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# ACT Math - Triangles: Help and Review Chapter Exam

Practice Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. In the picture shown below, there are three lines marking each side of the triangle. These lines give the indication that the triangle is:

####
Question 2
2.
The isosceles triangle pictured below shows one angle measuring 40 degrees. What is the measure of angle *x*?

####
Question 3
3.
In the right triangle pictured below, what is the value of angle *x*?

#### Question 4 4. The hypotenuse of a right triangle is 30. The lengths of the two shorter sides are x and x + 10. Is this a 3-4-5 right triangle?

#### Question 5 5. Which of these could not be the side lengths of a 3-4-5 right triangle?

### Page 2

#### Question 6 6. Susan leaves her house and walks 12 miles north. Then she turns and walks x miles west. When she's done walking, the distance between her and her house in a straight line is 15 miles. How many miles did she walk west?

#### Question 7 7. What is the Pythagorean Theorem and how is it used?

#### Question 8 8. Jerry wants to buy a TV online, but the ad for the TV he wants to buy does not say what the screen size is. He knows that TV screens are measured diagonally. This image shows the length and width of the screen, so he decides to use the Pythagorean Theorem to determine the diagonal screen size. What is the screen size of the TV that Jerry wants to buy (to the nearest inch)?

#### Question 9 9. Find the shortest distance between a and b by drawing a line connecting them and using the Pythagorean Theorem.

#### Question 10 10. If the short leg of a 30-60-90 triangle is 6, approximately how long is the hypotenuse?

### Page 3

#### Question 11 11. If the hypotenuse of a 45-45-90 triangle is 31, approximately how long is the leg?

#### Question 12 12. If the leg of a 45-45-90 triangle is 19, approximately how long is the hypotenuse?

#### Question 13 13. What is the area of ABCDE, as shown in the diagram?

#### Question 14 14. What is the area of the pictured rectangle?

#### Question 15 15. Sergeant Ketchup's billiards room is 15 feet wide and 25 feet long. How many square feet is the room in total?

### Page 4

#### Question 16 16. Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

#### Question 17 17. Brad places a marker on the ground 10 ft. away from the base of a tree at a botanical garden. He walks back towards the tree until he is standing 4 ft. away from the marker, and he is 6 ft. tall. Assuming that the top of Brad's head, the top of the tree, and the marker form two simliar triangles, how tall is the tree?

#### Question 18 18. Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

#### Question 19 19. Conclude whether triangle BEN is similar to triangle MAT.

#### Question 20 20. Mary claims that the triangles below are similar by AA. Do you agree or disagree with Mary?

### Page 5

#### Question 21 21. Is triangle ABC similar to triangle DEF?

#### Question 22 22. Jeremy's goal is to jog around the neighborhood park four times. If the park has four sides and each side is 100 meters, how many meters will Jeremy jog?

#### Question 23 23. Nicole wants to frame a photograph of her daughter. If the photograph has a height of 12 inches and a width of 9 inches, calculate the perimeter of the frame needed to frame the entire photograph?

#### Question 24 24. Joan is building a fence for her triangular garden. One side of the garden is 8 feet long, the second side is 10 feet long, and the third side is 12 feet long. If fencing costs $10 per foot, how much will Joan spend on fencing for her garden?

#### Question 25 25. A flat screen television has a 50 inch diagonal and a height of 25 inches. How wide is the television?

### Page 6

#### Question 26 26. A right triangle has one leg that measures 13 centimeters, and the hypotenuse is 17 centimeters. How long is the missing leg?

#### Question 27 27. A triangle has side lengths 0.3, 0.4, and 0.5. Do these side lengths form a Pythagorean Triple?

#### Question 28 28. What type of triangle is pictured?

#### Question 29 29. What's wrong with this triangle?

#### Question 30 30. You are standing at the point (2,3) on a graph. Which point is closer: (-1,2) or (4,6)?

#### ACT Math - Triangles: Help and Review Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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