EOI
PRACTICE
GEOMETRY
PROBLEMS 31-59
31. SUSAN’S CIRCULAR SWIMMING POOL HAS
AN AREA OF 314 SQUARE FEET. WHAT IS
THE APPROXIMATE DIAMETER OF THE POOL?
(USE 3.14 FOR . )
1.
2.
3.
4.
A 10 feet
B 20 feet
C 30 feet
D 60 feet
0%
1
0%
2
0%
3
0%
4
32. FOUR CIRCULAR PARKS OF DIFFERENT SIZES ARE TO BE
SURROUNDED WITH FENCE. PARK 1 HAS HALF THE DIAMETER OF
PARK 2, ONE THIRD THE DIAMETER OF PARK 3, AND ONE FOURTH
THE DIAMETER OF PARK 4. IF ONE BUNDLE OF FENCE EXACTLY
SURROUNDS PARK 2, HOW MANY BUNDLES OF FENCE WILL BE
USED IN THIS PROJECT?
1.
2.
3.
4.
A 3 bundles
B 5 bundles
C 6 bundles
D 8 bundles
0%
1
0%
2
0%
3
0%
4
33. WHICH ADDITIONAL FACT PROVES
THAT Δ RST AND ΔWJK ARE SIMILAR?
1.
2.
3.
4.
A The measure of ∠ J is 40°.
B The measure of ∠ J is 95°.
C The measure of ∠K is 40°.
D The measure of ∠K is 95°.
0%
1
0%
2
0%
3
0%
4
34. WHICH PAIR OF FACTS PROVES THAT
Δ RST AND ΔWXY ARE SIMILAR?
1.
2.
3.
4.
A ∠S ≅ ∠ X and ∠R ≅ ∠W
B ST ≅ WX and ∠T ≅ ∠W
C RS ≅ WY and ∠R ≅ ∠Y
D RS ≅ WY and RT ≅ WX
0%
1
0%
2
0%
3
0%
4
35. IF TRIANGLE RST AND TRIANGLE XYZ ARE
SIMILAR, WHICH OF THESE EQUATIONS
MUST BE TRUE?
𝑺𝑻
𝑹𝑻
A.
B.
C.
D.
𝒀𝒁
𝑺𝑻
𝒀𝒁
𝑹𝑻
𝒀𝒁
𝑹𝑻
𝑿𝒁
=
=
=
=
𝑿𝒁
𝑺𝑹
𝑿𝒁
𝑹𝑻
𝑿𝒁
𝑹𝑺
𝒀𝒁
0%
A.
0%
B.
0%
C.
0%
D.
36. CHRIS IS PLANNING A PLAY AREA SHAPED LIKE THIS
POLYGON. SHE DRAWS A MODEL SIMILAR TO THE DESIRED
PLAY AREA. IF THE LENGTH OF THE LONGEST SIDE OF HER
MODEL IS 33 CM, WHAT IS THE LENGTH OF THE SHORTEST
SIDE OF THE MODEL?
1.
2.
3.
4.
0%
1
0%
2
0%
3
A 9 cm
B 12 cm
C 13 cm
D 16 cm
0%
4
37. THE RATIO OF THE PERIMETER OF SQUARE
RSTU TO THE PERIMETER OF SQUARE WXYZ IS 1
TO 2. THE AREA OF SQUARE RSTU IS 25 SQUARE
INCHES. WHAT IS THE AREA OF SQUARE WXYZ?
1.
2.
3.
4.
A 20 sq in.
B 25 sq in.
C 50 sq in.
D 100 sq in.
0%
1
0%
2
0%
3
0%
4
38. WHICH ADDITIONAL FACTS PROVE
THAT Δ RST AND ΔWXY ARE CONGRUENT?
1.
2.
3.
4.
A RS ≅WX and ST ≅ XY
B RS ≅WX and RT ≅ XY
C RT ≅WY and ST ≅ XY
D RT ≅WY and RS ≅WX
0%
1
0%
2
0%
3
0%
4
39. IN THE DIAGRAM, ΔPQR ≅ ΔTSV.
WHICH OF THESE MUST BE TRUE?
1.
2.
3.
4.
A QR ≅ ST
B QR ≅ SV
C PR ≅ ST
D PR ≅ SV
0%
1
0%
2
0%
3
0%
4
40. WHICH ADDITIONAL FACTS PROVE
THAT Δ RST AND Δ ZXY ARE CONGRUENT?
1.
2.
3.
4.
A ∠R ≅ ∠Z and ∠T ≅ ∠Y
B ∠R ≅ ∠Y and ∠T ≅ ∠ Z
C RS ≅ ZX and RT ≅ ZY
D RS ≅ ZX and ST ≅ XY
0%
1
0%
2
0%
3
0%
4
41. WHICH ADDITIONAL FACTS PROVE
THAT ΔRST AND ΔWXY ARE CONGRUENT?
1.
2.
3.
4.
A RS ≅ XY and TS ≅WY
B RS ≅WX and RT ≅WY
C ∠R ≅ ∠W and RS ≅WX
D ∠R ≅ ∠W and ∠T ≅ ∠Y
0%
1
0%
2
0%
3
0%
4
42. Δ RST AND ΔWXY ARE CONGRUENT.
WHAT IS THE MEASURE OF 𝑾𝑿?
1.
2.
3.
4.
A 5 in.
B 8 in.
C 9 in.
D 10 in.
82%
6%
1
12%
0%
2
3
4
43. IF ΔMNP ≅ ΔXYZ , WHAT ARE M∠YXZ
AND M∠ ZYX?
1.
2.
3.
4.
A m∠YXZ= 40° and m∠ ZYX= 45°
B m∠YXZ= 45° and m∠ ZYX= 40°
C m∠YXZ= 40° and m∠ ZYX= 95°
D m∠YXZ= 95° and m∠ ZYX= 45°
65%
24%
12%
0%
1
2
3
4
44. CIRCLE R AND CIRCLE T ARE CONGRUENT. THE AREA OF
CIRCLE R IS 12.56 SQUARE FEET. TO THE NEAREST TENTH
OF A FOOT, WHAT IS THE CIRCUMFERENCE OF CIRCLE T?
(USE 3.14 FOR . )
1.
2.
3.
4.
A 3.1 feet
B 6.3 feet
C 12.6 feet
D 25.1 feet
47%
29%
12%
1
12%
2
3
4
45. THE CENTER OF THIS CIRCLE IS H.
WHAT IS THE MEASURE OF 𝑹𝑺?
1.
2.
3.
4.
A 15°
B 30°
C 60°
D 120°
53%
29%
12%
6%
1
2
3
4
46. THE CENTER OF THIS CIRCLE IS H.
WHAT IS THE MEASURE OF ∠RST ?
1.
2.
3.
4.
A 25°
B 50°
C 75°
D 100°
53%
24%
12%
1
2
3
12%
4
47. IN THIS CIRCLE, H IS THE CENTER, AND
ΔWXH IS AN EQUIANGULAR TRIANGLE. WHAT
IS THE MEASURE OF ARC WYX?
1.
2.
3.
4.
A 60°
B 120°
C 300°
D 320°
41%
29%
18%
12%
1
2
3
4
48. CHORDS RT AND WS INTERSECT AT
POINT H IN THIS CIRCLE. WHAT IS THE
MEASURE OF ∠RHW?
1.
2.
3.
4.
59%
24%
18%
0%
1
2
3
4
A 40°
B 75°
C 110°
D 150°
49. IN THE CIRCLE, H IS THE CENTER,
AND XY IS TANGENT TO THE CIRCLE.
WHAT IS THE MEASURE OF ∠ XHY?
1.
2.
3.
4.
A 25°
B 35°
C 90°
D 125°
71%
12%
12%
6%
1
2
3
4
50. CHORDS 𝑹𝑻 AND 𝑾𝑺 INTERSECT AT POINT H
IN THIS CIRCLE. WHAT IS THE VALUE OF X?
1.
2.
3.
4.
A2
B 2.5
C4
D5
47%
24%
18%
12%
1
2
3
4
51. THE MEASURE OF ARC RT IS 80°.
WHAT IS THE MEASURE OF ∠RST?
1.
2.
3.
4.
47%
29%
24%
0%
1
2
3
4
A 50°
B 80°
C 100°
D 160°
52. FOR THE RIGHT TRIANGLE RST,
WHAT IS THE LENGTH OF 𝑹𝑺?
1.
2.
3.
4.
A 4 feet
B 5 feet
C 12.5 feet
D 25 feet
59%
24%
12%
6%
1
2
3
4
53. WHICH SET OF MEASUREMENTS
COULD BE THE SIDE LENGTHS OF AN
OBTUSE TRIANGLE?
1. A 3 in., 4 in., 4 in.
2. B 5 in., 12 in., 13
in.
3. C 6 in., 7 in., 12 in.
4. D 6 in., 8 in., 9 in.
71%
18%
6%
1
6%
2
3
4
54. IN ISOSCELES TRIANGLE WXY, 𝑿𝒀 IS 13
INCHES IN LENGTH AND 𝑾𝒀 IS 10 INCHES IN
LENGTH. WHAT IS THE LENGTH OF 𝑿𝒁?
1.
2.
3.
4.
A 5 in.
B 6 in.
C 12 in.
D 18 in.
59%
24%
12%
6%
1
2
3
4
55. IN ΔRST, WHAT IS THE
LENGTH IN INCHES OF 𝑺𝑻?
1. A 6 in.
2. B 6 2in.
3. C 6 3 in.
4. D 12 in.
35%
35%
24%
6%
1
2
3
4
56. WHAT IS THE MEASURE OF ∠R?
1.
2.
3.
4.
A 30°
B 45°
C 60°
D 80°
71%
18%
12%
0%
1
2
3
4
57. IN RADICAL FORM, WHAT IS THE
PERIMETER OF THIS TRAPEZOID?
1. A 30 + 6 3+ 6 2 in.
2. B 34 + 6 3+ 6 2 in.
3. C 30 + 8 3+ 8 2 in.
4. D 38 + 8 3+ 6 2 in.
33%
33%
20%
13%
1
2
3
4
58. WHAT IS THE TANGENT
RATIO OF ANGLE W?
3
1. A
4
3
5
4
3
4
5
2. B
3. C
4. D
36%
36%
21%
7%
1
2
3
4
59. MICHAEL WANTS TO BUILD A RAMP TO REACH A
BASKETBALL RIM THAT IS 10 FEET HIGH, AND THE ANGLE
OF ELEVATION FROM THE FLOOR WHERE HE IS STANDING TO
THE RIM IS 20 DEGREES. WHICH EQUATION CAN BE USED
TO FIND THE LENGTH IN FEET OF THE RAMP, R?
1. A
2. B
3. C
4. D
10
sin 20° =
𝑟
10
cos 20° =
𝑟
𝑟
sin 20° =
10
𝑟
cos 20° =
10
36%
29%
21%
14%
1
2
3
4
THIS SHADED FIGURE IS COMPOSED OF 5
SQUARES. WHAT IS THE AREA OF THIS
SHADED FIGURE?
1.
2.
3.
4.
A 8 cm2
B 16 cm2
C 20 cm2
D 24 cm2
43%
36%
14%
7%
1
2
3
4
THE CENTER OF THIS CIRCLE IS P.
IF THE LENGTH OF PT IS 5 CM, WHAT IS
THE MEASURE OF ∠RPT ?
1.
2.
3.
4.
A 22.5°
B 45°
C 67.5°
D 90°
47%
33%
13%
7%
1
2
3
4
THE RADIUS OF CIRCLE H IS 10 INCHES.
WHAT IS THE ARC LENGTH OF 𝑹𝑺?
1. A
2. B
10
 inches
3
5
 inches
3
3. C 10 inches
4. D 20 inches
33%
33%
20%
13%
1
2
3
4