
18. A tree casts a shadow that is 3 feet 3 inches long. A
man is 6 feet tall and casts a shadow 1 foot long.
How tall is the tree?
A)
B)
C)
D)
19 ft 5 in.
19 ft 6 in.
19 ft 7 in.
19 ft 8 in.
CE = __________
23. If
KLM
XYZ, find the perimeter of
XYZ.
26.
Find FG, if BC =10, BA = 20, CA= 16, DC = 2,
DE = 2.5 and EF = 24
____________
_________
24.
ABC
BX.
JKL with altitudes BX and KY. Find
27. Find x.
BX = __________
25. Find x.
x = __________
Use the figure below.
28. Identify the similar triangles.
_____________________
___________
29. Find MN.
_________
30. Triangle
has vertices
and
31. Given:
Prove:
.
32. Given :
Prove:
is a midsegment.
and
is the midsegment of
. Verify that
Pre-AP Geometry Review Chapter 7
Answer Section
1.
The corresponding angles are congruent, and the measures of their corresponding sides are proportional.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
2. 2:1
Calculate the perimeter of polygon PQRS and the perimeter of polygon MNOS. Then find their ratio.
3. 9
The corresponding sides of similar figures are proportional to the scale factor.
4. 33.5
Calculate the lengths of MN and OS. Then find the sum of the four sides of the quadrilateral MNOS.
5.
The numerical ratio obtained by comparing the lengths of corresponding sides of similar figures is called the scale
factor.
6. 26
7.
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The measures of the corresponding sides of similar triangles are proportional.
8.
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The measures of the corresponding sides of similar triangles are proportional.
9.
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The measures of the corresponding sides of similar triangles are proportional.
10. 13.5
If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the
corresponding sides.
11. Not similar; SSA is not a valid similarity.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
12. yes;
by AA Similarity
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
13. C
14. 55, 66, 99
15. 16
An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two
sides.
16. C
17.
18. B
19.
20.
21.
22.
23.
24.
A
56
25
45
19.2
25.
26.
27.
28.
29.
30.
31.
32.
or
19.2
12
7.5
See solution
See solution
See solution
18.76