1.) Determine whether the following numbers could be the sides of a right triangle. Show your work.

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1 4Unit 2 review Version 1 Name: Date: 1.) Determine whether the following numbers could be the sides of a right triangle. Show your work. a. 7, 25, 19 b. 17, 15, 8 2.) What is the approximate length of the missing side of a right triangle with hypotenuse of 16 cm and other side of 15 cm? A. 5.6 cm B. 31 cm C. 481 cm D cm 3.) The Mendle Farm is 40 miles east of Buzzy s Barn. Alvin s Pond is 30 miles south of Buzzy s Barn. Sketch a diagram. What is the distance from Alvin s Pond to the Mendle Farm? 4.) Given parallel lines cut by a transversal, corresponding angles are A. Equal B. Supplementary C. Complementary D. Perpendicular 5.) Will the lengths 4, 9, and 5 form a triangle? Explain why or why not. 6.) If two sides of a triangle are 6.5 and 9.4, what are the possible lengths of the third side?

2 7.) Opposite sides of equal angles in an isosceles triangle are A. Equal B. Complementary C. Supplementary D. None of These 8.) Which of the following can be lengths for a triangle? I. 5, 6, 9 II. 4, 8, 12 III. 7, 8, 17 A. I only B. II only C. III only D. I and II E. I and III 9.) Marshall and Lily want to make a triangular shaped raised flowerbed in their yard. They already have two pieces of lumber, one measuring 8 feet long, and the other 12 feet long. What are the possible lengths of the third piece of lumber they will need for the bed s frame? Explain why.

3 10.) For each diagram calculate the value of x. Show your work and include an explanation of what you used (definitions and theorems) to solve the problem. Justify your work.

4 11.) Look at the following diagrams to the right. a. What is the? b. What is the value of x in the triangle? c. What is the value of y in the diagram showing vertical angles? d. What is the value of x in the triangle?

5 12.) Find the specified quantity. If not possible, state why. Show your work. a. Calculate the value of y. b. Calculate the value of x. c. Calculate the value of y. d. Calculate the value of x. 14.) Calculate the value of x.

6 15.) Identify the kinds of angles in each diagram and state whether the angles are equal or supplementary. 16.) If possible, draw a pair of angles that satisfy each condition. If such a figure is impossible, show and explain why. a. supplementary and equal b. vertical and adjacent c. adjacent and complementary d. vertical and acute 17.) In the problems below, name the kind of angle and/or the name of the angle relationship for the given angle(s). Consider complementary, supplementary, obtuse, right, acute, vertical, exterior, adjacent, corresponding, and alternate interior. Note that you are NOT being asked to calculate any angle measures; rather, the problem simply tests your ability to "speak the language" of the unit.

7 18.) Select all that apply: Two angles are complementary if A. They are equal. B. They sum to 90. C. They sum to 180. D. They are perpendicular. 19.) are angles. A. Corresponding B. Vertical C. Supplementary D. None of these 20.) The is A. 19º B. 20º C. 85º D. 95º 21.) The value of x is A. 65º B. 48º C. 13º D. 142º E. None of these

8 22.) The point A( 4, 1) is rotated 90º clockwise about the origin. The coordinate of A' is A. A'(1, 4) B. A'(1, 4) C. A'(4, 1) D. A'( 1, 4) E. None of these 23.) The formula to calculate the area of a parallelogram is A. B. C. bh D. a 2 + b 2 = c 2 24.) For each angle below, calculate the measure of the angle's complement.

9 25.) Calculate the area of each of these figures. Show your work. 26.) Calculate the area of each figure. Show your work.

10 27.) What is the area of each of the shaded region and the figure in part (c)? Show all sub problems and/or dissections. 28.) Find the area of this figure. Show your dissections and any sub problems you use. 29.) What is the perimeter and area of this figure? Show your work. 30.) What is the area of the shaded region in the figure at right? A. 1 B. 2 C. 4 D. 6 E. None of these

11 32.) For each diagram draw a height to the labeled base and label it 6'' long. Find the area of the figure. 33.) Solve for x in each of these figures. a. b. A square with an area of 1487 sq. cm. c. A rectangle with a perimeter of 84 inches. 34.) What is the area and perimeter of this figure? Show your work.

12 35.) What is the area of the shaded region at right? Show your dissections or sub problems. 36.) a. Graph each equation by the method of your choice: y = 2x + 6 and y = 3x + 6. b. What is the area of the triangle formed by the two lines and the x-axis? Show your work. 38.) The area of the trapezoid shown to the right is found by A. B. C. D. E. None of These 39.) Solve for x.

13 40.) The perimeter of ΔABC is 56 cm. The length of AB is A. 5 cm B. 16 cm C. 18 cm D. 20 cm E. None of these 42.) Use the Pythagorean theorem to show whether or not the given lengths of the sides are correct. 43.) Calculate the value of x. a. b.

14 45.) Find the maximum and minimum values for x. 47.) Sketch a height to each indicated base. a. b. c. 49.) The hypotenuse of ΔXYZ is A. XY B. XZ C. YZ D. None of these 50.) = A. 45º B. 90º C. 180º D. Cannot be determined

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