Jan15 Final Packet - WordPress.com · 1/1/2016 · 9) Look$at$number$3.$What$types$of$...
Transcript of Jan15 Final Packet - WordPress.com · 1/1/2016 · 9) Look$at$number$3.$What$types$of$...
GEOMETRY STUDY PACKET The following problems will help you to prepare for the Geometry Final Exam. Please take them seriously, as this final may have a serious impact on your Q2 grade. Your notebook will be a great friend to you as you work the problems, as well as the internet, your textbook and your actual friends. I can’t wait to see how well you will do! J Annotate and markup questions on this paper. Answer these questions on a separate sheet of paper. If you are finished with this packet before Tuesday (1/21) morning’s class, you will be in the best shape to ask
questions during the review. Your final will be Wednesday, January 23rd.
1) Name the image of R under a reflection in line m.
2) Name the planes intersecting plane BAGF.
3) Carly is planning to create a pattern of rockets along the ceiling in her daughter’s bedroom using a stencil. She wants all of the rockets to look exactly the same. What type of congruence transformation should she use? Why?
4) Circle the shapes that have rotational symmetry (A shape has Rotational Symmetry when it still looks the same after a rotation less than 360*.)
5) Define in your own words: a. Plane symmetry:
b. axis symmetry: c. What kinds of symmetry does this shape have?
6) Ray AP is an angle bisector of ∠𝑀A𝑄. The 𝑚∠𝑃A𝑄 = 4𝑥 + 1. Write an expression that represents 𝑚∠𝑀A𝑄.
7) Draw a reflection over line l
8) Define line symmetry: Does this shape have line symmetry? Why or why not?
9) Look at number 3. What types of symmetry does this figure have?
10) Fill in the missing reason.
11) A reflection is a slide, flip, turn, or shift?
12) If the slope of 𝑃𝑄 𝑖s !! and the slope of 𝑄𝑅 𝑖𝑠− !
!, find
the slope of 𝑆𝑅 so that PQRS is a parallelogram.
13) Find the sum of the measures of the interior angles of a convex 48-‐gon
14) Determine if the following is always true or if it is possible that it is false. Give a reason. Given: Point B is the interior of ∠𝐴𝐷𝐶. Conjecture: ∠𝐴𝐷𝐵 = ∠𝐵𝐷𝐶
a. False; 𝑚∠𝐴𝐷𝐵 + 𝑚∠𝐵𝐷𝐶 = 90° b. True c. False; just because its in the interior does not mean it is on the bisecting line
d. False; 𝑚∠𝐴𝐷𝐵 may be obtuse 15) Is it possible to form a triangle with side lengths 10, 6, 16? Why or why not?
16) Determine if the following is always true or if it is possible that it is false. Give a reason.
Given: Two angles are supplementary. Conjecture: They are both acute angles.
a. False; either both are right or one is obtuse. b. False; either both are right or they are adjacent. c. True d. False; they must be vertical angles.
17) Draw a smiley face
18) Find the coordinates of the intersection of the diagonals of parallelogram PRYZ with vertices P(2,5), R(3,3), Y(-‐2,-‐3), Z(-‐3,-‐1)
19) Is this a parallelogram? Why or why not?
20) Find a and b
21) This is made out of 6 congruent ____________________ (fill in the most specific shape name).
22) Are the pools similar? Why or why not?
23) A tall building casts a 156-‐foot shadow. A nearby lamppost that measures 12 feet 4 inches casts a 20-‐ foot shadow. Write a proportion that can be used to determine the height of the building. What is the height of the building?
24) Solve for x and y. !!𝑦 + 3 and !
!𝑦 + 6 are
corresponding angles.
25) Are the triangles similar? Write a similarity statement if yes.
26) What is x?
27) On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The distance from Wilmington to Ash Grove along Kendall is 1030 feet and along Magnolia, 900 feet. If the distance between Beech and Ash Grove along Magnolia is 400 feet what is the distance between the streets along Kendall?
28) JH is a midsegment of △ 𝐾𝐿𝑀. Define midsegment, then find x.
29) One ounce of swiss cheese contains 11 grams of fat. Five of the grams of fat are saturated fat. Find the ratio of saturated fats to total fat in an ounce of cheese.
30) Which triangles are similar and why?
31) This is a dilation from A to B. Is it an enlargement or a reduction? What is the scale factor?
32) Write a similarity statement between three similar triangles in the diagram.
33) Find x using two different methods.
34) Find x.
35) Find the length of the legs of a 45° − 45° − 90° triangle with a leg of 54 centimeters.
36) An equilateral triangle has an altitude of 91 feet. Determine the length of a side of the triangle.
37) Find sin L, cos L, tan L, sin M, cos M, tan M, sin N, cos N, and tan N. l = 20, m = 21, n = 29
38) Diego used a precision instrument to map a region of land for his class in geomorphology. To determine the elevation of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 36 meters and the angle was 21°. What is the height of the formation to the nearest meter?
39) Name the angle of depression and then the angle of elevation in the figure
below.
40) To find the distance from the edge of the lake to the tree on the island in the lake, Mabel set up a triangular configuration as shown in the diagram. The distance from location A to location B is 78 meters. The measures of the angles at A and B are 49° 𝑎𝑛𝑑 73°, respectively. What is the distance from the edge of the lake at B to the tree on the island at C?