Geometry PreAP Spring Final Exam Review 2017

Transcription

1 Name Period Date Geometry PreAP Spring Final Exam Review 2017 Topic 1: Similar Figures 1) What does it mean for two polygons to be similar? 2) Use the definition from #1 to determine whether or not the figures are similar. Explain why or why not. a) b) c) d) e) Determine whether ABC DEF. Justify your answer. f) Determine whether trapezoid ABCD trapezoid SPQR. Justify your answer. 3) For triangles, there is a shortcut called the AA Similarity Shortcut. Define the AA Similarity Shortcut.

2 Use the AA similarity shortcut to identify similar triangles and explain why they are similar. 4) 5) Identify the similar figures and use them to find the indicated information 6) 7) 8) In shown below, L is the midpoint of, M is the midpoint of, and N is the midpoint of. 9) If,, and, find the perimeter of trapezoid MNCB. 10) ABC XYZ, AB = 12, AC = 16, BC = 20, and XZ = 24. Find the perimeter of XYZ. 11) Find CD.

3 12) If ABC XYZ, find y. 13) The ratio of the measures of the sides of a triangle is 2:5:6. If the length of the longest side is 48 inches, find the perimeter. 14) ABC DEF, AB = 8, BC = 13, AC = 15, and DF = 20. Find the perimeter of DEF. 15) Identify the similar triangles and find the value of x 16) A radio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long. How tall is the radio tower? 17) On a sunny day, Bill wants to find the height of a tree. He walks 25 feet along the tree s shadow when he reaches its end. At the same time, his own shadow measures 9 feet. Bill is 6 feet tall. How tall is the tree? 18) Sandy is trying to measure the height of a nearby flagpole using a mirror. The mirror is 6 meters from the flagpole. When Sandy is 2 meters from the mirror, she can see the top of the flagpole in the center of the mirror. The height to her eyes is 1.57 meters. How tall is the flagpole? Topic 2: Right Triangles (Pythagorean Theorem, Special Right Triangles, and Trigonometric Ratios) For problems 19-21, find the value of x. Give your answer in simplest radical form. 19) 20) 21)

4 For problems 22-27, use special right triangle ratios to find the indicated values. 22) Find the value of x. Express your answer in simplest radical form. 23) Find the value of x 24) Find the value of x and y and use it to find the perimeter of the triangle. Express your answer in simplest radical form. 25) Find the value of x and y. 26) Find the value of x. 27) Find the value of x and y. Trigonometric Ratios 28) Find the indicated ratio. a) sin L 29) Use inverse trig functions to find m L and m M based upon the figure in problem 31. b) cos L c) tan M In problems 30-32, find all missing angle measures and side lengths for each triangle below 30) 31) 32)

5 For problems 33 35, find the value of x. 33) 34) 35) Trig Word Problems 36) The glide slope is the path a plane uses while it is landing on a runway. The glide slope usually makes a 3 degree angle with the ground. A plane is on the glide slope and is 1 mile (5280 feet) from touchdown. Determine the plane s altitude, to the nearest foot. 37) A road has a grade of 28.4%. This means that the road rises 28.4 ft over a horizontal distance of 100 ft. What angle does the hill make with a horizontal line? Round to the nearest degree. 38) Pet ramps for loading larger dogs into vehicles usually have slopes between 2 and 1. What is the range of angle 5 2 measures that most pet ramps make with a horizontal line? Round to the nearest degree. 39) Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42, and the angle of depression to his friends standing below is 80. How far from the entrance are his friends standing? Round to the nearest foot. 40) Find the height of the building to the nearest foot. 41) How far is tower A from the fire to the nearest tenth of a mile.

6 Topic 3: Polygons Define the following terms: polygon, regular polygon, irregular polygon, concave polygon, convex polygon, and diagonal. You should also know the names of all polygons that have between and including 3 and 10 sides. 42) How do you determine the sum of the interior angles of a convex polygon? 43) How do you determine the sum of the exterior angles of a convex polygon? Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. 44) 45) 46) 47) For a polygon to be regular, it must be both equiangular and equilateral. Name the only type of polygon that must be regular if it is equiangular. Tell whether each polygon is regular or irregular. Then tell whether it is concave or convex. 48) 49) 50) Find each lettered angle measure. 51) 52)

7 53) One exterior angle of a regular polygon measures 10. What is the measure of each interior angle? How many sides does the polygon have? 54) The sum of the measures of the interior angles of a regular polygon is How many sides does the polygon have? 55) Complete the table below Type of Polygon Interior Angle Sum Each Interior Angle Exterior angle Sum Each Exterior Angle b) regular c) regular Solve for the requested information. 56) x (11y) 92 (10x-2) 57) Regular Polygon with two sides extended. 58) y y 154 (5x) (4z) 112 (6x-21) x = y = 144 x = y = z = x = y = Topic 4: Quadrilaterals In Exercises 59 64, ABCD is a parallelogram. 59) Perimeter ABCD = 60) AO = 11, and BO = 7. AC =, BD = 61) Perimeter ABCD = 46. AB =, BC =

8 62) a =, b = c = 63) Perimeter ABCD = 119, and BC = 24. AB = 64) Perimeter ABCD = 16x 12. AD = 65) Find each lettered angle measure. Special Parallelograms

9 69) Square with a perimeter of 56 cm. 70) Parallelogram D A E B 3x-19 x BC x m CBD 6y-18 C m AED 36 AC 7y-14 6y-2 48 z 4y+6 60 x y z Perimeter 71) Rectangle 72) Rhombus x J y L 5z+5 z x L Perimeter 3z y 32 2z+5 KL K 6z M M P O 4x x+6 N x m MLO m LMO Perimeter MP PN 73) JKLM is a parallelogram. Find each measure. 74) Determine if TUVW is a parallelogram for a = 19.5 and b = 22. a) JK = b) LM = c) m L = d) m M =

10 75) Find the values of a and b that would make the quadrilateral a parallelogram. 76) Find the values of a and b that would make the quadrilateral a parallelogram. Topic 5: Area For problems 84-89, find the area of the shaded region. 77) 78) 79) 80) 81) 82)

11 83) ABCD is a parallelogram, ABDE is a kite, AD = 18 cm, and BE = 10 cm. Find the area of ABCDE. 84) Bert s Bigtime Bakery has baked the world s largest cake. It is a rectangular sheet cake that is 600 cm by 400 cm by 180 cm high. Bert wants to apply frosting to the four sides and the top. How many liters of frosting does he need if 1 liter of frosting covers about 1200 cm 2? 85) A bundle of hardwood flooring contains 14.5 ft 2 and costs $ a) How many square feet of flooring is needed to cover the kitchen and family room? Exclude the fireplace, hearth, and tiled area. b) You should buy 5% extra flooring to account for waste. How many bundles of flooring should you buy? What will be the cost? Topic 6: Surface Area and Volume 86) Find the surface area of the rectangular prism below. 87) Find the volume of the trapezoidal prism below. Measurements are in centimeters

12 88) Find the lateral surface area (everything but the base) of the square pyramid below. 89) Find the surface area of the figure below. 15 inches 16 inches 90) Tell what kind of three-dimensional figure can be made from each of the given nets. a. b. c. 91) A child s wading pool has a diameter of 7 feet and is 2/3 of a foot deep. How many gallons of water can the pool hold? One cubic foot of water is about 7.5 gallons. Round your answer to the nearest 0.1 gallon. 93) A farmer has two similar cylindrical grain silos. The smaller silo is 25 feet tall and the larger silo is 40 feet tall. If the smaller silo can hold 1500 cubic feet of grain, how much can the larger silo hold? 92) A king-size waterbed mattress measures 5.5 feet by 6.5 feet by 8 inches deep. How much does the water in this waterbed weigh? Water weighs about 63 pounds per cubic foot 94) Earth has a surface area of about 196,937,500 square miles. Mars has a surface area of about 89,500,000 square miles. How many times longer is the radius of the earth? Round to the nearest tenth.

13 95) The height of the regular hexagonal pyramid below is 14 feet. Find the volume. 96) The circumference of the base is 12π ft. Find the total surface area of the cone. 8 feet 8 feet Topic 7: Circles 97) Find the area of the shaded region. Round to the nearest tenth. 98) The Moon s orbit is not exactly circular, but the average distance from its surface to Earth s surface is 384,000 kilometers. The diameter of the Moon is 3476 kilometers. Find the distance from the surface of Earth to the visible edge of the Moon if the Moon is directly above the observer. Round to the nearest kilometer. (Note: The figure is not drawn to scale.) 99) Find the various arcs and angle measures.

14 100) Find the arc measure below. 101) Find the angle measure below. 102) Find the measure of angle E in the quadrilateral below. 103) Find the measure of angle U in the quadrilateral below. 104) Identify the following objects: Chord: Tangent: Diameter: Secant: Radius: