1. ACT ASPIRE
PART 1 Geometry
Pythagorean Theorem

2. Write down everything you know about right triangles
ACT ASPIRE
Write down everything you know about right triangles

3. Multiple Choice #1
Jamie’s rectangular garden has a length of 12 feet and a width of 19 feet. What is the length of the diagonal, in feet, of the garden?
A 505
B 31
C 23
D 22.5
E 7.8
Answer is D

4. Multiple Choice #2 Trapezoid JKLM is shown below.
What is the length, in centimeters, of KL ?
A 12
B 10
C 9
D 8 E
Answer is B

5. Multiple Choice #3
A right triangle has a hypotenuse measuring 26 inches and one leg measuring 10 inches. What is the length, in inches, of the other leg of the triangle?
A 24
B 36
C 16
D 50
E NH
Answer is A

6. Constructed Response #4
The dimensions of a trapezoid are shown in the diagram below.
What is the length, in feet, of k?
Answer is 5

7. Constructed Response #5
Devon designed a sign for his company. The sign is in the shape of a triangle with side lengths of 7 feet, 9 feet, and 15 feet.
a. Explain how you know that Devon’s sign is not a right triangle.
b. Devon wants to redesign the sign so that it is a right triangle with a hypotenuse of 15 feet. Describe the changes that Devon could make to either or both of the other two sides of the sign.
c. Devon wants to design a second sign that is a right triangle with a hypotenuse of 39 feet and a leg of 15 feet. What should be the length, in feet, of the other leg of Devon’s second sign?

8. ACT ASPIRE
PART 2 Geometry
Angles

9. DRAW THE DIAGRAM and WRITE DOWN EVERYTHING YOU KNOW

10. MULTIPLE CHOICE. Find the angle measure for both a and b.
ANSWER is D a b

11. Find x and how big the angles are.
x = 23 and the angles are 69˚ and 111˚

12. FIND x and how big the angles are.
x = 8.75 and both angles are 45˚

13. Find x
x = 100˚

14. FIND THE MISSING ANGLE MEASUREMENTS
B = 78
C = 58
D = 122
E = 26
F = 58

15. ACT ASPIRE
PART 3 Geometry
SHAPES

16. Multiple Choice #1
Drew has a sticker in the shape of a quadrilateral with exactly 2 right angles, exactly 1 pair of parallel sides, and no sides that are the same length.
What is the shape of Drew’s sticker?
A Rhombus
B Trapezoid
C Rectangle
D Parallelogram
E Square
Answer is B

17. Multiple Choice #2
Which of the following statements about quadrilaterals is always true?
A All parallelograms are similar.
B All squares are rhombuses.
C All rectangles are congruent.
D All trapezoids are parallelograms
E All rectangles are squares.
Answer is B

18. Multiple Choice #3
Which of these statements about triangles is not true?
A An isosceles triangle can also be a right triangle.
B An acute triangle can also be an equilateral triangle.
C A right triangle can also be an obtuse triangle.
D An obtuse triangle can also be an isosceles triangle.
E An acute triangle can also be an scalene triangle.
Answer is C

19. Find the area of the shaded region
6 cm
8 cm

20. ANSWER Area of Circle – Area of Rectangle A = ∏r² - lw
6 cm
8 cm
Area of Circle – Area of Rectangle
A = ∏r² - lw
A = (3.14)(5)² - (6)(8)
A =
A = 30.5 cm²

21. Find the area of the shaded region.
SQUARE ABCD has side lengths of 9.
6 cm

22. ANSWER SQUARE ABCD has side lengths of 9.
6 cm
SQUARE ABCD has side lengths of 9.
Area of Square – Area of Triangle
A = lw - ½bh
A = (9)(9) - ½(9)(6)
A = 81 – 27
A = 54 cm²

23. Rank the figures in terms of volume.

24. Answer 3rd 1st 2nd Rectangular Cylinder Triangular Prism Prism
V = lwh V = ∏r²h V = ½lwh
(6)(7)(10) (3.14)(5)(5)(10) ½(5)(10)(20)
420 cm³ cm³ cm³
3rd st 2nd