Geometry semester 2 model problems ca essential standards part 2
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Geometry Semester 2 Model Problems (CA Essential Standards) Part 2. PowerPoint by Kenneth C Utt John Kimball High -- TUSD. Model Problem #33. In the diagram shown, m  CBD = 95˚. What is the measure of  CDB ?. 44 o + 95 o + x o = 180 o 139 o + x o = 180 o x o = 180 o – 139 o

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Geometry Semester 2 Model Problems (CA Essential Standards) Part 2

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Geometry semester 2 model problems ca essential standards part 2

Geometry Semester 2 Model Problems (CA Essential Standards) Part 2

PowerPoint by

Kenneth C Utt

John Kimball High -- TUSD


Model problem 33

Model Problem #33

In the diagram shown, mCBD = 95˚. What is the measure of CDB ?

44o + 95o + xo = 180o

139o + xo = 180o

xo = 180o – 139o

xo = 41o

95o


Model problem 34

Model Problem #34

In the diagram shown, P is a point on ML. What is the measure of the angle marked X?

180 – (90 + 31) = MPN

180 – 121 = 59o

180 – (59 + 55) = LPQ

180 – 114 = 66o

180 – (90 + 66) = PQL

180 – 156 = 24o

180 – 24 = x = 156o

59o

66o

24o


Model problem 35

Model Problem #35

If ABC is rotated 90˚clockwise about the origin to form A’B’C’, what would be the coordinates of A’?

A’ =(-1,-3)

B’ = (-4,-4)

C’ = (-3,-2)


Model problem 36

Model Problem #36

The coordinates of the vertices of ∆JKL, are J(-2,-1), K(1,3), L(4,-3). If ∆JKL is translated 2 units down and 4 units to the right to create , what are the coordinates of the vertices of ∆J’K’L’?

J’ = (-2 + 4,-1 – 2) = (2,-3)

K’ = (1 + 4, 3 – 2) = (5, 1)

L’ = (4 + 4, -3 – 2) = (8,-5)


Model problem 37

Model Problem #37

If quadrilateral DEFG is reflected across the y-axis, it would create quadrilateral D’E’F’G’. What are the coordinates of point G’ ?

G’ = (6,2)


Model problem 38

Model Problem #38

A diagram from a proof of the Pythagorean Theorem is shown. Write an equation that represents the area of the entire square in two ways. On the left side, express the area as the product of the length and the width. On the right, represent the sum of the areas of the triangles and the smaller square. Then use the equation to prove the theorem.

(a + b)2

c2 + 4(a ∙ b) ÷ 2


Model problem 39

Model Problem #39

A right triangle’s hypotenuse has length 11. If one leg has length 6, what is the length of the other leg?

112 = 62 + b2

121 = 36 + b2

85 = b2

√85 = b


Model problem 40

Model Problem #40

In a basketball game, a player from the home team threw the ball from corner C to a player standing at point E. (E is the midpoint of AD). Then the player at point E threw the ball to a player at corner B. If the court was 80 feet long and 50 feet wide, how far was the ball thrown? (Leave in simplified radical form)

√4100 =

10√41 =

2 ∙10 √41

20√41

502 + 402 = h2

2500 + 1600 = h2

√4100 = h


Model problem 41

Model Problem #41

In the figure shown, sin A  0.4, cos A  0.5, and tan A  0.9. What is the approximate length of BC?

Sin A = 0.4 = BC/40

(40)(0.4) = BC

16 = BC


Model problem 42

Model Problem #42

In the figure below, if tan A = 4/3, what are sin A and cos A?

5

4

32 + 42 = h2

9 + 16 = h2

√25 = 5 = h

sin A = 4/5

cos A = 3/5

3


Model problem 43

Model Problem #43

A ladder is leaned against a wall at an angle of 65° to the ground. How far off the ground does the ladder touch the wall?

sin 65o = ?/30’

0.9 = x/30’

27’ = x


Model problem 44

Model Problem #44

Triangle JKL is shown in the diagram. Which equation should be used to find the length of LJ?

A sin 28o = LJ/54

B sin 28o = 54/LJ

C cos 28o = LJ/54

D cos 28o = 54/LJ

sin

cos


Model problem 45

Model Problem #45

On a swing set, on engineer used a support bar that was 20 feet long. If the support bar forms a 70° angle to the ground, how far apart will the support bars be at the base?

sin 70o = 0.94

cos 70o = 0.34

tan 70o = 2.75

sin 70o = 0.94

cos 70o = 0.34

tan 70o = 2.75

cos 70o = Adj/20

0.34 = Adj/20

6.8 = adj

6.8 ∙ 2 = 13.6


Model problem 46

Model Problem #46

In the diagram, mB = 75o and AC = 11.9 in. Which equation could be used to find BC?

A x = 11.9(tan 75o)

B x = 11.9(sin 75o)

C x = 11.9/tan 75o

C x = 11.9/sin 75o

tan 75o = 11.9 / x

tan 75o (x) = 11.9

x = 11.9 / tan 75o


Model problem 47

Model Problem #47

The right triangle in the diagram has one side with a length of 5√3. What is the length of the side marked x?

A 5

B 15

C 5√6

D 10√3

x

5√3

60o


Model problem 48

Model Problem #48

In the circle shown, the measure of BC= 60o, and the measure of ABD = 62o. What is the measure of CD?

Arc BD = 124o

124o – 60o = 64o


Model problem 49

Model Problem #49

In the circle shown, DF and CE are chords intersecting at G. If DG = 9, FG = 4, and EG = 12, what is the length of CG?

9

4 ∙ 9 = x ∙ 12

36 = 12x

3 = x

12

x

4


Model problem 50

Model Problem #50

In the circle shown, what is the measure of angle 1?

1 = ½(104o – 38o)

½(66o)

33o


Model problem 51

Model Problem #51

LM is tangent to a circle, whose center is C, at point M. MQ is a diameter. If mQNP = 65˚ and mNPM = 50˚, what is mPMR?

180o -65o = 115o

180o – (115o + 50o)

180o – 165o

15o

90o – 15o

75o

15o

115o


Model problem 52

Model Problem #52

A square is circumscribed about a circle. What is the ratio of the circumference of the circle to the perimeter of the square?

A ¼

B ½

C 2/

D /4

Square = 4 ∙10 = 40

Circle = 10 = 10

10/40

1/4

10


Model problem 53

Model Problem #53

A cylinder rolls across a table top for 10 complete revolutions. If the diameter of the base is 6 inches, how far did the cylinder travel? (Leave the answer in terms of ).

10 ∙  ∙ 6 =

60 ins.


Model problem 54

Model Problem #54

The prism shown has a base in the shape of a right triangle. What is the lateral surface area of the prism?

3 x 6 = 18

4 x 6 = 24

32 + 42 = h2

25 = h2

5 x 6 = 30

18 + 24 + 30 = 72 cm2


Model problem 55

Model Problem #55

What is the volume of the prism shown?

4 ( 8 + 6 ) ÷ 2 = 28 = Base

28 x 10 = 280 mm3


Model problem 56

Model Problem #56

A target for a yard game is made with areas that are alternately painted white and gray, as shown in the diagram. The inner circle is white and has a radius of 1 inch. Each of the other three rings has a radius 1 inch more than the ring before it. What is the area of the white portion of the target?

32 - 22 + 12

9 - 4 + 1

6 or 18.84


Model problem 57

Model Problem #57

A rectangle that is 12 feet wide has a perimeter of 40 feet. What is the area of the rectangle?

40 – (12 + 12) = 16

16 ÷ 2 = 8

8 ∙ 12 = 96 ft2


Model problem 58

Model Problem #58

Each side of a triangle measures 4 m. What is the area of the triangle? (Leave the answer in simplified radical form).

22 + b2 = 42

4 + b2 = 16

b2 = 12

b = √4 ∙ 3 or 2√3

4 ∙ 2√3 ÷ 2

4√3 m2


Model problem 59

Model Problem #59

Quadrilateral ABCD is a rhombus. If AC = 10 inches and BD = 8 inches, what is the area of ABCD?

4

10 ÷ 2 = 5 & 8 ÷ 2 = 4

4 ∙ (5 ∙ 4) ÷ 2 =

2 ∙ 20 = 40 in2

5


Model problem 60

Model Problem #60

The diagram shows a trapezoid with a height of 4 cm. What is the area of the trapezoid?

4 (3 + 9) ÷ 2

2 (3 + 9)

2 ∙ 12 = 24 cm2


Model problem 61

Model Problem #61

The volume of a right rectangular prism is calculated to be 18 cubic centimeters. If the length, the width, and the height of the prism are all doubled, what would be the volume of the new prism?

2 x 3 x 3 = 18

4 x 6 x 6 = 144 cm3


Model problem 62

Model Problem #62

The cylinder shown has a height of 4 cm and the diameter of the base is 10 cm. What is the volume of the cylinder?

V = Bh

V = 52 ∙ 4

V = 25 ∙ 4

V = 100

V = 314 cm3


Model problem 63

Model Problem #63

The pyramid shown has a square base that measures 8 cm on each side. The slant height of the pyramid is 6 cm. What is the surface area of the prism?

8 x 8 = 64

4 x 8 x 6 ÷ 2 = + 96

160 cm2


Model problem 64

Model Problem #64

Given: AB. What is the first step in constructing the perpendicular bisector to AB?

a. Draw a line segment connecting points E and F.

b. From point C, draw an arc that intersects the line at points A and B.

c. Draw a line segment connecting points A and B.

d. From points A and B, draw equal arcs that intersect at points E and F.


Model problem 65

Model Problem #65

Darla is constructing an equilateral triangle. Which of the following could be her first step?

AB

CD


Model problem 66

Model Problem #66

Marsha is using a straightedge and compass to do the construction shown. Which statement best describes the construction Martha is doing?

a. a line through P parallel to line l by constructing two lines perpendicular to the same line

b. a line through P parallel to line l by copying an angle

c. a line through P perpendicular to line l

d. a line through P congruent to line l


Model problem 67

Model Problem #67

Amina is bisecting an angle. Which of the construction diagrams shown below best represents the beginning of Amina’s construction?

AB

CD


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