Geometry B Unit Test Reviews

A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of the central angles has a measure of 40°. How many sides does the polygon have?

9

What is the area of triangle RST?

9

A regular hexagon is shown. What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.

9 in

Two sides of an acute triangle measure 5 inches and 8 inches. The longest side is unknown. What is the greatest possible whole-number length of the unknown side?

9 inches

Triangle XYZ is reflected over its hypotenuse to create a kite. What is the approximate distance from Y to Y'? Round to the nearest tenth.

9.2 units

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.

95

The measure of central angle XYZ is 3╓/4 radians. What is the area of the shaded sector?

96╓

Which polygon is a convex heptagon?

A

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3.14 for .

B

Which graph represents the equation x2 = 8y?

B

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?

Henry's design would result in a larger flower bed because its area would be 2,500 square feet.

Triangle JKL is equilateral. One side of the triangle, JL, is a diameter of circle M. Which is true about line segments JK and KL?

Neither segment is a chord nor tangent to circle M.

The angle measures of quadrilateral RSTU are shown. m∠R = (2x)° m∠S = (3x - 35)° m∠T = (x + 35)° The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

How do the areas of the parallelograms compare?

The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle. Which statements about the clock are accurate? Check all that apply.

The circumference of the clock is approximately 62.8 inches. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.

The length of segment XY can be found by solving for a in 202 - 7.652 = a2. The measure of the central angle, ∠ZXW, is 45°.

The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2. Which statement about use of public buses in the cities is most likely true?

The residents of City B are more likely to use public buses because their city has a greater population density.

Which statement proves that PQRS is a parallelogram? The slopes of SP and RQ are both -2 and SP = RQ

The slopes of SP and RQ are both -2 and SP = RQ = √45.

The table shows information about Town A in Illinois and Town B in Florida. If the two towns have the same population density, which must also be true?

Town B has a population of approximately 5,138.

What is the missing reason in the proof?

all sides of a square are congruent

Which concept can be used to prove that the diagonals of a parallelogram bisect each other?

congruent triangles

Given △ABC, sin(A) =

cos(c)

Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Figure WXYZ is a parallelogram. Which angle measures are correct? Check all that apply.

m∠X = 55° m∠W = 125° m∠Z = 55°

Which equation represents the general form a circle with a center at (-2, -3) and a diameter of 8 units?

x2 + y2 + 4x + 6y - 3 = 0

Angle G is a circumscribed angle of circle E. What is the measure of angle G, in terms of x?

x° + x°

Which equation represents the parabola shown on the graph?

y2 = -8x

What is the missing statement in step 4?

△RTS ≅ △VTU and △RTU ≅ △VTS

Given △ABC ~ △XYZ, what is the value of cos(Z)?

12/13

What is the area of triangle DEF?

2√14 square units

What is the best approximation of the value of a?

3.0 cm

What is the measure of each exterior angle of a regular hexagon?

60°

Arc QVT measures 156°. Which statement must be true?

Angles QRT and QST both measure 78°.

Which circle has a central angle that measures 40°?

B

Which circle shows AB that measures 60°?

C

Angle K measures 67º and angle L measures 119°. What are the measures of angles M and N?

M = 113° and N = 61°

A cylinder with a base diameter of x units has a volume of πx3 cubic units. Which statements about the cylinder are true? Check all that apply.

The radius of the cylinder is 1/2x units. The area of the cylinder's base is 1/4πx2 square units. The height of the cylinder is 4x units.

An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?

pentagon

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

rectangle

Which equation is correct and can be used to solve for the value of z?

sin(51°)/2.6 = sin(76°)/z

Which equation can be used to find the measure of angle LKJ?

sin-1(8.9/10.9) = x

Which is the base shape of this prism?

triangle

A parabola has a vertex at the origin. The focus of the parabola is located at (-2,0). Which is the equation for the directrix related to the parabola?

x = 2

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°. Law of cosines: a2 = b2 + c2 - 2bccos(A) What is x, the length of the diagonal, to the nearest whole number?

5

Given right triangle RST, what is the value of sin(S)?

5/13

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°. What are the two different angle measures of the parallelogram-shaped tile?

50° and 130°

Two similar cylinders have surface areas of 24π cm2 and 54π cm2. The volume of the smaller cylinder is 16π cm3. What is the volume of the larger cylinder?

54╓ cm

In circle O, MP is a diameter. If NP is 6 more than 5 times the measure of MN, what is NP?

151°

Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A?

16 inches

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image. What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°

A circular table top has a radius of 24 inches. What is the area of the table top, to the nearest square inch?

1809 in.2

What is the area of the shaded sector of the circle?

180╓ units

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.

183 meters

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the tissue paper in the packaging box?

198.264 cubic centimeters

What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?

2 units

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

2,125 cm2

The equation cos(35°) = a/25 can be used to find the length of BC. What is the length of BC? Round to the nearest tenth.

20.5

Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.

22

Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA. What is the measure of angle ADM?

22.5°

Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus?

24 square units

Points D, E, and F are on circle C and EF ≅ DF. What is the measure of ∠CDF?

26°

What is the perimeter of parallelogram WXYZ?

2√5 + 2√17 units

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles. Triangle 1: 3 in., 6 in., 7 in. Triangle 2: 3 in., 6 in., 8 in. Triangle 3: 3 in., 7 in., 8 in. Triangle 4: 6 in., 7 in., 8 in. How many of his triangles are obtuse?

3

A prism is enlarged by a factor of 4. The volume of the new prism is 576 cubic units. What could be the dimensions of the original prism?

3 by 3 by 1

Galina is finding the area of triangle RST. To do so, she follows the steps in the table. To solve the problem using these steps, what are the dimensions of the rectangle she should draw?

3 units by 4 units

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°. What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

3.2 yards

Line segment ON is perpendicular to line segment ML, and PN = 10. What is the area of triangle MOL?

300 square units

What is the area of triangle ABC? Round to the nearest square unit.

33

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder?

33.6π mm2

Rhombus LMNO is shown with its diagonals. Angle MLO measures 112°. What is the measure of angle MLP?

56°

Which is the best approximation for the measure of angle ABC?

58.3°

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile. How many deer live in the county? Round to the nearest whole number, if necessary.

5852

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. What is the approximate area of the hexagon?

672 cm2

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand. Law of cosines: a2 = b2 + c2 - 2bccos(A) Rounded to the nearest meter, the distance between the docks is _____ meters.

705

In parallelogram WXYZ, WY = 12 in., XZ = 16 in., WX = 10 in., and XY = 9 in. What is the length of line segment MX?

8 in.

Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. m∠DFE = 80°. What is the measure of ?

80

Which equation correctly applies the law of cosines to solve for an unknown angle measure?

8^2 = 7^2 + 11^2 - 2(7)(11)cos(P)

A parabola and its directrix are shown on the graph. What are the coordinates of the focus of the parabola?

(0,2)

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws. Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU?

(18 + 4)

The center of a circle represented by the equation (x − 5)2 + (y + 6)2 = 42 is

(5, -6)

Two circles are concentric if they have the same center. Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?

(x - 4)2 + (y - 6)2 = 16

Given right triangle QRS, what is the value of sin(30°)?

1/2

The equation tan(55°) = 15/b can be used to find the length of AC. What is the length of AC? Round to the nearest tenth.

10.5

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

102°

In quadrilateral QRST, measures (5x + 15)o. Angle TQR measures (4x + 3)o. What is the measure of angle RST?

105°

Consider circle C with angle ACB measuring 3╓/4 radians. If minor arc AB measures 9π inches, what is the length of the radius of circle C? If necessary, round your answer to the nearest inch.

12

Triangle BCD is isosceles and BC ≅ BD. What is the measure of BC?

130°

n circle O, AD and BE are diameters. What is mAE?

132°

The law of cosines is used to find the value of m. m2 = 272 + 182 - 2(27)(18)cos(28°) m2 = 729 + 324 - (972)cos(28°) m2 = 1053 - (972)cos(28°) To the nearest whole number, the value of m is ____

14

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown. What is the greatest possible whole-number value of the congruent side lengths?

14 cm

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

14.2 feet

Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY. The area of BXYC is 71.5 square units. What is the area of ABCD?

143 square units

Consider circle N with radius 30 cm and θ = ╓/6 radians. What is the approximate length of minor arc LM? Round to the nearest tenth of a centimeter.

15.7

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?

38.2 m

In parallelogram RSTU, SW = 4 cm, WT = 6 cm, RS = 5 cm, and ST = 7 cm. What is the length of line segment WU?

4 cm

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle. At approximately what angle does the wire meet the ground?

56.4°

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram?

4 cm and 7 cm

Circle O has a circumference of approximately 28.3 cm. What is the approximate length of the radius, r?

4.5 cm

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

4.7

What is the perimeter of square ABCD?

4√37 units