Geometry Study Guide for Chapters 1-10 (*Chapters 11 & 12 are most recent material & therefore not included on the SG)
1.Write an equation in slope-intercept form of the line through point P(6, –4) with slope5.
2.Which three lengths could be the lengths of the sides of a triangle?
A.22 cm, 7 cm, 11 cm B.14 cm, 7 cm, 21 cm C.10 cm, 15 cm, 23 cm D.9 cm, 24 cm, 12 cm
3.Name the smallest angle of
4.Which three lengths can NOT be the lengths of the sides of a triangle?
A.5 m, 7 m, 8 m B.21 m, 6 m, 11 m C.12 m, 15 m, 14 m D.24 m, 18 m, 11 m
5.Two sides of a triangle have lengths 7 and 8. What inequalities describe the possible lengths for the third side?
6.Write an equation in slope-intercept form of the line through points S(4,–8) and T(8,2).
7.Write an equation for the horizontal line that contains point E(–6, –10).
The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
8.The pentagons are regular.
9.
10.Find the missing angle measures.
Solve the proportion.
11.12.
13.Find .
14.Write a two-column proof.
Given:
Prove:
15.Find the values of x, y, and z.
16.Find the volume of the cone shown as a decimal rounded to the nearest tenth.
17.An artist’s canvas forms a golden rectangle. The longer side of the canvas is 28 inches. How long is the shorter side?
Round your answer to the nearest tenth of an inch.
18.Find the value of h in the parallelogram.
19.Find the volume of the cylinder in terms of .h = 6 and r = 3
20.Find the length of arc XPY. Leave your answer in terms of .
21.Find the values of x and y. The diagram is not to scale.
Find the value of x. Round to the nearest tenth.
22.
23.
24.
Find the volume of the given prism. Round to the nearest tenth if necessary.
25.
26.
27.The length of a rectangle is inches and the width is inches. What is the ratio, using whole numbers, of the length to the width?
28.In triangle MNP, name the angle included by the sides and
29.If the perimeter of a square is 88 inches, what is its area?
Find the surface area of the pyramid shown to the nearest whole number.
30.
31.
32.Name the ray that is opposite
33.Find the area of a regular hexagon with an apothem 8.7 centimeters long and a side 10 centimeters long. Round your answer to the nearest tenth.
34.LMNO is a parallelogram. If NM = x + 29 and OL = 4x + 8 find the value of x and then find NM and OL.
35.Given and , find and
36.If BCDE is congruent to OPQR, then is congruent to
37.For the parallelogram, if and find
38.Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
39.Find the value of x. The diagram is not to scale.
40.Q is equidistant from the sides of Find the value of x.
41.Given and , find the length of QS and TV.
Find the value of x. Round to the nearest degree.
42.
43.
44.Find the circumference of the circle in terms of pi.
45.Find the value of x. Round your answer to the nearest tenth.
Find the surface area of the cylinder in terms of .
46.
47. Find values of x and y for which ABCD must be a parallelogram.
Use formulas to find the lateral area and surface area of the given prism. Show your answer to the nearest whole number.
48.
49.
Find the area.
50.
51.
52.
53.Find The diagram is not to scale.
54.Find the values of the variables in the parallelogram.
55.Write a two-column proof to show that
Given: and
56.DEFG is a rectangle. DF = 5x – 6and EG = x + 42. Find the value of x and the length of each diagonal.
57.Find the distance between points P(9, 1) and Q(4, 5) to the nearest tenth.
58.Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
59.Solve for a and b.
60. Points B, D, and F are midpoints of the sides of EC = 38 and DF = 20.
Find AC.
61.The folding chair has different settings that change the angles formed by its parts. Suppose is 28 and is 79. Find . The diagram is not to scale.
62.Find the values of the variables and the lengths of the sides of this kite.
63.List the sides in order from shortest to longest.
Solve for x.
64.
65.
66.Find the surface area of the sphere with diameter of 12 cm. Leave your answer in terms of .
67.Can you conclude the triangles are congruent? Justify your answer.
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
68.
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.
69.
70.are base angles of isosceles trapezoid JKLM.If and
71.If T is the midpoint of find the values of x and ST. The diagram is not to scale.
72.The triangular playground has angles whose measures are in the ratio 7 : 2 : 6. What is the measure of the smallest angle?
73.Solve the extended proportion for x and y with x > 0 and y > 0.
74.The volume of a sphere is 4000 m. What is the surface area of the sphere to the nearest square meter?
75.In the figure, the horizontal lines are parallel and Find JM. The diagram is not to scale.
76.One side of a kite is 3 cm less than 5 times the length of another. The perimeter of the kite is 78 cm. Find the length of each side of the kite.
77.The volume of a cylinder is 980 in.. The height of the cylinder is 20 in. What is the radius of the cylinder?
78.Given: . Find the length of .
79.Name the major arc and find its measure.
80.If find the values of x, EF, and FG. The drawing is not to scale.
81.The figure is formed from rectangles. Find the total area. The diagram is not to scale.
82.Find the surface area of the cone in terms of .
83.Classify the triangle by its sides. The diagram is not to scale.
84. bisects and Solve for x and find
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
85.
86.Find the area of the rhombus.
87.A kite has diagonals 7.3 ft and 7 ft. What is the area of the kite?
Find the length of the missing side.
88.
89.
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
90.
91.
92. bisects Find the value of x.
93.Find the value of x to the nearest degree.
Find the geometric mean of the pair of numbers.
94.100 and 9
95.Find BD.
96.Classify ABC by its angles, when mA = 22, mB = 90, and mC = 68.
97.Name the ray in the figure.
98.What are three names for the angle?
99.Find the value of x. The diagram is not to scale.
100.Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
101.In triangle ABC, is a right angle and 45°. Find BC. If you answer is not an integer, leave it in simplest radical form.
102.The sides of an isosceles triangle have lengths , . The base has length . What is the length of the base?
103. bisects , and. Write an expression for . The diagram is not to scale.
104.What is the measure of a base angle of an isosceles triangle if the vertex angle measures 36° and the two congruent sides each measure 21 units?
105.Name the minor arc and find its measure.
106.Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.
107.Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
108.Find the coordinates of the midpoint of the segment whose endpoints are H(10, 3) and K(8, 1).
109.
110.Find the length of , given that is a median of the triangle and AC = 52.
111.Alan wants to put a fence around his rectangular garden. His garden measures 39 feet by 48 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Alan need to enclose the garden and path?
112.What is the intersection of plane STUV and plane UYXT?
113.The area of a square garden is 242 m2. How long is the diagonal?
114.To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole?
115.Find the area of the circle in terms of p.
116.Name the four labeled segments that are skew to
117.Are C, B, and D collinear? If so, name the line on which they lie.
118.You want to produce a scale drawing of your living room, which is 18 ft by 24 ft. If you use a scale of 2 in. = 4 ft, what will be the dimensions of your scale drawing?
119.Which point is the midpoint of ?
120.M(7, 9) is the midpoint of The coordinates of S are (9, 8). What are the coordinates of R?
121.Viola drives 200 meters up a hill that makes an angle of 5 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
122.Find a counterexample to show that the conjecture is false.
Conjecture: Any number that is divisible by 2 is also divisible by 4.
123.Find the exact area of the shaded region.
124.Find the length of the midsegment. The diagram is not to scale.
125. bisects , LM = 18, NO = 4, and LN = 10. Find OM.
126.Find the area of a sector with a central angle of 140° and a diameter of 7.9 cm. Round to the nearest tenth.
127.In DABC,G is the centroid and BE = 18. Find BG and GE.
128.A triangle has side lengths of 6 cm, 8 cm, and 10 cm. Classify it as acute, obtuse, or right.
129.Are the triangles similar? If so, explain why.
130.Based on the pattern, what are the next two terms of the sequence?4, 7, 10, 13, . . .
131.Find the probability that a point chosen at random from is on the segment .
132.Find the area of a rectangle with base 8 yd and height 5 ft.
133.Write a two-column proof.
Given: and
Prove: