Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 ( Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is an isosceles triangle. is the longest side with length. = and =. Find. 4 x x +8 8 x + 3 a. = 110 c. = 43 b. = 24 d. = 5 2. Find. L (4x + 7)º K (6x - 9)º 118º M N a. = c. = b. = d. = 3. Given: Identify all pairs of congruent corresponding parts. M O N

2 a.,,,,, b.,,,,, c.,,,,, d.,,,,, 4. Using the information about John, Jason, and Julie, can you uniquely determine how they stand with respect to each other? On what basis? Statement 1: John and Jason are standing 12 feet apart. Statement 2: Julie is standing 31º NW of Jason. Statement 3: John is standing 49º SW of Julie. a. No. There is no unique configuration. b. Yes. They form a unique triangle by SS. c. Yes. They form a unique triangle by S. d. Yes. They form a unique triangle by SSS. 5. etermine if you can use the HL ongruence Theorem to prove. If not, tell what else you need to know. P ^ ^ Q a. Yes. b. No. You do not know that and are right angles. c. No. You do not know that. d. No. You do not know that. 6. pilot uses triangles to find the angle of elevation from the ground to her plane. How can she find m? km 20 km O 20 km 12 km a. by SS and by PT, so m by substitution. b. by PT and by SS, so m by substitution. c. by S and by PT, so m by substitution. d. by PT and by S, so m by substitution.

3 7. Which of the following is not a positioning of a right triangle with leg lengths of 4 units and 5 units? a. y c. y x x b. 8 y d. 8 y x x Two Seyfert galaxies, W Tauri and M77, represented by points and, are equidistant from Earth, represented by point. What is m? 115 a. m = c. m = b. m = d. m = 9. Find.

4 ) ) s s 10 ) a. = 10 b. = 12 c. = 14 d. Not enough information. n equiangular triangle is not necessarily equilateral. 10. Given: diagram showing the steps in the construction Prove: omplete the paragraph proof. Proof: The same compass setting was used to create,, and, so [1]. y the [2], is equilateral. Since is equilateral, it is also [3]. So. Therefore,. a. [1] [2] definition of equilateral triangle [3] equiangular b. [1] [2] definition of equiangular triangle [3] equiangular c. [1] [2] definition of equilateral triangle [3] isosceles d. [1] [2] definition of angle bisector [3] acute 11. Each pair of suspension lines on a parachute are the same length and are equally spaced from the center of the chute. To turn, the sky diver shortens one of the lines. How does this help the sky diver turn?

5 a. Shortening one line moves the sky diver away from the perpendicular bisector of. This turns the sky diver toward the direction of the shortened line. b. Shortening one line moves the sky diver closer to the perpendicular bisector of. This turns the sky diver toward the direction of the shortened line. c. Shortening one line moves the sky diver away from the perpendicular bisector of. This turns the sky diver toward the direction of the longer line. d. Shortening one line moves the sky diver closer to the perpendicular bisector of. This turns the sky diver toward the direction of the longer line. 12. Given with,, and, find the length of midsegment. = 6 X Y = 5 3 a. XY = 3 c. XY = 2.5 b. XY = 1.5 d. XY = Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as shown in the diagram. What is the width of the reservoir ( across the base)? 120 m X 120 m 150 m 100 m Y 100 m a. 300 m c. 75 m b. 150 m d. 100 m 14. Tell if the measures 6, 14, and 13 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse. a. Yes; acute triangle c. Yes; right triangle b. Yes; obtuse triangle d. No. 15. Find all the values of k so that,, and are the vertices of a right triangle. a. c. b. d. 16. Find the value of x. Express your answer in simplest radical form.

6 5 x x a. c. x = b. x = d. x = x = 17. Find the measure of each exterior angle of a regular decagon. a. 45 c. 18 b d Write a two-column proof. Given: F and F are parallelograms. Prove: F omplete the proof. Proof: Statements Reasons 1. F and F are parallelograms. 1. Given [1] Opposite sides in a parallelogram are parallel [2] Substitution a. [1] In a parallelogram, opposite angles are congruent. [2] lternate Interior ngles Theorem b. [1] Vertical ngles Theorem [2] lternate Exterior ngles Theorem c. [1] PT [2] In a parallelogram, opposite angles are congruent. d. [1] In a parallelogram, consecutive angles are congruent. [2] In a parallelogram, all angles are congruent. 19. n artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are inches and inches. Find.

7 X a. = 7 inches c. = 5 inches b. = 10 inches d. = 14 inches 20. The side of a wooden chest is a quadrilateral with. If m, what is the most accurate description of? a. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a rectangle. b. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a square. c. oth pairs of opposite sides are parallel so is a rhombus. Since one angle measures 90, it is a right angle and a rhombus with one right angle is a square. d. oth pairs of opposite sides are parallel so is a parallelogram. One angle measuring 90 does not provide enough information to change its description. 21. n artist used perspective to draw guidelines in her picture of a row of parallel buildings. How many centimeters is it from Point to Point? 4 cm F 3 cm H 5 cm a. 1 cm c. 4 cm

8 b cm d. 2.4 cm 22. tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a 16-foot shadow. How tall is the tree, rounded to the nearest foot? a. 45 feet c. 42 feet b. 36 feet d. 7 feet 23. The figure shows the position of a photo. Which of the following is the drawing of the photo after a dilation with scale factor? 5 5 a. 5 c. 5 ' ' ' ' ' ' 5 ' ' 5 b. 5 d. 5 ' ' ' ' ' ' 5 ' ' Find the geometric mean of the pair of numbers 2 and 8. a. 8 c. 5 b. 16 d. 4

9 25. To estimate the height of a radio tower, Jody steps 25 feet away from the center of the tower s base, until his line of sight to the top of the tower and his line of sight to the center of its base form a right angle. His eyes are 6 feet above the ground. How tall is the radio tower to the nearest foot? 25 ft Jody 6 ft a. 98 feet c. 110 feet b. 104 feet d. 31 feet 26. Find GI and GH to the nearest hundredth. LK is 3.20 cm and LJ 3.67 is cm. G J M L H K I a. GI = cm; GH = 8.57 cm c. GI = cm; GH = cm b. GI = cm; GH = cm d. GI = cm; GH = 9.40 cm 27. Write the trigonometric ratio for cos Y as a fraction and as a decimal rounded to the nearest hundredth. Y 15 9 X 12 Z a. cos Y = c. cos Y = b. cos Y = d. cos Y = 28. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15. To the nearest hundredth of a foot, find the length of the ramp.

10 a feet c feet b feet d feet 29. Find. Round to the nearest tenth a. = 17.5 c. = 16.6 b. = d. = Three circular disks are placed next to each other as shown. The disks have radii of 4 cm, 5 cm, and 6 cm. The centers of the disks form. Find m to the nearest degree. 5 4 Y X 6 Z a. m = c. m = b. m = d. m = 31. Write the vector in component form. a. c. b. d. 32. stunt airplane travels at N 62 E at a constant speed of 400 mi/h. There is a 20 mi/h wind blowing due west. What is the plane s actual speed? Round to the nearest tenth. a mi/h c mi/h

11 b mi/h d mi/h 33. Identify the secant that intersects. l a. c. b. l d. 34. satellite rotates 50 miles above Earth s atmosphere. n astronaut works on the satellite and sees the sun rise over Earth. To the nearest mile, what is the distance from the astronaut to the horizon? (Hint: Earth s radius is about 4,000 miles.) a. 634 mi c. 630 mi b. 402,500 mi d. 397,500 mi 35.. Find. (3x + 2)º X W Y (4x 3)º Z a. = c. = b. = d. = 36. Find m. 35º 115º a. m = c. m = b. m = d. m = 37. Given m, m, and m, find m(arc).

12 G F a. m(arc) = c. m(arc) = b. m(arc) = d. m(arc) = 38. Write the equation of a circle with center M(7, 10) and radius 2. a. c. b. d. 39. Meteorologists are planning the location of a new weather station. To optimize radar coverage, the station must be equidistant from three cities located at,, and. What are the coordinates where the station should be built? a. c. b. d. 40. onvert to rectangular coordinates. a. c. b. d.