1. EOI Practice GEOMETRY
Problems 31-59

2. A 10 feet B 20 feet C 30 feet D 60 feet
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 . )
A 10 feet
B 20 feet
C 30 feet
D 60 feet

3. A 3 bundles B 5 bundles C 6 bundles D 8 bundles
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?
A 3 bundles
B 5 bundles
C 6 bundles
D 8 bundles

4. 33. Which additional fact proves that Δ RST and ΔWJK are similar?
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°.

5. 34. Which pair of facts proves that Δ RST and ΔWXY are similar?
A ∠S ≅ ∠ X and ∠R ≅ ∠W
B ST ≅ WX and ∠T ≅ ∠W
C RS ≅ WY and ∠R ≅ ∠Y
D RS ≅ WY and RT ≅ WX

6. 𝑺𝑻 𝒀𝒁 = 𝑹𝑻 𝑿𝒁 𝑺𝑻 𝒀𝒁 = 𝑺𝑹 𝑿𝒁 𝑹𝑻 𝒀𝒁 = 𝑹𝑻 𝑿𝒁 𝑹𝑻 𝑿𝒁 = 𝑹𝑺 𝒀𝒁
35. If triangle RST and triangle XYZ are similar, which of these equations must be true?
𝑺𝑻 𝒀𝒁 = 𝑹𝑻 𝑿𝒁
𝑺𝑻 𝒀𝒁 = 𝑺𝑹 𝑿𝒁
𝑹𝑻 𝒀𝒁 = 𝑹𝑻 𝑿𝒁
𝑹𝑻 𝑿𝒁 = 𝑹𝑺 𝒀𝒁

7. 36. Chris is planning a play area shaped like this polygon
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?
A 9 cm
B 12 cm
C 13 cm
D 16 cm

8. A 20 sq in. B 25 sq in. C 50 sq in. D 100 sq in.
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?
A 20 sq in.
B 25 sq in.
C 50 sq in.
D 100 sq in.

9. 38. Which additional facts prove that Δ RST and ΔWXY are congruent?
A RS ≅WX and ST ≅ XY
B RS ≅WX and RT ≅ XY
C RT ≅WY and ST ≅ XY
D RT ≅WY and RS ≅WX

10. 39. In the diagram, ΔPQR ≅ ΔTSV. Which of these must be true?
A QR ≅ ST
B QR ≅ SV
C PR ≅ ST
D PR ≅ SV

11. 40. Which additional facts prove that Δ RST and Δ ZXY are congruent?
A ∠R ≅ ∠Z and ∠T ≅ ∠Y
B ∠R ≅ ∠Y and ∠T ≅ ∠ Z
C RS ≅ ZX and RT ≅ ZY
D RS ≅ ZX and ST ≅ XY

12. 41. Which additional facts prove that ΔRST and ΔWXY are congruent?
A RS ≅ XY and TS ≅WY
B RS ≅WX and RT ≅WY
C ∠R ≅ ∠W and RS ≅WX
D ∠R ≅ ∠W and ∠T ≅ ∠Y

13. 42. Δ RST and ΔWXY are congruent. What is the measure of 𝑾𝑿 ?
A 5 in.
B 8 in.
C 9 in.
D 10 in.

14. 43. If ΔMNP ≅ ΔXYZ , what are m∠YXZ and m∠ ZYX?
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°

15. A 3.1 feet B 6.3 feet C 12.6 feet D 25.1 feet
44. Circle R and Circle T are congruent. The area of Circle R is square feet. To the nearest tenth of a foot, what is the circumference of Circle T? (Use 3.14 for . )
A 3.1 feet
B 6.3 feet
C 12.6 feet
D 25.1 feet

16. 45. The center of this circle is H. What is the measure of 𝑹𝑺 ?
B 30°
C 60°
D 120°

17. 46. The center of this circle is H. What is the measure of ∠RST ?
B 50°
C 75°
D 100°

18. 47. In this circle, H is the center, and ΔWXH is an equiangular triangle. What is the measure of arc wyx?
A 60°
B 120°
C 300°
D 320°

19. 48. Chords RT and WS intersect at point H in this circle
48. Chords RT and WS intersect at point H in this circle. What is the measure of ∠RHW?
A 40°
B 75°
C 110°
D 150°

20. 49. In the circle, H is the center, and XY is tangent to the circle
49. In the circle, H is the center, and XY is tangent to the circle. What is the measure of ∠ XHY?
A 25°
B 35°
C 90°
D 125°

21. 50. Chords 𝑹𝑻 and 𝑾𝑺 intersect at point H in this circle
50. Chords 𝑹𝑻 and 𝑾𝑺 intersect at point H in this circle. What is the value of x?
A 2
B 2.5
C 4
D 5

22. 51. The measure of arc RT is 80°. What is the measure of ∠RST?
B 80°
C 100°
D 160°

23. 52. For the right triangle RST, what is the length of 𝑹𝑺 ?
A 4 feet
B 5 feet
C 12.5 feet
D 25 feet

24. 53. Which set of measurements could be the side lengths of an obtuse triangle?
A 3 in., 4 in., 4 in.
B 5 in., 12 in., 13 in.
C 6 in., 7 in., 12 in.
D 6 in., 8 in., 9 in.

25. 54. In isosceles triangle WXY, 𝑿𝒀 is 13 inches in length and 𝑾𝒀 is 10 inches in length. What is the length of 𝑿𝒁 ?
A 5 in.
B 6 in.
C 12 in.
D 18 in.

26. 55. In ΔRST, what is the length in inches of 𝑺𝑻 ?
A 6 in.
B in.
C in.
D 12 in.

27. 56. What is the measure of ∠R?
B 45°
C 60°
D 80°

28. 57. In radical form, what is the perimeter of this trapezoid?
A in.
B in.
C in.
D in.

29. 58. What is the tangent ratio of angle W?
B 3 5
C 4 3
D 4 5

30. A sin 20° = 10 𝑟 B cos 20° = 10 𝑟 C sin 20° = 𝑟 10 D cos 20° = 𝑟 10
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?
A sin 20° = 10 𝑟
B cos 20° = 10 𝑟
C sin 20° = 𝑟 10
D cos 20° = 𝑟 10

31. This shaded figure is composed of 5 squares
This shaded figure is composed of 5 squares. What is the area of this shaded figure?
A 8 cm2
B 16 cm2
C 20 cm2
D 24 cm2

32. The center of this circle is P
The center of this circle is P. If the length of PT is 5 cm, what is the measure of ∠RPT ?
A 22.5°
B 45°
C 67.5°
D 90°

33. The radius of circle H is 10 inches. What is the arc length of 𝑹𝑺 ?
A  inches
B 5 3  inches
C 10 inches
D 20 inches