question

Figure ABCD is a parallelogram.
What is the value of p?

answer

6

question

Figure LMNO is a parallelogram.
What is the value of x?

answer

20

question

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

answer

n = 10
CF = 59
FE = 42

question

Figure ABCD is a parallelogram.
What are the measures of angles B and D?

answer

A. âˆ B = 55Â°; âˆ D = 55Â°

question

Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.
What is the value of x?

answer

20

question

Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown.
What is the value of y?

answer

7

question

The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles.
What is the sum of the lengths of the two trails?

answer

16 miles

question

A plot of land is in the shape of a parallelogram with the dimensions shown.
How many feet of fencing are needed to enclose the lot?

answer

68 feet

question

Figure ABCD is a parallelogram.
What are the measures of angles B and C?

answer

B. âˆ B = 65Â°; âˆ C = 115Â°

question

Figure ABCD is a parallelogram.
What is the perimeter of ABCD?

answer

44 unit

question

What is the perimeter of parallelogram LMNO?

answer

80

question

The perimeter of parallelogram ABCD is 46 inches. What is DA?

answer

4

question

What is the measure of angle O in parallelogram LMNO?

answer

105

question

In parallelogram ABCD, what is DC?

answer

13

question

In parallelogram PQSR, what is PQ?

answer

9

question

Given: AB â‰… CD and AD â‰… BC
Prove: ABCD is a parallelogram.
What is the missing reason in step 3?

answer

SSS congruency theorem

question

In parallelogram LMNO, what are the values of x and y?

answer

x = 55, y = 14

question

What is the measure of angle L in parallelogram LMNO?
mâˆ L =

answer

40

question

Which best explains if quadrilateral WXYZ can be a parallelogram?

answer

WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.

question

Given: AD â‰… BC and AD âˆ¥ BC
Prove: ABCD is a parallelogram.
What is the missing reason in step 6?

answer

CPCTC

question

Consider the diagram and proof below.
Given: WXYZ is a parallelogram, ZX â‰… WY
Prove: WXYZ is a rectangle
What is the missing reason in Step 7?

answer

consecutive âˆ s in a â–± are supplementary

question

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

answer

41 units

question

Rectangle PQRS is shown with its diagonals, PR and QS.
What type of triangle is â–³STR?

answer

isosceles triangle

question

Figure ABCD is a parallelogram.
If ABCD is also a rhombus, what must be the value of x?

answer

13

question

What is the approximate side length of the square?

answer

4.2 units

question

Rhombus LMNO is shown with its diagonals.
The length of LN is 28 centimeters. What is the length of LP?

answer

14

question

ABCD is a square.
What is the length of line segment DC?

answer

13

question

A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus.
Which measures are true for the quilt piece? Check all that apply.

answer

a = 60Â°
The perimeter of the rhombus is 16 inches.
The length of the longer diagonal is approximately 7 inches.

question

The figure shown is a rhombus.
Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?

answer

x + y = z

question

The perimeter of the rectangle is 146 units. What is the length of the longer side?

answer

45 units

question

Rectangle PQRS is shown with its diagonals, PR and QS.
What type of triangle is â–³STR?

answer

isosceles triangle

question

TREC is a rectangle. What is the length of ET?

answer

34 units

question

Which statements are true of all squares? Check all that apply.

answer

The diagonals are perpendicular.
The diagonals are congruent to each other.
The diagonals bisect the vertex angles.
The diagonals bisect each other.

question

The figure is a square. Its diagonals meet to form four right angles. What is the approximate value of x?

answer

5.7

question

The figure is a parallelogram. One diagonal measures 28 units.

answer

No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

question

Consider kite ABCD.
What are the values of x and y?

answer

x = 5, y = 22

question

Right trapezoid WXYZ is shown.
What is the measure of angle WXY?

answer

107Â°

question

If KM is drawn on this quadrilateral, what will be its length?

answer

18 units

question

A kite has a perimeter of 70 centimeters. One of the shorter sides measures 16 centimeters. What are the lengths of the other three sides?

answer

16 centimeters, 19 centimeters, and 19 centimeters

question

Which quadrilateral is a kite?

answer

B

question

Given: JKLM is an isosceles trapezoid, KL âˆ¥ JM
Prove: KM â‰… JL
What is the missing reason in step 4?

answer

base angles theorem

question

A kite has a perimeter of 108 feet. One of the longer sides measures 30 feet. What are the lengths of the other three sides?

answer

24 feet, 24 feet, 30 feet

question

If quadrilateral PQRS is a kite, which statements must be true? Check all that apply.

answer

QP â‰… QR
PM â‰… MR
âˆ QPS â‰… âˆ QRS

question

The diagram shows quadrilateral MNPQ.
What is the length of line segment MQ?

answer

11 units

question

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.
In trapezoid EFGH, EF â‰… HG. What is the measure of the angle between Elm Street and Pine Avenue?

answer

72Â°

question

Which statement proves that quadrilateral JKLM is a kite?

answer

LM = JM = 3 and JK = LK = .

question

In the diagram, WZ = square root 26
The perimeter of parallelogram WXYZ is +

answer

8 units.

question

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

answer

Use the distance formula to find the length of each side, and then add the lengths.

question

In the diagram, DG âˆ¥ EF.
What additional information would prove that DEFG is an isosceles trapezoid?

answer

DE â‰… GF

question

In the diagram, KL = 2 square root 2 , LM = square root 5, and MN = square root 2 . What is the perimeter of isosceles trapezoid KLMN?

answer

C. 3 square root 2 + 2 square root 5 units

question

In the diagram, AB = 10 and AC = 2 square root 10. What is the perimeter of â–³ABC?

answer

D. 20 + 2 square root 10 units

question

HIJK is a parallelogram because the midpoint of both diagonals is which means the diagonals bisect each other.

answer

(1,0)

question

Which statement proves that parallelogram KLMN is a rhombus?

answer

The slope of KM is 1 and the slope of NL is -1.

question

Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?

answer

The midpoint of both diagonals is 4 1/2 , 5 1/2 the slope

question

What is the perimeter of â–³LMN?

answer

8 + square root 10 units

question

Given: ABCD is a kite.
Prove: BD bisects AC.
What is the missing reason in step 5?

answer

corresponding parts of congruent triangles are congruent

question

Kite ABCD represents a softball field that is being built.
If AC = 48 meters, what is the perimeter of the field?

answer

140 meters

question

Maggie puts together two isosceles triangles so that they share a base, creating a kite. Each leg of the upper triangle measures 41 inches and each leg of the lower one measures 50 inches.
If the length of the base of both triangles measures 80 inches, what is the length of the kite's shorter diagonal?

answer

39 inches

question

What is the perimeter of square ABCD?

answer

B. 4 square root 37

question

Figure ABCD is a square. Prove BD â‰… AC.
What is the missing reason in the proof?

answer

all sides of a square are congruent

question

The diagram shows the shape of a plot of land that Maria will use for her garden.
She needs to know the length of each side so she can buy fencing. What is the length of line segment FJ?

answer

42 feet

question

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?

answer

38.2 m

question

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

answer

56

question

What is the perimeter of parallelogram WXYZ?

answer

B. 2 square root 5 + 2 square root 17 units

question

Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD.
What is the measure of angle DCU?

answer

135o

question

The perimeter of a rhombus is 28 centimeters. What is the length of each side of the rhombus?

answer

7

question

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

answer

rectangle

question

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

answer

8

question

Given: RT â‰… TV and ST â‰… TU
Prove: RSVU is a parallelogram.

answer

â–³RTS â‰… â–³VTU and â–³RTU â‰… â–³VTS

question

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

answer

50Â° and 130Â°

question

In circle D, which is tangent to the circle?

answer

AB

question

Which equation can be used to find the measure of ?

answer

m:EHG + 80 + 35 = 360

question

What does CDE most specifically describe?

answer

a major arc

question

Segments AC and BD are diameters of circle O.
What is the measure ADE of ?

answer

253

question

In circle D, which is a secant?

answer

GH

question

Which is true regarding chords and diameters of circles?

answer

Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.

question

In circle O, SU is a diameter.
What is m:ST?

answer

130

question

What is the measure of CED?

answer

212

question

In circle O, RT and SU are diameters.
If m:RV = m:VU, what is mVU?

answer

64

question

The measure of BAC is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?

answer

2:1

question

Line segment XY is tangent to circle Z at point U.
If the measure of UV is 84Â°, what is the measure of ?

answer

42

question

Angle KJL measures (7x - 8)o. Angle KML measures (3x + 8)o.
What is the measure of arc KL?

answer

40

question

Given: Circle M with inscribed angel KJL and congruent radii JM and ML
Prove: m angel MJL = 1/2 { m: KL}
What is the missing reason in step 8?

answer

substitution property

question

In circle V, angle WXZ measures 30Â°. Line segments WV, XV, ZV, and YV are radii of circle V.
What is the measure of WUX in circle V?

answer

120

question

Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)Â°.
What is the value of x?

answer

21

question

Line EF is tangent to circle G at point A.
If the measure of angel CAE is 95Â°, what is the measure of CBA ?

answer

190

question

Line segment BD is a diameter of circle E.
What is the measure of BC ?

answer

78

question

In circle D, angle ADC measures (7x + 2)Â°. Arc AC measures (8x - 8)Â°.
What is the measure of angel ABC ?

answer

36

question

What is the measure of arc EF in circle H?

answer

41

question

Given: Circle O with diameter LN and inscribed angle LMN
Prove: LMN is a right angle.
What is the missing reason in step 5?

answer

inscribed angle theorem

question

RT and GJ are chords that intersect at point H.
If RH = 10 units, HT = 16 units, and GH = 8 units, what is the length of line segment HJ?

answer

20

question

What is the length of line segment XZ?

answer

16

question

AX and EX are secant segments that intersect at point X.
What is the length of DE?

answer

3 units

question

Circle C is inscribed in triangle QSU.
What is the perimeter of triangle QSU?

answer

40

question

Line segment BA is tangent to the circle.
What is the length of line segment BA? Round to the nearest unit.

answer

98

question

The circle is inscribed in triangle AEC.
Which are congruent line segments? Check all that apply.

answer

EF and ED
CB and CD

question

What is the length of line segment SV?

answer

16 units

question

Point O is the center of the circle.
What is the perimeter of quadrilateral DOBC

answer

28 units

question

Line segment QP is tangent to the circle.
What is the length of line segment QP? Round to the nearest unit.

answer

20 units

question

SU and VT are chords that intersect at point R.
What is the length of line segment VT?

answer

13 units

question

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

answer

B. 27 r units2

question

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.
What is the area of circle C, which passes though points W and Z?

answer

324 r units

question

The measure of central angle XYZ is 1.25 radians.
What is the area of the shaded sector?

answer

40

question

The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.
Since the circumference of the circle can be represented by 2Ï€r, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure?

answer

C.

question

Point G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are on line segment GX.
What would be the area of a new circle that has line segment GX as its diameter?`

answer

49

question

Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?

answer

49

question

The measure of central angle RST is radians.
What is the area of the shaded sector?

answer

8

question

Which statements are true about circle Q? Check all that apply.

answer

The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.

question

The smallest of the three circles with center D has a radius of 8 inches and
CB = BA = 4 inches.
What is the sum of the areas of all three circles?

answer

464

question

In circle V, r = 14ft.
What is the area of circle V?

answer

196

question

Points E, F, and D are on circle C, and angle G measures 60Â°. The measure of arc EF equals the measure of arc FD.

answer

âˆ EFD â‰… âˆ EGD
ED = FD
mFD = 120Â°

question

Major arc JL measures 300Â°.
Which describes triangle JLM?

answer

equilateral

question

Line segment ON is perpendicular to line segment ML.
What is the length of chord ML?

answer

24 units

question

Angle G is a circumscribed angle of circle E. Major arc FD measures 280Â°.
What is the measure of angle GFD?

answer

40Â°

question

Angle BCD is a circumscribed angle of circle A.
What is the measure of minor arc BD?

answer

100Â°

question

Angle X is a circumscribed angle of circle V.
Which name best describes figure VWXY?

answer

square

question

Points A, B, C, and D lie on circle M. Line segment BD is a diameter.
What is the measure of angle ACD?

answer

67.5

question

What is the measure of circumscribed âˆ X?

answer

90

question

What is the measure of angle COA?

answer

160

question

Points N, P, and R all lie on circle O. Arc PR measures 120Â°.
How does the measure of angle RNQ relate to the measure of arc PR?

answer

Angle RNQ is equal in measure to arc PR.

question

Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: (x2 - x1)2 + (y2-y1)2

answer

A. 2, 21

question

Mrs. Culland is finding the center of a circle whose equation is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her work is shown.
x2 + y2 + 6x + 4y - 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4

answer

(x + 3)2 + (y + 2)2 = 42, so the center is (-3, -2).

question

What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?

answer

2

question

Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?

answer

(x + 4)2 + (y - 9)2 = 25

question

Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?

answer

(x + 3)2 + (y + 5)2 = 36

question

The center of a circle represented by the equation (x + 9)2 + (y âˆ’ 6)2 = 102 is .

answer

(-9,6)

question

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

answer

(x - h)2 + (y - k)2 = r2

question

Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z?

answer

The radius is the square root of the constant term, z.

question

What is the center of a circle whose equation is x2 + y2 + 4x - 8y + 11 = 0?

answer

(-2, 4)

question

Does the point (2,6 ) lie on the circle shown? Explain.

answer

D. No, the distance from (0, 0) to (2,6 ) is not 3 units.

question

Which graph represents the equation y2 = -4x?

answer

A

question

A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis.
Which part of the graph will the directrix pass through?

answer

the negative part of the x-axis

question

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = -4.
In which direction does the parabola open?

answer

right

question

A parabola can be represented by the equation y2 = -x.
What are the coordinates of the focus and the equation of the directrix

answer

A

question

A parabola can be represented by the equation x2 = -20y.
What are the coordinates of the focus of the parabola?

answer

(0,-5)

question

The focus of a parabola is located at (0,-2). The directrix of the parabola is represented by y = 2.
Which equation represents the parabola?

answer

x2 = -8y

question

A parabola has a vertex at (0,0). The focus of the parabola is located on the positive y-axis.
In which direction must the parabola open?

answer

up

question

Which equation represents the parabola shown on the graph?

answer

x2 = 6y

question

A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis.
Which statements about the parabola are true? Check all that apply.

answer

The directrix will cross through the positive part of the y-axis.
The equation of the parabola could be x2 = -1/2 y.

question

A parabola is represented by the equation x2 = 4y.
What are the coordinates of the focus of the parabola?

answer

(0,1)

question

If line segment AB measures approximately 8.6 units and is considered the base of parallelogram ABCD, what is the approximate corresponding height of the parallelogram? Round to the nearest tenth.

answer

4.8 units

question

What is the area of triangle QRS?

answer

7

question

What is the area of triangle GHJ?

answer

6 square units

question

If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

answer

1.6 units

question

What is the area of parallelogram ABCD?

answer

13

question

Which expression can be used to find the area of triangle RST?

answer

(8 âˆ™ 4) - 1/2 (10 + 12 + 16)

question

What is the area of triangle ABC?

answer

3

question

What is the area of triangle LMN?

answer

4 square units

question

What is the area of parallelogram ABCD?

answer

20 square units

question

Michael is finding the area of parallelogram ABCD. To do this, he follows the steps in the table.
To solve the problem using these steps, what are the dimensions of the rectangle he should draw?

answer

4 units by 4 units

question

How do the areas of the parallelograms compare?

answer

The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

question

If line segment RU is considered the base of parallelogram RSTU, what is the corresponding height of the parallelogram?

answer

5.4 units

question

Payton cut out two shapes, as shown, that she will later put together to resemble a house.
What is the total area of the two shapes

answer

21 square units

question

What is the area of triangle ABC?

answer

7

question

A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.
What is the area of the piece of red paper after the hole for the photograph has been cut?

answer

47 square units

question

A kite has vertices at (2, 4), (5, 4), (5, 1), and (0, -1).
What is the approximate perimeter of the kite? Round to the nearest tenth.

answer

16.8 units

question

A company designs a logo using a kite figure around the letter t.
The logo is 12 centimeters wide and 16 centimeters tall. What is the area of the logo?

answer

96 sq. cm

question

The area of the trapezoid is 40 square units.
What is the height of the trapezoid?

answer

5

question

Trapezoid ABCD is graphed in a coordinate plane.
What is the area of the trapezoid?

answer

24 square units

question

Kite WXYZ is graphed on a coordinate plane.
What is the approximate perimeter of the kite? Round to the nearest tenth.

answer

16.2 units

question

What is the area of the rhombus?

answer

24

question

A kite is inscribed in a square with a side length of 9 units.
What is the area of the kite?

answer

40.5 square units

question

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x - 1.
What is the value of x?

answer

10

question

Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units.
What is the length of AC?

answer

12 units

question

In the kite, AC = 10 and BD = 6.
What is the area of kite ABCD?

answer

30 square units

question

Which statements are true about the regular polygon? Check all that apply.

answer

Each interior angle measures 108Â°.
All of the angles are congruent.
The sum of the measures of the interior angles is 180(5 - 2)Â°.

question

Which is a correct description of the polygon?

answer

It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

question

What is the value of x?

answer

8

question

What type of polygon is shown?

answer

convex hexagon

question

What type of polygon is shown?

answer

concave heptagon

question

What is the value of x?

answer

130Â°

question

Which polygon has an interior angle sum of 1080Â°?

answer

A

question

Which polygon has an interior angle sum of 900Â°?

answer

D

question

Which statements are true about polygons? Check all that apply.

answer

The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.
If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon.

question

What is the sum of the measures of the interior angles of a 12-gon?

answer

1800