Geometry Sem 2 REVIEW for Final Part A ink.notebook · PDF fileGeometry Sem 2 REVIEW for Final...

Geometry Sem 2 REVIEW for Final Part A ink.notebook

1

May 11, 2017

Geometry Sem 2 Review for Final

Part A

Find the missing sides of each triangle.

m = _____, n = _____

60°4'

m

n30°

60°

x

y

15 m

x = _____, y = _____

1. 2.Leave answers as simplified radicals.


45°14" x

y45°

x = _____, y = _____

3.Leave answers as simplified radicals.


12"x

9"

4.Round to the nearest tenth if necessary.


2

May 11, 2017

18 mx

13 m


7'

x

25'

5. 6.Round to the nearest tenth if necessary. 7. Use trig to find the value of x.

25°14

x

Round to the nearest tenth.

8. Use trig to find the value of x. x

12

25°Round to the nearest tenth. 9. Use trig to find the value of x.

16 10

θ°

Round to the nearest tenth.


3

May 11, 2017

10. Use trig to find the value of x.

124

x71°

Round to the nearest tenth. 11. Find the indicated ratios.

a) sin A = ______

b) tan A = ______

c) cos A = ______ A

B

C

8

15

17

12. A 12 ft ladder makes a 38° angle with the ground. How many feet up a wall will it reach? Show your equation and round to the nearest tenth.

180 ft

?

32°

13. Stan observes a plane on the runaway from a tower 180 feet up with an angle of depression of 32°. How far from the base of the tower is the plane? Show your equation and round to the nearest tenth.


4

May 11, 2017

70.4

2900 meters

14. An archaeological team is excavating artifacts from a sunken merchant vessel on the ocean floor. To assist the team, a robotic probe is used remotely. The probe travels approximately 2,900 meters at an angle of depression of 70.4 degrees from the team’s ship on the ocean surface down to the sunken vessel on the ocean floor. The figure shows a representation of the team’s ship and the probe.

How many meters below the surface of the ocean will the probe be when it reaches the ocean floor? Justify your answer and give it to the nearest hundred meters.

Find the volume of each.

11 m

10 m

12 m

15.

Find the volume of each.

24 cm

16.Find the volume of each.

8 cm

15 cm

17.


5

May 11, 2017

5 m

12 m

Find the volume of each.18.

24 m

19. Find the VOLUME of the pyramid. Round to the nearest tenth if necessary.

5

6

20. Name the solid of revolution produced by rotating the shape 360° about the given axis. Then sketch and label the 3dimensional figure.

11 m11 m

6 m

21. Two water tanks are shown. Tank A is a rectangular prism and Tank B is a cylinder. The tanks are not drawn to scale. Tank A is filled with water to the 10meter mark. The volume of water that leaves Tank A is transferred to Tank B, and the height of the water in Tank B is 10 meters. Calculate the volume of water remaining in tank A.


6

May 11, 2017

12

2.5

3

3.75

1.5

Determine whether each pair of triangles is similar. Justify your answer.

22.88°62°

88°

62°

Determine whether each pair of triangles is similar. Justify your answer.

23.

A

B

C

D

E

F

G

H

25x°

100°45°

150°

65°

24. Quadrilateral ABCD ~ quadrilateral EFGH. Find the value of x.

M

B

P

N

Q

5

8 x + 3

2x 7

25. ËMQB ~ ËPNB. Find MB by showing all work.


7

May 11, 2017

26. For the pair of similar figures, find the ratio of the area of the first figure to the area of the second.

3

17

8

27. A man 6 feet tall casts a shadow 4 feet long. At the same time, a building casts a shadow 20 feet long. How tall is the building?

30 ft

28. A billboard at ground level has a support length of 30 feet that extends from the top of the billboard to the ground. A post that is 5 feet tall is attached to the support and is 3 feet from where the base of the support is attached to the ground. In the figure shown, the distance, in feet, from the base of the billboard to the base of the support is labeled x.

Create an equation that can be used to determine x. Discuss any assumptions you made concerning the equation or the drawing. Use your equation to find the value of x. Show your work and explain your answer.

A

B

C

DE

F4

12x - 5 18

29. Identify the similar triangles in corresponding order. Then find x.

ËABC ~ ______

x = _____


8

May 11, 2017

30. If ËABC ~ ËADE, find x by showing your work.

A

BC

DE

5

x

4

7

13

31.A

BC

R

ST

D

N

814

12

Q

R

P

S

2 in

9 in

11 in

X

10 in

32. 33. Use the circle at the right.

AB

C

D

EF

47° 32°

a) find m⁄DAF


9

May 11, 2017

R

56°

T

S34. Find m⁄R 35. a) Find CD. Assume that segments that appear to be tangent

are tangent.

8

x

A

BC

17D

b) Which property justifies your answer?

77°

x°

140° y°

36. Find the value of y.

A B

C

D

E

F

O

37. In ÀO, AB = 22 cm, OE = 3 cm, and OF = 3 cm. Find FD.


10

May 11, 2017

95°

135°

A

B

C

38. Find m⁄ABC.

(3x)°

(5x 6)°

39. a) Find x and m⁄T by writing and solving an equation.

b) Explain using proper vocabulary how you created your equation.

40. Complete the sentence:

If a shape is a parallelogram, then…

a) opposite sides are _____________ and ______________,

b) consecutive angles are ___________________________,

c) the diagonals_____________________________________, and

d) opposite angles are ______________________________.

Point each set of points and determine the most specific name for the quadrilateral formed.

41. A(2, 2) B(6, 5) C(10, 2) D(6, –1)Justify your answer.


11

May 11, 2017

Point each set of points and determine the most specific name for the quadrilateral formed.

42. A(–2, 6) B(–2, –1) C(–9, –1) D(–9, 6)Justify your answer.

a) kiteb) rhombusc) trapezoidd) square

43. MC: The diagonals of which quadrilateral are NOT perpendicular?

44. Determine the value of x for which XYZW is a rectangle.

2x + 2

3x 2x + 6

10

45. Find the value of x.

x°


12

May 11, 2017

46. Find the values of x and y.

x = _____

y = _____

x° y°

82°58°

A

B C

D

E

47. The figure shows parallelogram ABCD.

Find your answer and justify with a property below.

BE = 6x – 28 and let DE = 4x. What are the lengths of

Match each property listed below with ALL of the types of quadrilaterals listed below that have this property. (Hint: Some may have more than one letter apply.)

81. _________Exactly one pair of opposite sides are parallel.82. _________Diagonals are congruent.83. _________All sides are congruent.84. _________Both pairs of opposite sides are congruent.85. _________Diagonals are perpendicular.86. _________All angles are congruent.

A. parallelogram B. rhombus C. rectangleD. square E. none of the above

Geometry Sem 2 REVIEW for Final Part A ink.notebook · PDF fileGeometry Sem 2 REVIEW for Final...

Documents

Transcript of Geometry Sem 2 REVIEW for Final Part A ink.notebook · PDF fileGeometry Sem 2 REVIEW for Final...