NAME:_________________________

St. Francis High School Geometry Mastery Skills Workbook Use this workbook to help prepare for the Mastery Skills test that will be given in the first week of school to all students enrolled in Advanced Algebra or Honors Advanced Algebra Trig. The format of the test is multiple choice. Do the first Practice Test – it contains samples of the types of problems on the test. If you are having trouble with any section more problems can be found in the following pages of the workbook or by searching the internet or in workbooks available in bookstores. The test will be taken WITHOUT calculators. Answers are provided at the back of the workbook. Work through the skill sections during the summer. A sample multiple choice test is included at the end of the workbook. Take this sample test the week before schools starts and brush up on any sections that you found difficult. You will be asked to do extra work on the skills you do not successfully master. Good luck.

GEOMETRY MASTERY SKILLS PRACTICE

TEST

The test you will take on the first day of school has question similar to this test. You are not expected to get 100%, but you should get most problems in each skill correct. Practice for this and you will start your year off right. NO CALCULATOR!!! SKILL G1: Parallel and Perpendicular Lines 1. Line k is parallel to line m. 2. Line k is parallel to line m. If 1  2 x  5 , find the value of x. If 1  2 x  15 and 2  3x  85 , find the measure of 1 . k

k

125°

2

1

m

1

m

4. Name the lines that must be parallel if 5  2

3. Given the figure, find the measure of x. x

H 1 2 3

G

F 4

45°

55° SKILL G2: Vocabulary 5. A and B are complementary angles. If they are angles in a triangle, the third angle measures _______ degrees.

L

8 7 K

6

J

ABC is isosceles with vertex C. What is the perimeter? B

6.

5

7.

AB bisects DAC . If BAC equals 48°, then DAC =______.

10 A

6

SKILL G3: Area, Perimeter, and Volume 8. Find the perimeter and area of the parallelogram. 15

C 9. Use the formula V = Bh to find the volume of the cylinder pictured below.

13

5 cm 5

10. Use the formula V = Bh to find the volume of the prism pictured below.

11. Use the formula Lateral Area =  rl to find the lateral area of the cone pictured. ( l  slant height)

15 cm 8

5 6 6 cm Geometry Mastery Skills Workbook

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p. 2

SKILL G4: Right Triangles 12. Find the length of the hypotenuse (leave in simplified radical form):

13. Use trig to find x to the nearest tenth.

x

4

x

10

10 35°

14. From a point 65 feet from the base of a building, the angle of elevation to the top of the building is 55◦. To the nearest foot, how high is the building?

A

Solve for the two missing sides. (Leave answer in radical form.)

15. Find the diagonal of a rectangle whose sides are 21 and 72.

18. What is the diagonal of a square if the side is 5?

16. AB =__________

17. AC=__________ B

SKILL G5: Radicals

60° 5

C

Simplify. Leave all answers in simplified radical form.

50  32

20.

19. 3 50

21. 5 2  3 15

22.

3 2 6

SKILL G6: Coordinate Geometry y

E



23. Find the midpoint of DE



24. Find the distance between the points.



D 







25. What is the slope of DE ?



Geometry Mastery Skills Workbook

to DE ?_______ 28. Find the coordinates of the point 3 units to the right of point D. ______

 x



26. What is the slope of the line parallel to DE _______ 27. What is the slope of the line perpendicular

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p. 3

29. Find the coordinates of the new point when E is reflected over the y axis. _________

SKILL G7: Quadrilaterals Always, Sometimes or Never?

32. ABCD is a parallelogram.

A  x , D  (2 x  6) . Find C .

30. ______A trapezoid is a parallelogram.

A

B

31. ______A square is a rectangle. C

D

33. ABCD is a parallelogram. AB = 2x + 3, BC = 6, CD = x + 4. Find the perimeter of ABCD. A

B

34. TRAP is a trapezoid. TP = 3x+2, TR= 5x-3, RA = 7x-6, AP = 6x+5. What value of x would make TRAP an isosceles trapezoid? T

C

D

R

E P

SKILL G8: Similarity Find the missing values.

ABC

A

37. Find the missing value.

XYZ

A

x

C B

a X

2 Y

15

8

5

8

12

y Z

4

35. a =__________ 36. y=__________ 38. If the smallest sides of two similar triangles are 3 and 8 and the perimeter of the smaller triangle is 12, what is the perimeter of the larger triangle?

Geometry Mastery Skills Workbook

’14-‘15

x=__________ 39. The blueprint of a bedroom in a new house measures 4 inches by 5 inches. If the larger dimension of the bedroom is actually 15 feet, how many square feet of carpet will I need?

p. 4

MASTERY SKILLS PRACTICE SECTIONS SKILL G1: PARALLEL AND PERPENDICULAR LINES  Definition of parallel – two lines in a plane that will never intersect  Definition of perpendicular – two lines that intersect to make right angles  Given two parallel lines and a transversal, o Alternate Interior(Z), Alternate Exterior and Corresponding (F) angles are congruent o Same-side Interior (U)and Same-side Exterior are supplementary 1. Given the figure, find the 2. Given the figure, find the measure 3. Given the figure, find the measure of x. of x. measure of x. x 120°

x x

155°

70°

4. Given the figure, find the measure of x.

5. Given the figure, find the measure of x.

6. Given the figure, find the measure of x. x

(x+20)°

85° x

42°

130°

7. Line k is parallel to line m. If 1  2 x  3 , find the value of x.

8. Line k is parallel to line m. If 1  3x  7 , find the value of x.

m

125°

9. Line k is parallel to line m. If 1  3x  28 and 2  5 x  72 , find the value of x.

m

56°

m

1

1

k

k

1 k 2

Geometry Mastery Skills Workbook

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p. 5

10. Line k is parallel to line m. If 1  2 x  17 and 2  4 x  37 find the value of 1 .

11. Line k is parallel to line m. If 1  3x  28 and 2  4 x  85 find the measure of  2 .

12. Line k is parallel to line m. Find the value of  2 . (5x+8)° m

2

m

2

(7x-32)°

m

2 1 1

k

k

k

13. Given the figure, find the measure of x. x

50°

14. You have traveled 3 miles on Road A and then turn onto Road B which is perpendicular to Road A. You travel 4 miles on Road B and stop. What is the distance between your starting point and stopping point?

15. Given the figure, find the measure of x.

63°

60°

16. In triangle ABC, AB is perpendicular to BC . If ACB is 68°, find the measure of BAC

17. Name the lines that must be parallel if 4  1 G

L

Given the figure, find the missing angles. 4 1

H 1 2 3

8 7 K

x

18. . Name the lines that must be parallel if 1  7 G

4

6

H 1 2 3

F 4

5 J

L

8 7 K

6

5 J

19. If 1 =105°, 3 =_____

22. If  4 =120°, 3 =_____

20. If  2 =65°,  4 =_____

23. If  2 =70°, 1 =_____

21. If 5 =110°,  4 =_____

24. If 1 =130°, 5 =_____

2 5 3

Geometry Mastery Skills Workbook

F

147°

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p. 6

SKILL G2: VOCABULARY  Supplementary (two angle sum of 180°) and Complementary (two angle sum of 90°)  Midpoints and Bisectors divide a segment or angle into 2 congruent parts.  Triangles: o acute (all angles between 0° and 90°), obtuse (one angle between 90° and 180°), right (one angle = 90°) o Scalene (no sides congruent), isosceles (at least 2 sides congruent), equilateral (all sides congruent) o Congruent – all corresponding angles and sides are congruent  Polygon names (# sides): Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6), Octagon (8), Decagon (10) o Interior angles sum: S = (n-2)180° S= angle sum o Exterior angle sum is ALWAYS 360° n= number of sides or o Interior angle and Exterior angle are supplementary angles 360 360 o Each exterior angle of a REGULAR polygon: E  or n  E = one exterior angle n E d= number of diagonals n(n  3) o Number of diagonals: d  2

 

Circle: center, radius, chord, diameter, secant, tangent, central angle, inscribed angle Solids: o Prisms (two parallel polygonal bases, lateral faces are rectangles) o Cylinder (two parallel circular bases) o Pyramid (one square or equilateral triangular base, lateral faces are isosceles triangles) o Cone (one circular base with vertex directly above the center of the base) Sample Problems: 1. Fill in the following table: 2. One of two complementary angles What is the measure of each is 40° more than the other. What exterior angle of a regular: Angle Complement Supplement is the measure of the larger angle? A 17° 3. hexagon B 50° C

42°

D

71°

4. decagon

E

112°

F

165° 7.

A triangle has angles that measure 2x, 5x, and x + 20.

ABC is isosceles with vertex A. What is the

perimeter?

B 10

5. Is this triangle acute, obtuse, or right? 6. Is this triangle scalene, isosceles or equilateral? 8. What is the measure of each interior angle of a regular decagon?

Geometry Mastery Skills Workbook

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A 8 9. How many diagonals does an octagon have?

p. 7

C

Use the following words to answer # 11-30. Words may be used more than once or not at all. Central angle Diameter Isosceles Trapezoid Radius Scalene Center Equiangular Kite Rectangle Slant height Chord Height Obtuse Regular Square Cone Inscribed angle Prism Rhombus Tangent Cylinder Isosceles Pyramid Secant Triangle 10. Does P inscribe or Give the best name for: circumscribe the 18. This solid is a _______________ 12. DC A quadrilateral? 19. AC is the ________ D 13. DC __________. • 14. P 20. AP is the ___________ P A P B 15. DB 11. Below is an example C of_______ 16. PD 17. AB B

P

21. The lateral faces of a _____________ are isosceles triangles. 22. The bases of a ________________ are always congurent circles. 23. A(n) __________________angle in a circle equals half the measure of its arc. 24. All equilateral triangles are _______________________. 25. A triangle with no sides congruent is __________________. 26. A triangle with one angle larger than 90° is ______________. 27. An equiangular quadrilateral must be a ___________________. 28. An equilateral quadrilateral must be a ___________________. 29. A polygon with all sides congruent and all angles congruent is a ______________ polygon. 30. The sum of the angles of a ____________ is 180°. Fill in the blanks. 31. A and B are complementary angles. If they are angles in a triangle, the third angle measures _______ degrees. 32. How many faces does a square pyramid have? ________ 33. Can a triangle be isosceles and right? _______ 34. In circle P, If LAPC = 35°, then AC = ______. 35. The longest side of a right triangle is the ________________. A

36. AB bisects DAC . If BAC equals 68°, then DAC =______. 37. What is a name for the parallogram at the right? AB__ __

Geometry Mastery Skills Workbook

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p. 8

C

B

D

C

SKILL G3: AREA, PERIMETER, AND VOLUME

Find the area and perimeter of each figure. Leave 1. Triangle



in the answer. 2. Triangle

10

24 10

3. Circle P.

4. Find the area of a circle if the perimeter is 12π

P

3

5. Rectangle

6. Rectangle

4 7

7. Find the area of triangle ABC

8. Find the area and perimeter of the Parallelogram.

A 4 1

13

3 10

B

C 10

Geometry Mastery Skills Workbook

5

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p. 9

Problems 9 through 26 use the following symbols:

B = area of the Base h = height of the solid 9. The formula for volume of a right cylinder is Volume = πr2h

r = radius of circular base l = slant height 10. Use the formula from problem #9 to find the volume of the cylinder pictured below.

Use this formula to find the volume of the cylinder pictured below. 12

11 9

6

11. The formula for volume of a right prism is Volume = Bh

12. Use the formula from problem #11 to find the volume of the prism pictured below.

Use this formula to find the volume of the prism pictured below.

F A

5 15

10

20 B 18

Geometry Mastery Skills Workbook

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p. 10

3

C

13. The formula for volume of a right cone is Volume =

14. The formula for lateral area of a cone is

1 2 r h 3

Lateral Area =  rl Use this formula to find the lateral area of the cone pictured.

Use this formula to find the volume of the cone pictured below:

12

5

15. The formula for volume of a right pyramid is Volume =

1 Bh 3

16. Use the formula from problem #15 to find the volume of the pyramid pictured below.

Use this formula to find the volume of the pyramid pictured below.

h = 6 cm h =5 cm

w = 8 cm l = 10 cm

w =6 cm l = 8 cm 17. The formula for volume of a sphere is

4 Volume   r 3 3

18. Use the formula from problem #17 to find the Volume of the sphere pictured below:

Use this formula to find the volume of the sphere pictured below:

r=9m

Geometry Mastery Skills Workbook

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p. 11

SKILL G4: RIGHT TRIANGLES Pythagorean Theorem Right Triangle- Families (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) 30-60-90, 45-45-90 Triangles SOH – CAH – TOA 1. Find the length of the 2. Find the length of the hypotenuse hypotenuse: (leave in radical form):

x

15

3. Find the length of the missing leg:

25

x

12

20

24

24

4. Find the length of the missing leg:

Using opp (opposite), adj (adjacent) and hyp (hypotenuse), define these trig ratios:

5. A ladder 6.0 meters long rests against the sill of a second-story window. The base of the ladder is 3.6 meters from the base of the wall). How far is the window sill above the ground?

Given this triangle ABC, give the trig ratios:

6. A kite gets caught in the top of a tree. The string is 65ft. long. The boy is holding the string 60 ft. from the base of the tree, how tall is the tree?

Find the length of x in the triangle below:

7. Sin x =

8. Cos x =

10. sin B = 11. cos C =

9. Tan x =

13. x = 12. tan C =

Geometry Mastery Skills Workbook

’14-‘15

x

p. 12

14. From a point 78 feet from the base of a building, the angle of elevation to the top of the building is 57 degrees. To the nearest foot, how high is the building?

15. Given right triangle ABC. The tangent of angle A is 4/3. The length of the side opposite A is 12. What are the lengths of the other 2 sides?

16. The measure of angle A is 30 degrees, and side b is 8. What is side a? (Leave answer in radical form)

17. Find the diagonal of a rectangle whose side s are 24 and 32.

18. Solve for the two sides.

19. Solve for the two sides. (Leave answer in radical form)

8

20. Solve for the two sides.

Geometry Mastery Skills Workbook

3

5 3

21.

’14-‘15

22. The angle of depression from the top a lighthouse on the shore to a ship at sea is 32°. If the lighthouse is 30 ft. high, how far, to the nearest foot, is the ship from the shore?

p. 13

SKILL G5: RADICALS Radicals a. Simplify b. Addition and Multiplication c. Rationalize Simplify. Leave all answers in simplified radical form. 1.

80

4.

6 18

7.

3 5 5

2.

75

3.

a6

6 45x 5

6.

3y 24y 9

8. 2 6  7 6

9.

4 12  8 27

10. 3 9  5 8  2 4

11. 11 18  72  4 45

12. 2 16  5 20  6 12

13. 3 18  4 14  5 8

14. 3 6  6 3

15.

Geometry Mastery Skills Workbook

5.

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p. 14

5 5

16.

11  3

19. 2 5  4 6

22.

25.

36 12

5 36

28.

17.

20.

7 8



3 2 3 5 7

18.



23.

24.

26.

5 2

2 3 6 27.

8 3 20

Geometry Mastery Skills Workbook



4 6 3 7 9 2

45 5

30.

29.

21.

10  5

4 25

32.

5 2 5

8 6 2 2

31.

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33.

p. 15



SKILL G6: COORDINATE GEOMETRY Coordinate Geometry  Reflection of point over an axis  Coordinates of points on vertical or horizontal lines  Midpoint formula  Distance formula  Slopes of parallel or perpendicular lines 1. Find the coordinates of the point 3 units directly above (–3,–5)

2. Find the coordinates of the point 3 units directly to the right of (–3,–5)

3. Find the coordinates of the point 4 units to the right and 6 units down from (–3,–5)

4. Find the coordinates of the new 5. Find the coordinates of the new point when (2,5) is reflected over point when (3, –2) is reflected the x-axis. over the x-axis.

6. Find the coordinates of the new point when (7, –4) is reflected over the x-axis

7. Find the coordinates of the new 8. Find the coordinates of the new point when (2,5) is reflected over point when (3, –2) is reflected the y-axis. over the y-axis

9. Find the coordinates of the new point when (7, –4) is reflected over the y-axis

10. Find the midpoint between (–3,6) and (8,–5)

11. Find the distance between (–3,6) and (8,–5)

12. Find the slope between (–3,6) and (8,–5)

13. Find the midpoint between (0,2) and (8,4)

14. Find the distance between (0,2) and (8,4)

15. Find the slope between (0,2) and (8,4)

Geometry Mastery Skills Workbook

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p. 16

16. Find the midpoint between (8,–6) and (8,10)

17. Find the distance between (8,–6) and (8,10)

18. Find the slope between (8,–6) and (8,10)

Given the following A (-1,3) 

y

19. Find the slope between the points.



20. Find the midpoint

 x 















21. Find the distance between the points



 

22. What is the slope of the line parallel to AB ?

B (2,-2)



23. What is the slope of the line perpendicular to AB ?

Given the following 

y

24. Find the slope between the points. E(4,3)



25. Find the midpoint



D(–2,1) 26. Find the distance between the points

 x 

















27. What is the slope of the line parallel to ED ?



28. What is the slope of the line perpendicular to ED ?

Geometry Mastery Skills Workbook

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p. 17

SKILL G7: QUADRILATERALS 1. 2. 3. 4. 5.

Quadrilateral Family Tree

Opposite angles of a parallelogram are ____________________. Diagonals of a Rectangle are ________________________. Diagonals of a Rhombus are ___________________. If TRAP is an isosceles trapezoid, what can you say about LP and LR? __________________ What can you say about quadrilateral QUAD If

Q Angle sum is 360°

P

K

diag. bis. ea. other consec. angles supp opp. angles congruent

QA is  bisector of UD ? 6. 7. 8.

9.

__________________ Does a rectangle have opposite sides congruent? ____ Are the diagonals of the isosceles trapezoid bisectors of each other? _____ Name three quadrilaterals that will always have congruent diagonals. ______________________ A parallelogram is (Always, Sometimes, Never) a rectangle.

T

IT Rh

R

diag. perpendicular diag. bis angles

diag. congruent

diag. congruent

ALWAYS

S

SOMETIMES

R & Rh

NEVER

10. A square is (Always, Sometimes, Never) a rhombus.

IN EACH OF THE FOLLOWING PROBLEMS ABCD IS A PARALLELOGRAM. 11. AD = x + 5, AB = x + 9, BC = 2x + 12. LA = x°, LD = (3x-4)°. Find LC 1 Find DC. A B A

A

B

D

C

Geometry Mastery Skills Workbook

’14-‘15

B

C

D D

13. In order for ABCD to be a rectangle, what must the value of x be if LADB = (2x + 6)° and LBDC=42°?

p. 18

C

REMEMBER: ABCD is a parallelogram. 14.

AB = 2x + 6, BC = 8, CD = x + 8. Find the perimeter of ABCD. A

B

15. AB = 3x + 4, BC = 5x – 2, 16. AD = y + 4, and BC = 3y – 8. The DC = x + 10, and LAEB = (5y – 20) °. perimeter is 40. What is the What value of x and y would make best name for ABCD? ABCD a square? A B

A

E

C

D

B

C

D

Work each of the following problems. 17. KITE is a kite. KI=10, IT=17, and KA=6. Find KT. I

K

A

C

D

18. TRAP is a trapezoid. TP = 5x – 2 and RA = 3x + 10. What value of x would make TRAP an isosceles trapezoid? T R

19. TRAP is an isosceles trapezoid. PE = x + 5, ER = 2x – 1, TA = 13. Find PE T R E

T

E P P

E

Geometry Mastery Skills Workbook

’14-‘15

A

p. 19

A

SKILL G8: SIMILARITY  Triangle proportions  Scale factor Find the missing values for the similar figures below. 1.

ABC

2.

XYZ

X

c

6

5

3

B

4

a=__________

c=__________

3.

Y

8

3

a

y

2

A

C

a

a=__________ 4.

ABC

Z

4

y=__________

XYZ

C

b 10

b

c

15

A

13

x

Z

Y 4

10 X

5

12

B

b=__________

c=__________

5.

b=__________

x=__________

6. 5

10

5 25

6

x

x=__________

Geometry Mastery Skills Workbook

x=__________

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p. 20

7

x

7.

8. x

12 3

12

x

8

5

6

x=__________

x=__________

9.

10.

4

12 26

3

5

x 9

x

x=__________ 11. If the side ratio of two similar figures is 2:3, what is the perimeter ratio?

x=__________ 12. If the perimeter ratio of two similar figures is 3:4, what is the Area ratio?

14. If the smallest sides of two similar triangles are 6 and 10 and the perimeter of the smaller triangle is 24, what is the perimeter of the larger triangle?

Geometry Mastery Skills Workbook

’14-‘15

13. If the Area ratio of two similar figures is 36:25, what is the perimeter ratio?

15. If two triangles are similar and the smallest sides are 6 and 10 and the Area of the larger triangle is 200, what is the area of the smaller triangle?

p. 21

Solve the following scale factor problems. 16. The scale on a map is 1 inch equals 10 miles. If the distance from Chicago to Wheaton on the map is 3.5 inches, how far apart are the cities?

17. The floor plan of my room in our new house is 2 inches by 3 inches. If the smaller dimension is really 8 feet, how many square feet of carpet will I need?

18. The John Hancock Building in Chicago is 459 meters tall. If the Lego store in Schaumburg wanted to build a scale model of the Hancock Building using the scale of 3m:2cm, how tall would the scale model be?

19. A model airplane has a wing span of 3 inches and a length (nose to tail) of 9.5 inches. If the real airplane is 200 meters long, what is its wingspan rounded to the nearest tenth?

20. Walter E. Smythe is furnishing your living room. You have to bring a scale drawing of this room to your designer. If a wall that is actually 20 ft., is drawn as 5 inches in your drawing, how long should your 15 foot wall be in your drawing?

21. Two similar garden plots have a perimeter ratio of 2:3. If the area of the smaller garden is 160 square ft. , what is the area of the larger garden?

Geometry Mastery Skills Workbook

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p. 22

GEOMETRY MASTERY SKILLS PRACTICE TEST MULTIPLE CHOICE TESTTETESTTETESTTESTTEST The test you take the first week of school is very similar to this test. You should get most problems in each skill correct. Practice for this and you will start your year off right. NO CALCULATORS SKILL G1: Parallel and Perpendicular Lines 1. Given the figure, find the measure 2. Line k is parallel to line m. of x. 1  5x  15 and 2  4 x  20 Find the value of x x. k 42° m

53°

3. Line k is parallel to line m. If 1  2 x  15 , find the value of x. k

1

135°

2

1

m

a) 96°

b) 65°

a) 15

b) 40

a) 30

b) 60

c) 74°

d) 85°

c) 5

d) 90

c) 45

d) 15

SKILL G2: Vocabulary 4. One of two supplementary angles is 30 more than the other. What is the measure of the smaller angle?

5.

ABC is isosceles with vertex C. What is the perimeter?

6.

XY and XV trisect WXZ . If YXV equals 50°, then WXZ =______.

14 12

a) 150°

b) 105°

a) 38

b) 12

a) 50°

b) 100°

c) 15°

d) 75°

c) 40

d) 14

c) 150°

d) cannot be determined

Geometry Mastery Skills Workbook

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p. 23

SKILL G3: Area, Perimeter, and Volume 7. Find the area of the 8. Use the formula V = Bh to find parallelogram. the volume of the cylinder pictured below. 18

5 cm

9. Use the formula Lateral Area =  rl to find the lateral area of the cone pictured. ( l  slant height)

10

10 cm 6

12 9

a) 144

b) 180

a) 250π

b) 100π

a) 108π

b) 135π

c) 60

d) 56

c) 50π

d) 150π

c) 972π

d) 1205π

SKILL G4: Right Triangles 10. Find the length of the hypotenuse (leave in simplified radical form):

11. Find the measure of AC.

12. Find the diagonal of a rectangle whose sides are 4 and 10.

A x

4

30° 18

6 B

a) 2 5

b) 2 13

a) 9 2

c)

d)

c) 9 3

20

52

Geometry Mastery Skills Workbook

’14-‘15

C

b) 9

a) 2 21 c)

p. 24

14

b) 2 29

13. Write the trig equation used to find x.

14. From a point 30 feet from the base of a building, the angle of elevation to the top of the building is 25◦. Write the trig equation used to find the height of the building.

8

55° x

a) c)

x 8 8 tan 55  x

cos 55 

b) d)

SKILL G5: Radicals

x 8 8 cos 55  x

sin 55 

a) c)

30 h h tan25  30 tan25 

b) d)

h 30 30 cos 25  h

sin 25 

Simplify. Leave all answers in simplified radical form.

15. 3 24

90  40

16.

a)

2 6

b)

12 6

a)

130

c)

6 6

d)

6 3

c)

13 10

b)

5 10

17.

2 3 2

a)

6

c)

3

b)

6 2

SKILL G6: Coordinate Geometry 19. Find the distance between D and E.

y 



20. Find the coordinates of the point 2 units to the left of point E.

E



a) (1, 5)

b) (-1, 3)

c) (-4, -1)

d) (4, 3)

 x 

D





21. What is the slope of the line parallel to DE ?







18. Find the midpoint of DE a) (0, 1.5)

b) (-1.5, 1)

a) 5

c) (-0.5, 1)

d) (1.5, 0)

c)

Geometry Mastery Skills Workbook

’14-‘15

b)

5

7

a) c)

p. 25

3 4 4 3

b) d)

2 1 4 3

SKILL G7: Quadrilaterals 22. ABCD is a parallelogram.

D  11x  10  , B  (20 x  26) . Find A . A

23. RHOM is a rhombus. If RDH  7 x  8 , what is the value of x?

B

A

R

M

24. ABCD is a parallelogram. AD = 3x – 4, BC = 5, CD = x + 4. Find the perimeter of ABCD. B

D D

C

D

O

82 7

a) 54°

b) 126°

a) 14

c) 4°

d) 176°

c) not enough information

SKILL G8: Similarity 25. Find the value of x. 6 18

C

H

b)

26. ABC XYZ AB=5, AC= 10, BC = 4, XY=3. Find XZ.

x 6

a) 7

b) 12

c) 3

d) 24

27. If the smallest sides of two similar triangles are 3 and 8 and the perimeter of the smaller triangle is 21, what is the perimeter of the larger triangle?

28

a) 14

b) 7

c) 9.3

Geometry Mastery Skills Workbook

a) 16.6

b) 2.4

c) 6

’14-‘15

p. 26

a) 32

b) 7.875

c) 56

d) not enough information

ANSWERS PRACTICE TEST 1. 30

2. 125°

3. 80°

6. 22 11. 60π

7. 96 12. 2 29

8. 56, 180 13. 17.4

16. 10

17. 5 3

21. 15 30

22.

3 2 31. Always 16 36. or 3.2 5

26.

3

2 3 32. 62 37. 10

27.

4. HK , FJ 9. 720π 14. 93

5. 90

18. 5 2 23. (0, 2.5)

19. 15 2

28. (2, 1)

29. (–1, 4)

20. 9 2 3 25. 2 30. Never

33. 22 38. 32

34. 2 39. 180

SKILL G1: Parallel and Perpendicular lines. 1. 70 2. 60 3. 155 9. 22 10. 59 11. 143 17. KH / / JF 18. KJ / / HF 19. 105 SKILL G2: Vocabulary 1A. 73, 163 1B. 40, 130 2. 65 3. 60 8. 144 9. 20 14. Center 15. Chord 20. Height 21. Pyramid 25. Scalene 26. Obtuse 31. 90 32. 5 33. Yes

SKILL G3: Area, Perimeter, and Volume 1. A=120, p=60 2. A=192, p=64 6. A=480, p=92 7. A=20 11. V = 2160 12. V = 60 16. V=160 17. V=972π

SKILL G4: Right Triangles 1. 25 2. 12 5

opp adj 17. 40 9.

b a 18. AC=10 BC=5

10.

3. 7 11.

12.

19. AB = 8 3 BC = 8

Geometry Mastery Skills Workbook

5. 85 13. 70 21. 110

’14-‘15

c b

35. 10

6. 48 14. 5 22. 120

1D. 19, 161 5. Obtuse 11. Prism 17. Tangent 23. Inscribed 28. rhombus 35. Hypotenuse

3. A=9π, p=6π 8. A=132, p=48 13. V=12π 2048 18. V   3

4. 10

b a

24. 13

4. 30 12. 72 20. 115

1C. 48, 132 4. 36 10. Circumscribe 16. Radius 22. Cylinder 27. rectangle 34. 35

10. 180 15. 75

8. 39 16. 22 24. 130

1E. 68, 22 1F. 15, 75 6. Isosceles 7. 26 12. Secant 13. Diameter 18. Cone 19. Slant height 24. Isosceles or equiangular 29. regular 30. triangle 36. 136 37. DC

4. A=36π 9. V=396π 14. V=65π

5. 4.8

6. 25

13. 8

14. 120

20. AC=4 BC=4

21. 56

p. 27

7. 29 15. 57 23. 110

5. A=28, p=22 10. V=972π 15. V= 80

opp hyp 15. AC=9 AB=15 7.

22. 48

8.

adj hyp

16. 8 3

SKILL G5: Radicals 1. 4 5 2. 5 3 9. 32 3 20. 6  5 21 10 2

26.

4. 18 2

14. 54 2

11. 39 2  12 5 15. 5 16. 33

10. 5  10 2

2  4 14

13.

3. a3

21. 12 42  72 3 27.

2

28.

22.

29. 10

4 15 5

SKILL G6: Coordinate Geometry 1. (-3, -2) 2. (0, -5) 3. (1, -11) 8. (-3, -2) 9. (-7, -4) 10. (2.5, 0.5) 15.

16. (8, 2)

1 4

22. 

5 3

23.

3 5

24.

1 3

SKILL G7: Quadrilaterals 1.  2.  3.  8. IT, R, S 9. Sometimes 10. Always 15. x=3, y=22 16. rhombus 17. 21 SKILL G8: Similarity 1. a=8, c=10 6. 35 11. 2:3 16. 35 21. 360

2. a=6, y= 16/3 7. 7.5 12. 9:16 17. 96

Multiple Choice Practice Test 1. D 2. C 8. A 9. B 15. C 16. B 22. B 23. A

3. D 10. B 17. A 24. D

Geometry Mastery Skills Workbook

’14-‘15

8. 5 6

7. 4 5

12. 8  10 5  12 3 17. 2 14 23. 3

3

18. 5 2 2 24. 5

19. 8 30 25.

5 6

30. 4 3

4. (2, -5) 11. 11 2 18. None (vertical line) 25. (1, 2)

17. 16

6. 6 y 5 6 y

5. 18 x 2 5 x

5. (3, 2) 12. –1

6. (7, 4) 13. (4, 3)

7. (-2, 5) 14. 2 17

5 3 26. 2 10

20. (0.5, 0.5)

21.

19. 

4. P  R 11. 13 18. 6

3. b=24, c=26 8. 8 13. 6:5 18. 306

4. D 11. C 18. C 25. B

5. Kite 12. 46 19. 8

28. 3

1 3

6. Yes 13. 21

4. b=12.5, x=12 9. 10 14. 40 19. 63.2

5. C 12. B 19. A 26. C

p. 28

27.

6. C 13. A 20. B 27. C

34

7. No 14. 36

5. 12 10. 8 15. 72 20. 3.75

7. A 14. C 21. D