4c. The angles of a triangle are in the ratio 4:5:9. Find the measure of the smallest angle.

Transcription

1 GEOMETRY SEM 2 FINAL EXAM REVIEW 1 Name: Hour: SC31: I can identify a dilation as a reduction or enlargement. I can determine the scale factor of a dilation. 1. Which choice below correctly identifies the dilation and scale factor? 14 (A) reduction; k = (C) reduction; k = (B) reduction; k = (D) enlargement; k = (E) enlargement; k = 36 SC31: I can use the scale factor of a dilation to solve problems. 2. The dilation has center E. Find the values of x and y. (A) x = 7.5, y = 21 (B) x = 10, y = 15 (C) x = 6, y = 3.5 (D) x = 7.5, y = 14 SC32: I can use ratios to set up a proportion and solve for a missing value. 3. The ratio of the side lengths of ΔOMN to ΔHGI is 4:3. Find x and y. Round to nearest tenth. x = y = SC32: I can use ratios to set up an equation and solve for a missing value. 4a. The area of a rectangle is 160ft 2. Its width to length ratio is 2:5. What is its length? 4b. The perimeter of a rectangle is 100m. Its width to length ratio is 3:7. What is its width? 4c. The angles of a triangle are in the ratio 4:5:9. Find the measure of the smallest angle.

2 SC33: I can state the properties of similar polygons. I can use the properties of similar polygons to solve problems. 5. The triangles are similar. Which choice below is NOT a correct statement? (A) B F (B) ΔBAC~ΔFDE (C) BA FE BC FD (D) AC BC DE FE (E) A D SC33: I can state the relationship between the scale factor of similar polygons and the ratio of their perimeters or areas. 6a. If the scale factor of two similar pentagons is 4:7, what is the ratio of their perimeters and the ratio of their areas? 6b. If the ratio of the perimeters of two similar trapezoids is 3:5, what is the ratio of their sides and the ratio of their areas? 6c. If the ratio of the areas of two similar triangles is 4:9, what is the ratio of their perimeters and the ratio of their sides? SC34: I can name the shortcuts used to prove triangles are similar. I can use the triangle similarity shortucts to determine whether triangles are similar. 7. Which of the following statements is not true? (A) ΔABC ~ ΔEDC by SAS~ (B) ΔABC ~ ΔEDC by AA~ (C) ΔABC ~ ΔEDC by SSS~ (D) ΔCDE ~ ΔCBA by SAS~ SC35: I can appropriately apply the side-splitter theorem. 8. Find x and y. Round to nearest tenth. x = y =

3 SC37: I can classify triangles as acute, right, or obtuse. 9. Which set of numbers can represent the side lengths of an acute triangle? (A) 6, 6, 10 (B) 6, 10, 10 (C) 0.6, 0.8, 1.0 (D) 8, 4, 6 SC36-40: I can use methods like geometric means, Pythagorean theorem, special right triangles, and trigonometry to solve right triangles. 10a. Find the length of CD. Round to nearest tenth. 10b. Find the length of CB. Round to nearest tenth. 11. Find the value of x. Round answer to nearest tenth. 12. Find the values of x and y. Express answers in simplest radical form. x= (a) y= x= (b) y= SKIP 13. Find the sine of <T. Round to four decimal places. 14. Find x.

4 15. Find the measure of <R. SC41: I can use the Law of Sines to solve for sides or angles of oblique triangles. 16. Use the Law of Sines: a b c sin A sin B sin C to solve for the indicated values below. (a) Find the length of AB (b) Find the m<b. 17. Use the Law of Cosines: c 2 = a 2 + b 2 2ab(cos<C) to solve for the indicated values below: (a) Find the length of AB (b) Find x SC42: I can write the equation of a circle. 18. Write the equation of a circle with the given information: (a) center at (-2,4) and radius 3cm. (b) center at (3,-1) and diameter 18in. (c) center at (-1,1) and point on circle at (-1,-3). (d) center at (2,2) and point on circle at (-1,6).

5 SC42: I can determine if a point is on the circle, inside the circle, or outside the circle. 19. Given the equation (x 4) 2 + (y + 7) 2 = 36, determine if the given points are on, inside, or outside the circle. (a) (3,3) (b) (-2,-7) (c) (2,-2) SC43: I can use properties of arcs and angles to solve problems. 20. Find. 21. If = 300, find the value of y. SC44: I can use the properties of inscribed quadrilaterals to solve problems. 22. Find the measure of <F. SC45: I can use properties of angles with the vertex inside and outside the circle to solve problems. 23. Find the measure of <1 in the diagram. 24. Find the measure of <1 in the diagram. SC46: I can name and identify segments and lines in a circle. 25. Use the diagram to identify the following: (a) (b) (c)

6 SC47: I can use properties of chords, secants, and tangents to solve problems. 26. Find the value of x. (a) (b) (c) SC48: I can find an arc length. 27. Find the length of. SC48: I can find the area of a sector of a circle. 28. Find the area of the shaded region. SC49: I can find the sum of the interior and exterior angles of a polygon. I can find the measure of each interior and exterior angle of a polygon. 29. Find the value of x.

7 30. Find the value of x. SC50: I can find the area of a regular polygon given apothem, side length, or radius. 31. Find the area of the following polygons: (a) A regular octagon with apothem 9cm (b) A regular nonagon with side length 12in (c) A regular hexagon with radius 8ft SC51: I can name polyhedron. 32. Name the following polyhedron. (a) (b) SC52: I can calculate the surface area of prisms and cylinders. SC53: I can calculate the surface area of pyramids and cones. 33. Find the surface area of the cylinder. 34. Find the surface area of the reg pyramid.

8 SC54: I can calculate the surface area of a sphere. SC56: I can calculate the volume of a sphere. 35. Use the sphere to calculate the following: (a) surface area of sphere (b) volume of sphere SC55: I can calculate the volume of prisms, cylinders, pyramids, and cones. 36. Find the volume of the prism. 37. Find the volume of the cone. SC57: I can calculate the probability of events. 38. What is the probability of rolling a number greater than 3 on a cube? SC 58: I can calculate the probability of a mutually exclusive or non-mutually exclusive event. 39a. In a class of 30 students, 8 of the students received an A on the last test and 12 of the students received a C. What is the probability that a randomly chosen student received an A or a C? 39b. Jalen rolls a six sided number cube (a dice). What is the probability that the number rolled is a 3 or a number greater than 2? SC 59: I can determine if an event is independent or dependent. I can calculate the probability of an independent or dependent event. 40a. A coin is flipped and a card is drawn from a standard deck of cards. What is the probability of getting heads and a red face card? 40b. A bag contains three green marbles and four black ones. What is the probability of selecting a black marble (no replacement) and another black marble?

9 ANSWERS 1. B 2. D 3. x = 13.3 y = a. 20ft 4b. 15m 4c C 6a. 4:7 and 16:49 6b. 6c. 7. C 8. x= B 10a b :5 and 9:25 2:3 and 2:3 y= a. x = 10 y = b. x = 24 y = a. 6 b a. 6.7 b a. (x + 2) 2 +(y 4) 2 = 9 b. (x 3) 2 +(y + 1) 2 = 81 c. (x + 1) 2 +(y 1) 2 = 16 d. (x 2) 2 +(y 2) 2 = a. Outside b. On c. Inside 25. a. Tangent b. Secant c. Chord 31. a sq cm b sq in c sq ft π = cubic in a. 3 b c a. Triangular Prism b. Hexagonal Pyramid cm sq ft sq 324π cm = sq cm 35. a. 7.8π = 24.6 sq m b. 3.7π = 11.5 cubic m cubic in % 39a. 67% 39b. 67% 40a. 6% 40b. 29%