Web viewFind missing side lengths and angle measures of congruent polygons. 4.3. ... Word. Definition & picture. ... Exactly four angles of a hexagon are congruent

Geo C - Final Exam – Study Guide & Review Packet

Triangle Congruence and ProofsObjective: You will be

asked to… Section Problem # Note to Self

1.

Classify polygons 1.6 1-42 Find the measure of

interior and exterior angles of polygons.

6.1 5-12

3.

Name congruent polygons. 4.3 13-164.

Find missing side lengths and angle measures of congruent polygons.

4.3 13-16

5.

Use SSS and SAS to show that triangles are congruent.

4.4 17-23

6.

Use ASA and AAS to show that traingles are congruent

4.5 17-23

7.

Use algebra to write two column proofs.

2.6 248.

Use triangle congruency theorems to write two column geometric proofs.

2.8 24

TransformationsObjective: You will be

asked to…Sectio

nProblem

# Note to Self1. identify transformations as

reflections, rotations, translations

4.725

2. reflect points over a line 9.1 26-32

3. describe a reflection and find the line of reflection 9.1 26-32

4. translate points if given vector notation or function notation

9.226-32

5. describe a translation using vector notation or function notation

9.226-32

6. rotate points (90, 180, or 270 degrees) around the origin

9.326-32

7. describe a rotation 9.3 26-32

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SimilarityObjective: You will be

asked to…Sectio

nProblem # Note to Self

1. write and solve proportions 7.1 34-37

2. use proportions to identify similar polygons 7.2 34-37

3. solve problems using the properties of similar polygons

7.234-37

4. identify similar triangles 7.3 40-43

5. solve problems using similar triangles 7.3 40-43

Right TrianglesObjective: You will be

asked to…Sectio


1. use 45-45-90 right triangles to solve problems 8.3 45-48

2. use 30-60-90 right triangles to solve problems 8.3 45-48

3. dilate a figure using a given scale factor and center of dilation

9.633

4. predict and apply the relationship between the scale factor and side lengths

9.644

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AreaObjective: You will be

asked to…Sectio


1. identify and use parts of circles 10.1

60-61

2. find the measure of central angles and arcs 10.1 55

3. calculate the area of parallelograms and triangles 11.1 49-50, 52

4. calculate the area of trapezoids, kites, and rhombi

11.251

5. calculate the circumference and area of circles 11.3 53-54

6. calculate the area of sectors 11.3 55

7. calculate the area of regular polygons 11.4 56

8. calculate the area of composite figures 11.4 57, 62

9. use ratios to calculate the perimeter and area of similar figures

11.558-59

3-D FiguresObjective: You will be

asked to…Sectio


1. calculate the lateral area and surface area of a prism

12.263, 65

2. calculate the lateral area and surface area of a cylinder

12.267, 73

3. calculate the lateral area and surface area of a pyramid

12.364, 68, 70

4. calculate the lateral area and surface area of a cone 12.3 69

5. calculate the volume of a prism 12.4 63, 66

6. calculate the volume of a cylinder 12.4 67, 73

7. calculate the volume of a pyramid 12.5 64, 68, 70

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8. calculate the volume of a cone 12.5 69

9. calculate the surface area of a sphere 12.6 71, 72

10.calculate the volume of a sphere 12.6 71, 72

To Help You Review Practice problems are in this packet. Review past tests and quizzes to find areas where you need improvement Raise specific questions or ask to see specific problems during the review As part of the review, we will go over problems that students request (as time permits). Review the attached study and test-taking tips

Study Tips1. Get help ASAP. Do not wait until the day before an assessment to see the

teacher for extra help. If you show up with questions regarding 12 different topics, and there are several other students seeking help, you might not be able to get all your questions cleared up.

2. Do not wait until the night before to start studying. If you wait, you might not be able to ask your teacher for help if you have trouble. The more prepared you are, the less stress you should feel during the assessment.

3. Complete any practice tests. These are found in most textbooks. If no practice test is available, try a few problems from each relevant section/topic. Try them under test conditions (no notes, quiet environment, set amount of time). Check your answers with the back of the book. Bring SPECIFIC questions to your teacher.

4. Try the teacher’s examples on your own. Check and compare your work to the teacher’s solutions from the notes. Bring SPECIFIC questions to your teacher.

5. Review notes for all sections and topics. Be sure you understand the definitions, rules, formulae, processes, strategies, and examples. Bring SPECIFIC questions to your teacher.

6. Make and study flashcards. Include:

Subject of Card Front BackVocabulary Word Definition & picture

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Theorems / Postulates Name Wording & pictureProperties Name Wording & exampleFormulae Formula What each variable

representsNecessary units of measure

Process What the type of problem is called or what it looks like

Steps on how to solve it (put in your own words, if desired)

Strategies Topic of problem Strategies talked about in class

Common errors Topic of problem Things to watch out for

7. Avoid some stress: On the day of the assessment, do not talk to other students about it unless you think they can clarify a problem you are having.

Test-Taking Tips1. Bring a calculator with which you are familiar. While dividing decimals by

hand is noble, it eats up your time and takes your focus away from the test material.

2. Use a pencil and eraser. Crossing out mistakes leaves you with work that may be difficult for you to read.

3. Write as neatly as possible. Many students misread their own writing. Also be sure you have correctly copied all the information from the problem.

4. Write information down as soon as you get the test. Write formulae, rules, etc. somewhere on the test so you do not forget them later.

5. Read the instructions carefully. Be sure you are answering the question being asked, and that you are answering all parts. You are not always just solving for X.

6. Do the easy problems first. This lets you spend more time on difficult problems. If you are prepared, some of the problems (vocabulary, fill-ins, etc.) should be very quick to complete. Do problems in this order: easy problems, problems with the highest point value, then do the remaining problems.

7. Do not spend too much time on one problem. Go back if you get stuck. Something that comes up later in the test may help you.

8. Remember the questions the teacher asks the class when solving similar problems. It’s easy to “get it” in class because the teacher leads you to the solution with these questions. Lead yourself with these same questions.

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9. Check your work and your answers when you finished the test. Plug answers back into equations. Check to make sure your answers are reasonable and/or realistic: Could the length of a ladder really be -0.5ft?

Final Exam Information Check weekly syllabus for date/time of final exam Bring a #2 pencil, calculator, and something to read (in case you finish early). You will be given a copy of the formula sheet that is attached at the end of this

guide Final Exam Breakdown:

Non-Calculator: ~ 14 multiple choiceCalculator: ~ 27 short answer

~1 open response Your Final Exam grade is 10% of your grade for the entire year.

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1. Is the figure a polygon? If not, tell why.a. b. c. d.

Find a polygon in each photograph. Classify the polygon.2. 3. 4.

Solve for each variable.5. 6. 7.

8. The sum of the measures of the angles of a regular polygon is 4500. How many sides does the polygon have?

9. Exactly four angles of a hexagon are congruent. The other two angles are complementary. What is the measure of one of the four congruent angles?

10. What is the sum of the measures of the interior angles of a 25-gon?

11. What is the measure of an exterior angle of a regular polygon with 36 sides?

12. How many sides are in a regular polygon whose exterior angles measure 15°?

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13. 14. Find the value of the variables.15. Find the perimeter of PMYKF.

∆HLN ∆GST, mH = 66°,and mS = 42°. What is mT?

16. Is ∆ABC ∆XYZ? Explain.

Can you prove each pair of triangles is congruent? Show work by marking your diagram.

If you can prove it:a. Tell what theorem you would use (name one theorem only)b. Name the congruent trianglesc. Name all pairs of congruent parts that support your theorem

If you can NOT: Write “Not possible” on line “a”.

17. 18. 19.

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20. 21. 22.

23.

24.

Given: JL bisects ∠KLM

Prove: ∆ JKL≅ ∆JML

Statement Reason1. ∠K ≅∠M 1.

2. JK≅ JM 2.

3. JL bisects ∠KLM 3.

4. ∠KLJ ≅∠MLJ 4.

5. ∆ JKL≅ ∆JML 5.

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Transformations

25. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Graph each pair of triangles with the given vertices. Then, identify the transformation.

26. A(2, 2), B(4, –1), C(1, –2);

M(–4, –1), N(–1, –2), P(–2, 2)

27. A(–1, –1), B(–1, –4), C(2, –4);

M(–1, 1), N(–4, 1), P(–4, 4)

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Graph each figure and its image under the given reflection.28. ΔABC with vertices

A(–1, –4), B(–5, 3), and C(0, 5)in the line y = x

29. quadrilateral WXYZ with vertices

W(–3, –2), X(–4, 1), Y(1, 4), and Z(2, –2)in the y-axis

Graph each figure and its image after the specified rotation about the origin.

30. ΔPQR with vertices P(–1, –2), Q(–5, –4), and R(–3, –6); 90°

31. parallelogram WXYZ with vertices W(–3, 3), X(–2, 7), Y(4, 5) and Z(3, 1); 180°

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Graph each figure with the given vertices and its image after the indicated translation.

Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor.

32. ΔDEF: D(–5, 1), E(–3, 5), F(0, 3)

Translation: along <4, 3>

33. A(–5, –4), B(–2, –3), C(–1, –6), D(–4, –8); k = 12

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Similarity & Right Triangles

Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.

34. 35.

Each pair of polygons is similar. Find the value of x.36. 37.

Determine whether the triangles are similar. If so, write a similarity statement.38. 39.

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40.When Rachel stands next to her cousin, Rachel’s shadow is 2 feet long and her cousin’s shadow is 1 foot long. If Rachel is 5 feet 6 inches tall, how tall is her cousin?

41.

42.

43.

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44.Jason wants to determine if his foosball table is a dilation of his school’s soccer field. The dimensions of the table are 30 inches by 55.5 inches, and the dimensions of the field are 60 yards by 110 yards. Is the table a dilation? Explain.

Find x.45. 46. 47.

48.

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Area

Find the perimeter and area of each figure. Round to the nearest tenth if necessary.

49. 50. 51.

52.The height of a parallelogram is three times its base. If the area of the parallelogram is 108 square meters, find its base and height.

Find the indicated measure. Round to the nearest tenth.53. 54. 55.

The area of a circle is 201 square meters. Find the radius.

Find the diameter of a circle with an area of 79 square feet.

Find the area of the sector.

56. 57.Find the area of a regular hexagon that has an apothem of 6√3 cm and a side length of 12 cm.

Find the area of the composite figure below.

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58. The pentagons are similar. Find the area of the small pentagon.

59. The triangles are similar find x.

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Circles

In circle M, MZ = 12 and WY = 20. Find each measure. Round to the nearest hundredth.

60. CM

61. XC

62. Quadrilateral ABCD is circumscribed about H. Find m.

Page 18 of 22


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3D Figures

63. Find the lateral area, surface area, and volume of the figure on the right.


Sarah has a fish tank with the dimensions shown.

65. What is the surface area of the fish tank?

66. If Sarah fills the tank to a depth of 17 inches, what will be the volume of the water in the tank?

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68. Find the lateral area, surface area, and volume of the square pyramid on the right.



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71. Find the surface area and volume of the figure on the right.

72. Find the surface area and volume of the figure on the right.

73.An office has recycling barrels that are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall with a diameter of 30 inches. How many square feet of cardboard are used to make each barrel?

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Documents

Web viewFind missing side lengths and angle measures of congruent polygons. 4.3. ... Word. Definition & picture. ... Exactly four angles of a hexagon are congruent