Final Review ANSWERS PERIOD:

Transcription

1 Geometry Semester 2 Final Review NSWERS NME:KRUZY S KEY TE: PERIO: You will need to show your work on another piece of paper as there is simply not enough room on this worksheet. This is due in completion on the day of your assigned final eam time. 20 points. 1. Identifying Types of Symmetry: (all boes are squares) a. Which pictures shown above demonstrate reflectional symmetry? and b. Which pictures have rotational symmetry? and c. Which pictures have translational symmetry? and and d. Show or describe the symmetry for each part a-c. has vertical line down the center has vertical line and horizontal lines down centers and 180 degree rotation has 180 rotational symmetry They can all slide to produce original picture 2. Writing Ordered Pair Rules: a. Write an ordered pair rule for a translation 3 units down and 5 units right. (, y) (+5, y-3) b. Write an ordered pair rule for a translation 1 unit left and 4 units up. (, y) (-1, y+4) c. Write an ordered pair rule for a reflection over the -ais. (, y) (, -y) d. Write an ordered pair rule for a reflection over the y-ais. (, y) (-, y) e. Write an ordered pair rule for a reflection over the line y. (, y) (y, ) Kruzich 11 - Geometry Semester 2 Final Review nswer Key 1

2 3. Find the missing sides in these triangles: 3cm e a b 30 h 8cm 15cm f g 30 c cm d a = 6 cm c = 4 3 cm e = 5 3 cm g = 9 cm b = 3 3 cm d = 4 cm f = 10 3 cm h = 18 cm 4. Find the missing sides in these isosceles right triangles: w z u v 4 2cm y 6cm 5cm u = 5 cm w = 4 cm y = 3 2 cm v = 5 2 cm = 4 cm z = 3 2 cm 5. Proof Vocabulary: escribe the difference between a postulate and a theorem. postulate is assumed true within the mathematical community. theorem is proven using deductive reasoning. 6. Fill in the missing step of the following proof. This problem checks on your understanding of algebra and the official POE names. Remember POE, Properties of Equality? Given: Prove: 1 Statement Reason Given ddition Property of Equality 3.? ?Subtraction POE Multiplication Property of Equality Symmetric Property of Equality Kruzich 11 - Geometry Semester 2 Final Review nswer Key 2

3 7. ndrena watched a bug crawl along an arc of 12 along the rim of her bike wheel. If the radius of the wheel was 3 inches, how far did the bug crawl? This is asking you to find the length of the arc L. %of circle circumference (2 3) (6 ) in in Trigonometry: Find in the following right triangles. a. b. c. 5 in 32 7 in 15in 18in 26 = = = d. guy wire is anchored 8 meters from the base of a pole. The wire makes a 62 degree angle with the ground. How long is the wire? m 9. istance Formula: Find the perimeter of with vertices ( 3,4), (2,5) and ( 6, 2). Perimeter = and it s scalene 10. rea Formulas: Find the areas of the following... a. b. rea = 160 sq in c ft 60 10in 8in Find Perimeter area = perimeter = 60 in area = 408 d. Regular Heagon e. f. ircle whose g. apothem = 4.6 in circumference side lengths = 5.9 in 30 = 12 in 20in 8in shaded area & r=6in area = area = 33 area = 36 area = in h. Find the area of an equilateral triangle with one side that is 8 inches Kruzich 11 - Geometry Semester 2 Final Review nswer Key 3

4 i. circle is inscribed inside a square. The square measures 12 cm per side. Find the area outside the circle but inside the square Surface rea: Find the S or the indicated parts for the following. a. Sphere b. ylinder c. Square ased Pyramid radius = 11 in radius = 5 in base sides = 5in height = 8 in slant height = 16in S = 484 S = 130 S = 185 d. one e. Rectangular Prism f. Sphere S = 576 diameter = 10 in S = 340 sq in Find Radius. slant height = 16 in height = 5 in length = 10 in Find width. S = 105 w = 8 r = 12 in 12. Volume Formulas: Find the Volume or the indicated parts for the following. a. Sphere b. Half of a ylinder c. Square ased Pyramid radius = 11 in radius = 5 in base sides = 5in height = 8 in height = 14in V = V = 100 V = d. 3 one Vol = 720in e. Triangular Prism height = 14 in at the right... Find Radius. V = 280 Find iameter. 5in r in d in 8in 14in f. Trapezoidal ased Pyramid g. Hemisphere V = 525 radius = 9 cm 3 V 486 cm 13. Pythagorean Theorem: a. Find. b. Find = 113 = 99 Kruzich 11 - Geometry Semester 2 Final Review nswer Key 4 15

5 c. Is this a right triangle? d. Is this a right triangle? No b/c but yes b/c e. Find. f. Find the length of the diagonal in the bo from the front upper left corner to the back lower right corner iagonal = = Similarity Ratios and alculating rea: Two triangles are similar and have side ratios 2:3. 12 a. Find the ratio of their heights. 2:3 b. Find the ratio of their medians. 2:3 c. Find the ratio of their perimeters. 2:3 d. Find the ratio of their areas. 4:9 e. 2 If the area of the larger triangle is 50in, then find the area of the smaller triangle. Smaller area = Similarity Ratios and alculating Volume: Two cylinders are similar and have a volume ratio of 8:343 a. What is the ratio of their radii? 2:7 b. What is the ratio of their diameters? 2:7 c. What is the ratio of their heights? 2:7 d. What is the ratio of their surface areas? 4:49 e. 3 If the volume of the smaller cylinder is 100cm, the find the volume of the larger cylinder. Volume larger = Kruzich 11 - Geometry Semester 2 Final Review nswer Key 5

6 16. Similarity onjectures: a. Name the three triangle similarity conjectures. b. raw a picture of each. Similarity SSS Similarity SS Similarity = 6.10 cm ' = 3.05 cm ' ' ' = 4.42 cm ' = 2.21 cm = 6.00 cm ' = 3.00 cm = 6.10 cm ' = 3.05 cm ' ' ' = 6.00 cm ' = 3.00 cm 17. Writing and Solving Proportions from Figures: a. Find. b. Find and y. X = 12 = 10 and y = ft 7ft 8ft 5ft 8ft 42ft y F c. Find the requested measurements. d. If a 16 m street light casts a 15 m ll units are in centimeters. shadow at the same time a person casts HPIE~FORTH a 4 m shadow, how tall is the person? 4.266m 6 H P 7 4 P 10 E I O EI H T R FH 22.4 RT 12.8 Kruzich 11 - Geometry Semester 2 Final Review nswer Key 6

7 18. Equations of ircles: a. Write the equation of a circle if the radius is 5 and the center is at (0, 4). ( y 4) 25 b. Write the equation of a circle if the radius is 6 and the center is at (-1, -2). ( 1) ( y 2) 36 c. If ( 5) ( y 3) 49, then find the radius and the center. Radius = 7 enter = (5, -3) d. If ( y 9) 1, then find the radius and the center. Radius = 1 enter = (0, 9) 19. The radius is 15 mm. Find the length of arc Q. There are for sure TWO arc length problems on the final!! Remember that arc measure uses degrees, but, arc length uses lengths like inches or millimeters L. %of circle circumference (2 15) (30 ) mm E O 40 Q 20. Proving Triangles ongruent: a. GIVEN: Isosceles is the altitude of PROVE: is an isosceles Given efinition of Isosceles is the altitude of = 90 = 90 Given efinition of ltitude Transitive POE HL Refleive Kruzich 11 - Geometry Semester 2 Final Review nswer Key 7

8 b. GIVEN: E is the midpoint of E PROVE: E S S S 3 different solutions possible E E E E Given E or E I is the midpoint of E Given E efinition of Midpoint E S or S E Vertical ngle onjecture 21. Finding rc Length: a. Find the arc length of SR b. Find the arc length of if the radius is 11 cm. if the radius is 17 m. 77 cm cm cm cm 9 Q R S Kruzich 11 - Geometry Semester 2 Final Review nswer Key 8

9 22. etermine the type of triangle if it has vertices at (5,4) and (7,12) and (13,6). Measure the length of each side using distance formula or by making right triangles and using Pythagorean theorem. Triangle is ISOSELES because 2 sides are equal. 68, 68, Find the area of an equilateral triangle whose sides are 6 cm each. You must draw in the height of the triangle which creates two triangles. 1 2 So height = 3 3. Therefore the area = (6)(3 3) 9 3 cm The base is a trapezoid where h = 9 cm. Find the volume of the trapezoidal based pyramid. 1 Volume (area of base)( height) Volume (10) Volume 1152cm The surface area of the rectangular prism is 430 square inches. alculate the value for the side labeled. Find the area of each surface and they must add up to Find the area of the shaded sector. 3 of total circle area rea ( 9 ) in The lengths of the corresponding sides of two similar trapezoids are in the ratio 3:7. If the area of the smaller trapezoid is 27 square inches, what is the area of the larger trapezoid? Make sure you use the ratio 9:49 for area!! (not 3:7 b/c that is ONLY used for lengths) 2 area of the larger 147in Kruzich 11 - Geometry Semester 2 Final Review nswer Key 9

10 28. guy wire from the top of a telephone pole is anchored to the ground 19.2 m from the base of the tower. The wire makes a 57 angle with the ground. To the nearest tenth of a meter, what is the length of the guy wire? 19.2 cos57 This is a trig problem so draw a picture and be sure you use cosine. w w m 29. E is similar to what triangle? Which Similarity conjecture confirms this? Similarity ONLY b/c all the angles are congruent. There is not enough information to show the sides maintain the same ratio. Kruzich 11 - Geometry Semester 2 Final Review nswer Key 10