ACT ASPIRE

•PART 1 Geometry•Pythagorean

Theorem

ACT ASPIRE

•Write down everything you know about right triangles

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

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 6

Answer is B

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

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

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?

ACT ASPIRE

•PART 2 Geometry•Angles

DRAW THE DIAGRAM and WRITE DOWN EVERYTHING YOU KNOW

MULTIPLE CHOICE. Find the angle measure for both a and b.

a

b

ANSWER is D

Find x and how big the angles are.

x = 23 and the angles are 69˚ and 111˚

FIND x and how big the angles are.

x = 8.75 and both angles are 45˚

Find x

x = 100˚

FIND THE MISSING ANGLE MEASUREMENTSA = 102B = 78C = 58D = 122E = 26F = 58

ACT ASPIRE

•PART 3 Geometry•SHAPES

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

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

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

Find the area of the shaded region

6 cm

8 cm

ANSWER

• Area of Circle – Area of Rectangle• A = ∏r² - lw• A = (3.14)(5)² - (6)(8)• A = 78.5 - 48• A = 30.5 cm²

6 cm

8 cm

Find the area of the shaded region.

• SQUARE ABCD has side lengths of 9.

6 cm

ANSWER

• 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

6 cm

Rank the figures in terms of volume.

Answer

• 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 785 cm³ 500 cm³

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