Download Finish and Check Similarity Quiz Review

Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Similarity Quiz Review
Students Will Be Able To:
! Determine the scaling factor between two similar figures or solids.
! Use the properties of similarity to determine lengths and angles of two similar figures.
! Use the properties of similarity to find the area or volume of similar polygons/solids.
! Determine if two figures are similar (using AA, SSS or SAS similarity for triangles, or
definition of similarity for more complex figures).
! Write proofs that involve similarity.
Practice Problems:
1.
Determine whether the polygons are similar. Explain your response.
a.
b.
21
7
130°
5
5
15
15
40°
7
21
2. If CT || MD use the givens in the diagram to find these side lengths and angle measurements:
MA = _______
AD = _______
MD = _______
∠M = 46°
∠A = _______
∠D = _______
M
46°
2
CA = 2
AT = ________
CT = 0.75
C
∠TCA = _______ ∠CTA = 85°
0.75
D
2
1.5
85°
T
A
1
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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3. All measurements are in centimeters unless otherwise specified.
a.
b.
c.
d.
The triangular prisms shown are similar
and the ratio of a:b is 5:2. The volume of
the large prism is 250 cm3. Find the
volume of the small prism.
e.
2
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
!"
Name:
Date:
!"
4. Given: !" = !"
Prove: 𝐷𝐾 || 𝐶𝐻
5. Given: 𝑀𝑌 || 𝑂𝐸, 𝑂𝑌 ⊥ 𝑀𝑌, ∠𝐾𝐸𝑂 is a right angle
!"
!"
Prove: !" = !"
3
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
6. Find the missing length.
a.
b.
c.
d.
7. If ΔBIG ~ ΔDOG, use the information given below to find the rest of the side lengths and
angle measurements: Hint: Redraw the triangles so that they aren’t overlapping.
BI = 4 cm
IG = ______
BG = 5 cm
∠GBI = ______
∠GIB = ______
∠G = 42°
DO = 6 cm
OG = 9 cm
DG = _______
∠D = ______
∠O = 53°
G
B
I
D
O
4
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
8. Sunrise Road is 42 miles long between the edge of Moon Lake and Lake Road 𝐴𝐵 and 15
miles long between Lake Road and Sunset Road 𝐵𝐶 . Lake Road 𝐵𝐷 is 29 miles long.
Find the length of Moon Lake 𝐴𝑀 .
A
B
M
!"
C
D
!
9. The two pentagons below are similar and !" = !. If the area of DAISY = 4 cm2, then
what is the area of CROWN?
I
A
O
S
R
D
Y
W
C
N
10. The two similar triangular prisms with bases ΔINY and ΔRAG have volumes of 27 mm3 and
64 mm3 respectively. If the height TI of the tiny
prism is 6 mm, find:
a. LA = _______
b. area of ΔINY = __________
c. area of ΔRAG = __________
L
T
N
R
I
Y
A
G
5
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
11. Are the following pairs of triangles similar? Explain how you know, either way. If they are
similar, write the similarity statement (ex. ΔABC ~ ΔDEF) that indicates how they are similar
and give the similiarity theorem.
a.
5
M
A
O
2
4
6
3
E
L
K
8
C
b.
O
5
9
X
A
65°
6
c.
N
A
65°
3
P
36°
57°
4.5
E
B
36°
87°
I
H
T
6
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
12. Determine whether the triangles are similar. If they are, state how you know and complete the
similarity statement. If not, explain why not.
a.
b.
c.
d.
∆𝐿𝑀𝐾 ~ ________
∆𝑃𝐻𝑌 ~ ________
7
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Similarity Quiz Review – SOLUTIONS
1.
a. The figures are not similar because the angles are not congruent.
b. The figures are not similar because the sides are not proportional.
2. MA = 4, AD = 3, MD =1.5, ∠𝐴 = 49°, ∠𝐷= 85°, AT = 1.5, ∠𝑇𝐶𝐴 = 46°
3.
a. 5.4 cm
b. 4 cm
c. 25:4
d. 16 cm3
e. 20 cm
4. Answers may vary, example given.
Statement
Reason
!"
!"
1. Given
1.
=
!"
!"
2. ∠𝐷𝐾𝑅 ≅ ∠𝐶𝐾𝐻
3. ∆𝐷𝐾𝑅 ~ ∆𝐻𝐾𝐶
4. ∠𝐷 ≅ ∠𝐻
5. 𝐷𝑅 || 𝐶𝐻
5. Answers may vary, example given.
Statement
1. 𝑀𝑌 || 𝑂𝐸, 𝑂𝑌 ⊥ 𝑀𝑌, ∠𝐾𝐸𝑂 is right
2. ∠𝑂𝑌𝑀 is right
3. ∠𝐾𝐸𝑂 ≅ ∠𝑂𝑌𝑀
4. ∠𝑂𝑀𝑌 ≅ ∠𝐾𝑂𝐸
5. ∆𝑂𝑀𝑌 ~ ∆𝐾𝐸𝑂
6.
!"
!"
=
!"
!"
2. Vertical angles are congruent
3. SAS triangle similarity theorem
4. Corresponding angles in similar triangles are
congruent.
5. If alternate interior angles are congruent, then
lines are parallel.
Reason
1. Given
2. Definition of perpendicular
3. All right angles are congruent
4. If lines are parallel, corresponding angles are
congruent.
5. AA triangle similarity theorem.
6. If triangles are similar, that corresponding sides
are proportional.
6.
a. ? = 6
b. ? = 40
c. ? = 45
d. ? = 3
7. IG = 6 cm, ∠𝐺𝐵𝐼 = 85°, ∠𝐺𝐼𝐵 = 53°, DG = 7.5 cm, ∠𝐷 = 85°
8. 110.2 miles.
9. The area of CROWN is 2.25.
10. LA = 8 mm, Area of ∆𝐼𝑁𝑌 = 4.5 mm2, Area of ∆𝑅𝐴𝐺 = 8 mm2.
11.
a. The triangles are not similar because the sides are not proportional.
b. ∆𝐶𝐴𝑁 ~ ∆𝑂𝐵𝑋 by SAS triangle similarity theorem
c. ∆𝐸𝐴𝑇 ~ ∆𝑃𝐼𝐻 by AA triangle similarity theorem
12.
a.
b.
c.
d.
Not similar because the angles are not congruent.
∆𝑉𝑈𝑇 ~ ∆𝑉𝐿𝑀 by SAS triangle similarity theorem.
∆𝐿𝑀𝐾 ~ ∆𝑂𝑁𝐾 by AA triangle similarity theorem
∆𝑃𝐻𝑌 ~ ∆𝑌𝐻𝑇 ~ ∆𝑃𝑌𝑇 by SSS triangle similarity theorem.
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