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ACT Geometry Review Problems, Lecture notes of Geometry

Tarlac State University (TSU)Geometry

ACT Geometry Review Problems. Choose the correct answer. NOTE: Figures are not drawn to scale. ... Use the picture of ∆ABC to answer questions 25 – 28.

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ACT Geometry Review Problems
Choose the correct answer.
NOTE: Figures are not drawn to scale.
1. In the figure, AC = 24, AB = 6x – 6, BC = 5x – 3 and BE = 3x + 2. Which do you know is true?
I. AC bisects DE.
II. DE bisects AC.
III. DE bisects AC.
a) I only b) II only c) III only d) I and II only e) II and III only
2. Find the values of x and y.
a) x = 20, y = 34 b) x = 10, y = 52
c) x = 12, y = 18 d) x = 11, y = 7
3. In the figure, BD bisects ∠ABE, BE bisects ∠ABG, m∠EBF = 37, and m∠CBG = 44.
Find m∠DBF.
a) 68 b) 34 c) 82 d) 71
4. ∠ABC and ∠CBD are adjacent congruent angles, and m∠ABD = 160. What are the two possible
measures for ∠ABC?
a) 80, 160 b) 100, 160 c) 80, 100 d) 90, 180 e) 160, 200
5. Find m∠ADC.
a) 53 b) 43 c) 137 d) 127
•
C
•
A
•
E
•
D
B
(4x – 3)°
(11x + 3)°
(2y + 9)°
•
C
•
A
•
B
•
G
F
•
D
•
•
E
(x + 10)°
(3x - 2)°
A
D
B
C
!
!
pf3
pf4
pf5
Discount

On special offer

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ACT Geometry Review Problems Choose the correct answer. NOTE: Figures are not drawn to scale.

  1. In the figure, AC = 24, AB = 6 x – 6, BC = 5 x – 3 and BE = 3 x + 2. Which do you know is true? I. AC bisects DE. II. DE bisects AC. III. DE bisects AC. a) I only b) II only c) III only d) I and II only e) II and III only
  2. Find the values of x and y. a) x = 20, y = 34 b) x = 10, y = 52 c) x = 12, y = 18 d) x = 11, y = 7
  3. In the figure, BD bisects ∠ABE, BE bisects ∠ABG, m ∠EBF = 37, and m ∠CBG = 44. Find m ∠DBF. a) 68 b) 34 c) 82 d) 71
  4. ∠ABC and ∠CBD are adjacent congruent angles, and m ∠ABD = 160. What are the two possible measures for ∠ABC? a) 80, 160 b) 100, 160 c) 80, 100 d) 90, 180 e) 160, 200
  5. Find m ∠ADC. a) 53 b) 43 c) 137 d) 127

C

A

  • E

• D

B (11 x + 3)° (4 x – 3)° (2 y + 9)°

C

A

B

• G

F •

D •

• E

( x + 10)° (3 x - 2)° A D B C

  1. If AB || CD, AB = CD and AF = FD = DE. What can you conclude? I. ∆ABF ≅ ∆DCE II. ∆ABF ≅ ∆DBF III. ∆DBF ≅ ∆DCE a) I only b) II only c) III only d) I, II and III
  2. The ratio of the measures of two supplementary angles 7:8. Which proportion(s) could you use to find the measures of the angles? I. 8

y x II. 7

y x III. 8

− x x IV. 7

− x x a) I only b) II only c) I and II only d) III and IV only e) I, II III, and IV

  1. Quad. ABCD ~ Quad. HGFE. Find the perimeter of ABCD. a) 88 b) 22 c) 66 d) 31
  2. A ladder 6 m long just reaches the top of a building and its foot makes a 76° angle with the ground. Which of the following equations could be used to calculate the height, h , of the building? I. 6 sin 76 h ° = II. 6 ⋅ cos 14 °= h III. 6 cos 76 h ° = a) I only b) II only c) III only d) I and II only e) I, II and III
  3. Find the measure of AB. a) 34 b) 26 c) 86 d) 76
  4. A square garden enclosed by a fence with perimeter 40 m is to be expanded so it includes 300 m^2 more area but is still square. If the gardener can reuse the old fence pieces, what length of new fence must the gardener buy? a) 10 m b) 20 m c) 40 m d) 100 m A F D^ E B C B A C D F E H G 4 3 8 12 21 A B 100° 140° 67° 87°
  1. If point R has coordinates ( x , y ) and point S has coordinates ( x + 1, y + 1), what is the distance between R and S? a) 2 b) x^2 + y^2 c) 2 d) x^2 + y^2 + 2 e) x + y + 1
  2. Will is standing 40 yards due North of point P. Grace is standing 60 yards due West of point P. What is the shortest distance between Will and Grace? a) 20 yds b) 20 13 yds c) 80 13 yds d) 4 13 yds e) 80 yds
  3. The circle in the figure is inscribed in a square with a perimeter of 20 inches. What is the area of the shaded regions?
  4. A trapezoidal flower garden is shown below. What is the area of the garden?
  5. In the figure below, x =? a) 45 b) 60 c) 90 d) 105 e) 120
  6. In the figure below, l 1 is parallel to l 2. Which of the following must be true? I. w = a II. y + b = 180° III. x + d = 180° a) I only b) II only c) I and II only d) II and III only e) I, II and III 13 m 9 m 10 m l 3 l 1 l 2 x ° z ° y ° w ° b ° d ° c ° a ° x y 30°

Use the picture of ∆∆∆∆ ABC to answer questions 25 – 28.

  1. In the figure, AB =? a) 2 b) 2 3 c) 4 d) 4 2 e) 8
  2. What is the ratio for sinB. a) 5

b) 5

c) 45 ° d) 5

e) 34

  1. What is the ratio for tanC? a) 4

b) 3

c) 3

d) 3

e) 34

  1. Find the measure of ∠B. a) 90 b) 36.9 c) 53.1 d) 30.9 e) 45
  2. In the figure, what is the sum of the indicated angles? a) 540 b) 720 c) 900 d) 1, e) 1,
  3. If the area of a circle is 9π, which of the following is(are) true? I. The radius is 3. II. The diameter is 6. III. The circumference is 6π. a) I only b) II only c) III only d) I and II only e) I, II and III B A^ C 5 3

ACT Geometry Review Answers:

  1. B not enough info to tell BD!BD be sure, never assume!
  2. C linear pair
  3. D straight line = 180
  4. C 160 /2 and 360-160 then /
  5. D Same Side Interior angles (only if parallel lines! Look for arrows)
  6. A Mark ≅ sides with tick marks. Look for corresponding angles.
  7. D 7x + 8x = 180
  8. C ratio is 12:
  9. D SOHCAHTOA
  10. C inscribed angles
  11. C add old and new area and find the sides.
  12. B outside area minus inside area
  13. D minute hand goes around the full circle twice
  14. D midpoint formula
  15. A longest side is across from the largest angle
  16. D ¼ area of the circle minus the area of the triangle
  17. C remote interior angle theorem or linear pair & add 2 ∠s then subtract from 180
  18. C Pythagorean theorem (make sure you subtract!)
  19. A distance formula
  20. B Pythagorean theorem
  21. 25-6.25π (or 5.37)
  22. 123.5 m 2
  23. E Right angle = 90 and linear pair
  24. C Alternate Interior, Corresponding, Alternate Exterior, Same Side Interior
  25. C Pythagorean theorem
  26. A SOHCAHTOA
  27. C SOHCAHTOA
  28. B SOHCAHTOA (press 2 nd on your calculator. Calculator in degree mode.)
  29. C (n-2)180 (sum of the interior angles)
  30. E Area of circle = πr^2 , Circumference = 2πr
  31. D 45-45-90 and 30-60-90 triangles
  32. B Pythagorean theorem
  33. D straight line = 180 and vertical angles are !. Plug x in to 2x-
  34. B 40 ∼ 20 so each side is twice as big
  35. B Pythagorean theorem