ACT ASPIRE PART 1 Geometry Theorems ACT ASPIRE

ACT ASPIRE • PART 1 Geometry • Theorems

ACT ASPIRE Write down everything you know about including specific examples about……… (1)Pythagorean Theorem (2)Triangle Inequality Theorem

FIND THE MISSING LENGTHS y Perimeter is 40 What are the 3 lengths?

Constructed Response • Do the sides 6, 7, 10 form a…… • (1) triangle • (2) right triangle • Prove it.

Constructed Response • Do the sides 6, 7, 10 form a…… • (1) triangle. YESSSSSSS • (2) right triangle. NOOOOO

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 B C D E 505 31 23 22. 5 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 B C D E 24 36 16 50 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. ANSWER is D b a

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˚

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

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 B C D E Rhombus Trapezoid Rectangle Parallelogram Square Answer is B

Multiple Choice #2 • Which of the following statements about quadrilaterals is always true? • • • A B C D E All parallelograms are similar. All squares are rhombuses. All rectangles are congruent. All trapezoids are parallelograms 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 6 cm 8 cm • • • Area of Circle – Area of Rectangle A = ∏r² - lw A = (3. 14)(5)² - (6)(8) A = 78. 5 - 48 A = 30. 5 cm²

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

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

Rank the figures in terms of volume.

Answer • Rectangular Prism • V = lwh (6)(7)(10) 420 cm³ Cylinder V = ∏r²h (3. 14)(5)(5)(10) 785 cm³ 3 rd 1 st Triangular Prism V = ½lwh ½(5)(10)(20) 500 cm³ 2 nd