Geometry B Midterm REVIEW

Transcription

1 Geometr Midterm REVIEW Name HR: 1. The measures of the angles of a triangle are in the etended ratio 2 : 3 : 7. What is the measure of the largest angle? 2. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 136 feet, what is the length of the rectangle? 3. What is the solution of the proportion?. If, then =. 5. The polgons are similar, but not necessaril drawn to scale. Find the value of re the polgons similar? If the are, write a similarit statement and give the scale factor. S V T R 15 29º W 29º U 33 Not drawn to scale. 7. re the polgons similar? If the are, write a similarit statement and give the scale factor. 10 N 1.2 K D 10 M 1.2 L Not drawn to scale.

2 . The polgons are similar, but not necessaril drawn to scale. Find the value of. 9. ampsites F and G are on opposite sides of a lake. surve crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. 62 m 10. re the triangles similar? How do ou know? State whether the triangles are similar. If so, write a similarit statement and the postulate or theorem ou used.

3 ) 12. Michele wanted to measure the height of her school s flagpole. She placed a mirror on the ground feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her ees were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. 13. Find the geometric mean of the pair of numbers. 22 and 1. What similarit statement can ou write relating the three triangles in the diagram? T U V W 15. What are the values of a and b? ) 5 3 a b 16. Find the length of the altitude drawn to the hpotenuse. The triangle is not drawn to scale. 6 2

4 17. Kristen lives directl east of the park. The football field is directl south of the park. The librar sits on the line formed between Kristen s home and the football field at the eact point where an altitude to the right triangle formed b her home, the park, and the football field could be drawn. The librar is 2 miles from her home. The football field is miles from the librar. Park Home Librar 2 miles miles Football field a. How far is librar from the park? b. How far is the park from the football field? 1. What is the value of? > > > What is the value of, given that? P 12 Q What is the value of to the nearest tenth? )) )) 12.2 Not drawn to scale.

5 21. Find the length of the missing side. The triangle is not drawn to scale Find the length of the missing side. Leave our answer in simplest radical form. 13 ft 10 ft Not drawn to scale 23. triangle has sides of lengths 2, 13, and 15. Is it a right triangle? Eplain. 2. Find the value of the variable(s). If our answer is not an integer, leave it in simplest radical form Not drawn to scale 25. In triangle, is a right angle and 5. Find. If our answer is not an integer, leave it in simplest radical form. 10 ft Not drawn to scale 26. Find the length of the hpotenuse

6 27. Find the value of and rounded to the nearest tenth The students in Mr. ollin s class used a surveor s measuring device to find the angle from their location to the top of a building. The also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. uilding 90 ft 29. Write the ratios for sine, cosine, and tangent for. (Not drawn to scale) P 17 R 15 Q 30. Find the value of. Round to the nearest tenth. (Not drawn to scale) Find the value of to the nearest degree. (Not drawn to scale) 15 9

7 32. Use a trigonometric ratio to find the value of. Round our answer to the nearest tenth. 33. large Not totem drawn pole to scale in the state of Washington is 100 feet tall. t a particular time of da, the totem pole casts a 29-foot-long shadow. Find the measure of to the nearest degree. 100 ft 29 ft 3. What is the description of as it relates to the situation shown? n airplane pilot over the Pacific sights an atoll at an angle of depression of 5. t this time, the horizontal distance from the airplane to the atoll is 629 meters. What is the height of the plane to the nearest meter? 629 m Not drawn to scale 36. Use the Law of Sines to find the missing angle of the triangle. Find to the nearest tenth

8 37. Use the Law of Sines to find side b of the triangle. 50 b 5 3. Use the Law of osines to find the missing angle. Find, given a = 12, b = 17, and c = Use the Law of osines to find the missing angle. In, g = 5 ft, h = 22 ft, and = 50. Find the measure of f. Round our answer to the nearest whole number. 0. What is a rule that describes the translation? ' ' D D' '

9 1. Find the translation rule that describes the translation E. E D 2. Describe in words the translation of X represented b the translation rule. 3. For each triangle graph its reflection image over the -ais? The vertices of a triangle are P( 2, ), Q(2, 5), and R( 1, ). Name the vertices of.

10 5. The heagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. Find. R F G Q H P O I N J M L K 6. a. Graph the quadrilateral WXYZ with vertices W(3, 5), X(1, 3), Y( 1, 5), and Z(1, 7). b. Graph and state the coordinates of the vertices. 7. Find P l m n. What is true about the reflection lines when the composite isometr results in each of the following?. reflection. rotation

11 9. Find the glide reflection image of the black triangle for the composition omplete the sequence of rigid motions... E D F P 51. The dashed-lined figure is a dilation image of EFGH. Is an enlargement or a reduction? What is the scale factor n of the dilation? E F H G

12 52. What are the vertices of for? Graph. O 53. Graph (EFGH) E F H G What composition of rigid motions and a dilation maps EFGH to the dashed figure? 6 E 2 F G 12 H 2 6