Geometry
Geometry 2nd Semester 2017 Final Review
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Name: _________________________________
Period:
May
from
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Learning Targets
Unit 6: Quadrilaterals
I can produce transformations to map a figure onto another figure to prove the figures are congruent. G.CO.6
I can prove that the opposite angles of a parallelogram are congruent. G.CO.11
I can prove that the diagonals of a parallelogram bisect each other. G.CO.11
I can prove that if a parallelogram is a rectangle then the diagonals are congruent. G.CO.11
I can use the distance formula and slope formula to prove or disprove a figure is a type of quadrilateral. G.GPE.4
I can find a point on a line segment that divides the segment into a given ratio. G.GPE.6
I can find the equation of a line parallel or perpendicular to a given line that passes through a given point. G.GPE.5
Unit 7: Circles
I can explain the formula for the circumference and area of a circle. G.GMD.1
I can prove all circles are similar using the ratio of the diameter to circumference. G.C.2
I can use definitions, properties, and theorems to identify and describe relationships among inscribed angles, radii, and chords. G.C.2
I understand that inscribed angles on a diameter are right angles. G.C.2
I understand that the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G.C.2
I can prove properties of angles for a quadrilateral inscribed in a circle. G.C.3
I can use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius. G.C.5
I can identify the constant of proportionality as the radian measure of the angle. G.C.5
I can find the arc length of a circle. G.C.5
I can use similarity to derive the formula for the area of a sector. G.C.5
I can find the area of a sector in a circle. G.C.5
I can use the Pythagorean theorem to derive the equation of a circle, given the center and the radius. G.GPE.1
I can complete the square, when given an equation of a circle, to find the center and radius of a circle. G.GPE.1
Unit 8: Polygons (Area)
I can describe objects using geometric shapes, their measures, and their properties. G.MG.1
I can apply geometric concepts in modeling situations. G.MG.3
I can find the area of regular polygons with and without the use of trigonometry. G.SRT.5
I can find the area of parallelograms, trapezoids, rhombuses, kites, and circles.
Unit 9: Solids (Surface Area & Volume)
I can use geometric shapes, their measures, and their properties to describe objects. G.MG.1
I can explain the formula for the volume of a prism, cylinder, pyramid, cone or sphere by determining the meaning of each term or
factor. G.GMD.1
I can apply the volume formula of a prism, cylinder, pyramid, cone or sphere to solve a problem. G.GMD.3
I can identify the cross section shape of a three-dimensional object. G.GMD.4
I can identify the three-dimensional figure generated by rotating a two dimensional figure. G.GMD.4
I can mathematically communicate that a cross-section of a solid is the intersection of a plane (two-dimensional) and a solid
(three-dimensional). G.GMD.4
Unit 6
Targets: I can prove theorems about parallelograms and their converses. G.CO.11
Determine whether each of the following quadrilaterals is a parallelogram. Clearly explain your reasoning using precise
language.
1)
________________________________________________________________
________________________________________________________________
2)
_______________________________________________________________
_______________________________________________________________
3) Find the values of x and y so that DAVE is a rhombus.
4) ABCD is a Rhombus. Find the length of each side. If necessary, round to the nearest tenth.
5) PAWS is a parallelogram. Find the values of x and y.
Target: I can apply properties of quadrilaterals.
6) Find x.
7) Find the length of the long diagonal in this kite. If necessary, round to the nearest tenth.
8) Find x. ABCD is an isosceles trapezoid.
9) Which quadrilateral listed is not a parallelogram?
A. Rhombus
B. Kite
C. Square
10) A square is ____________ a rhombus. (Always, Sometimes, Never)
D. Rectangle
Target: I can use the distance formula and slope formula to prove or disprove a figure is a type of quadrilateral. G.GPE.4
11) Determine the most precise name for quadrilateral QBHA.
y
Q(-4,2) B(0,8) H(6,8) A(2,2)
x
Unit 7
I can explain the formula for the circumference and area of a circle. (G.GMD.1)
12) Find the circumference. Leave your answer in terms of 𝜋.
13) Find the area of the circle. Leave your answer in terms of 𝜋.
I can use definitions, properties, and theorems, to identify and describe relationships among inscribed angles, radii, and chords. (G.C.2)
14) RC = 4, CE = 6, CL = 12, Find IL.
15) Find AD. Round to the nearest tenth if necessary.
D
8
A
8
B
15
C
16) The figure consists of a chord, a secant and a tangent to the circle. Find x.
(Round to the nearest hundredth, if necessary.)
17) Find the value of x. (Round to the nearest hundredth, if necessary.)
18) Find the measure for each angle with a variable
d

O
a
c
b
19) In the diagram, 𝐴𝐵 is a diameter, and 𝐴𝐵  𝐶𝐷. Find m  CAP for m  CBD = 70°.
(The diagram is not drawn to scale.)
C
A
P
D
B
20) m  O = 74°. O is the center of the center. Find m∠R.
N
O
Q
R
̂.
̂ = 96° find m𝐵𝐶
21) m  A = 37°, m𝐷𝐸
D
B
A
C
E
̂ = 135° and m𝐴𝐷
̂ = 103°.
22) Find the measure of angle x if m𝐶𝐵
I understand that inscribed angles on a diameter are right angles. (G.C.2)
23) Find the value of x.
I understand that the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (G.C.2)
24) In circle S, RA = 6, RS = 10. Find RU
I can prove properties of angles for a quadrilateral inscribed in a circle. (G.C.3)
25) Find the value of x and y.
I can use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius (G.C.5)
̂ . Round to the nearest tenth, if necessary
26) Find the length of 𝑇𝑂
I can identify the constant of proportionality as the radian measure of the angle. (G.C.5)
27) Find the measure of x in degrees given the length of the arc is 6. Round to the nearest degree.
I can find the length of an arc in a circle. (G.C.5)
̂ , 𝐴𝐶
̂ and the area of sector AOC given OC = 3m. Leave your answer in terms of .
28) Find the length of 𝐴𝐵𝐶
̂ __________
length of 𝐴𝐵𝐶
̂ __________
length of 𝐴𝐶
I can find the area of a sector in a circle (G.C.5)
29) Find the area of the figure to the nearest tenth.
area of sector AOC __________
I can use the Pythagorean Theorem to derive the equation of a circle, given the center and the radius. (G.GPE.1)
30) Write the standard equation for the circle given the center at (-1, -4) and a radius of length √7.
I can complete the square when given an equation of a circle to find the center and the radius of a circle. (G.GPE.1)
31) Find the center and radius for the equation of the circle given (x – 11)2 + (y + 6)2 = 81
32) Find the center and radius for the equation of the circle given (𝑥 − 7)2 + (𝑦 − 2)2 = 51
33) Find the equation of a circle with center (a,b) and radius c.
I understand the radius is perpendicular to a chord if and only if the radius bisects the chord and its arc (G.C.U5)
34) Find the value of x. The diagram is not drawn to scale. Round to the nearest tenth, if necessary.
Unit 8
Target: I can describe objects using geometric shapes, their measures, and their properties. G.MG.1
Target: I can apply geometric concepts in modeling situations. G.MG.3
Target: I can find the area of regular polygons with and without the use of trigonometry. G.SRT.5
Target: I can find the area of parallelograms, trapezoids, rhombuses, kites, and circles. G.SRT.5
35) Find the area of this parallelogram. (not drawn to scale)
36 in.
40 in.
30in.
in.
33
36) Find the area of this trapezoid.
19 in.
12.6 in.
14.5 in.
29.2 in.
37)
Find the area of a polygon with the vertices of (–2, 3), (1, 3), (5, –3), and (–2, –3).
38)
A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?
39) The apothem of a regular hexagon is 6√3 ft. Find the area. Leave your answer in simplest radical form.
40) The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. (not drawn to
scale)
15
18
41) Find the area of the triangle to the nearest tenth.
42) The area of a rhombus is 60 m2. One diagonal is 10 m. Find the length of the other diagonal.
43) Find the area of this figure.
44) Find the area of the shaded region.
45) Find the area of a regular pentagon with a side of 10 inches and an apothem of 7 inches.
46) What is the measure of an exterior angles of a regular decagon?
47) What is the measure of an interior angle of a regular hexagon?
48) Find the value of m in the regular pentagon.
49) Find the value of x.
50) Find the value of x.
51) What is the measure of an interior angle of a regular octagon?
52) Find the value of m in the regular octagon.
53) What geometric polygon(s) make up this trampoline?
Unit 9
Target: I can use geometric shapes, their measures and their properties to describe objects. (G.MG.1)
54) Name the geometric solids that model the sharpened pencil pictured.
Target: I can explain the formula for the volume of a prism, cylinder, pyramid, cone, or sphere by determining the meaning of each term or factor. (G.MGD.1)
Target 3: I can apply the volume and surface area formulas of a prism, cylinder, pyramid,
cone, or sphere to solve a problem. (G.MGD.3)
55) Use the cone below to find exact answers for the following:
a) surface area
b) volume
56) Use the cylinder below to find exact answers for the following:
a) surface area
b) volume
57) Use the triangular right prism below to find exact answers for the following:
a) surface area
b) volume
58) Use the square pyramid below to find exact answers for the following:
a) surface area
b) volume
59) Use a sphere with a radius of 6 yards to find exact answers for the following:
a) surface area
b) volume
60) Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in. and the height is 21 in. The
second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?
Target: I can identify the cross section shape of a three-dimensional object (G.GMD.4)
Target: I can mathematically communicate that a cross-section of a solid is the intersection of a plane and a solid (G.GMD.4)
61) Provide 2 different geometric solids that have a cross section of a rectangle.
(Drawing a picture may help.)
62) What geometric solid will a semi-circle create if it is rotated around the y-axis?