1. ACT Review Concepts
15-16

2. 13. In the figure below, C is the intersection of and
13. In the figure below, C is the intersection of and If it can be determined, what is the measure of <bac?
80o
100o
110o
115o
Cannot be determined from the given information
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3. Vertical angles and parallel lines
Vertical angles are always equal
With parallel lines:
Alternate Interior angles are equal
Corresponding angles are equal
Same-side Interior angles are supplementary
Angle Sum Theorem – interior angles of a triangle add to 180o

4. 14. Antwan drew the circle graph below describing his time spent at school in 1 day. His teacher said that the number of hours listed were correct, but that the central angle measures for the sectors were not correct. What should be the central angle measure for the Core subjects sector?
72o
80o
160o
200o
288o
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5. Circles and central angles
Central Angles are formed by 2 radii
Measure of the Central Angle = Measure of the Intercepted Arc
Sector – area contained within 2 radii and the intercepted arc
Like a piece of pizza
Entire circle = 360o
Inscribed Angle vs. Central Angle and their measures

6. 20. For trapezoid abcd shown below, , the measures of the interior angles are distinct, and the measure of <D is xo. What is the degree measure of <A in terms of x?
(180 – x)o
(180 – 0.5x)o
( x)o
(180 + x)o xo
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7. Angle relationships/quadrilaterals
Properties of quadrilaterals
Parallelogram, rectangle, rhombus, square, kite, trapezoid, isosceles trapezoid

8. 27. What is the perimeter, in inches, of the isosceles right triangle shown below, whose hypotenuse is inches long? 8
8 + 16
16 +
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9. Special right triangles
Classifications of Triangles
Scalene, Isosceles, Equilateral, Right, Obtuse, Acute
Triangles
Ratio
Triangles
Perimeter vs. Area

10. 30. The radius of the base of the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, θ, of the angle formed by a slant height of the cone and a radius?
tan θ =
sin θ =
cos θ =
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11. Trig Ratios SOHCAHTOA for right triangles Take trig ratio of the angle
Set up proportions to solve

12. 40. Trapezoid abcd is graphed in the standard (x,y) coordinate plane below. When abcd is reflected over the y-axis to a’b’c’d’, what are the coordinates of d’?
(-12, 1)
(-12, -1)
(12, -1)
(1, 12)
(1, -12)
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13. Geometric transformations
Reflections
Rotations
Translations
Dilations

14. 45. Given that for some real number a, what is x+z?
4/3
27/2 26 27 48
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15. matrices
Matrix Addition
Scalar Multiplication

16. 50. You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters by 30 centimeters and is filled with water to a depth of 20 centimeters. The object sinks to the bottom, and the water level goes up by 0.25 centimeters. What is the volume, in cubic centimeters, of the object?
300
240
200
150 75
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17. Volume of solids

18. 53. A formula for the surface area (a) of the rectangular solid shown below is a =2lw+2lh+2wh, where l represents length, w represents width, and h represents height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor? 2 4 6 8 12
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19. Surface area of solids
Surface Area = sum of the areas of all faces of the solid

20. 60. The sides of an acute triangle measure 14 cm, 18 cm, and 20 cm respectively. Which of the following equations, when solved for θ, gives the measure of the smallest angle of the triangle?
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21. Law of sines and law of cosines
General Rule:
Use Law of Sines when you are given more angles than sides in the triangle
Use Law of Cosines when you are given more sides than angles in the triangle