geometry
Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. What is the missing reason in step 6?
CPCTC
In the diagram, AB = 10 and AC = 2 square root 10. What is the perimeter of △ABC?
D. 20 + 2 square root 10 units
The circle is inscribed in triangle AEC. Which are congruent line segments? Check all that apply.
EF and ED CB and CD
The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
Use the distance formula to find the length of each side, and then add the lengths.
Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is △STR?
isosceles triangle
Figure CDEF is a parallelogram. Which measures are correct? Check all that apply.
n = 10 CF = 59 FE = 42
The figure shown is a rhombus. Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?
x + y = z
If KM is drawn on this quadrilateral, what will be its length?
18 units
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees. What is the value of x?
20
Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)°. What is the value of x?
21
AX and EX are secant segments that intersect at point X. What is the length of DE?
3 units
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?
39 inches
What is the approximate side length of the square?
4.2 units
Circle C is inscribed in triangle QSU. What is the perimeter of triangle QSU?
40
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 ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue?
72°
Which is true regarding chords and diameters of circles?
Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.
Which expression can be used to find the area of triangle RST?
(8 ∙ 4) - 1/2 (10 + 12 + 16)
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?
16 centimeters, 19 centimeters, and 19 centimeters
Figure LMNO is a parallelogram. What is the value of x?
20
What is the measure of CED?
212
What is the area of the rhombus?
24
Angle KJL measures (7x - 8)o. Angle KML measures (3x + 8)o. What is the measure of arc KL?
40
Rhombus LMNO is shown with its diagonals. Angle MLO measures 112°. What is the measure of angle MLP?
56
Which statement proves that quadrilateral JKLM is a kite?
LM = JM = 3 and JK = LK = .
Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z?
The radius is the square root of the constant term, z.
What is the area of parallelogram ABCD?
13
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?
2
The perimeter of parallelogram ABCD is 46 inches. What is DA?
4
Points A, B, C, and D lie on circle M. Line segment BD is a diameter. What is the measure of angle ACD?
67.5
Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown. What is the value of y?
7
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 the diagram, WZ = square root 26 The perimeter of parallelogram WXYZ is +
8 units.
What is the perimeter of parallelogram LMNO?
80
A parabola can be represented by the equation y2 = -x. What are the coordinates of the focus and the equation of the directrix
A
If quadrilateral PQRS is a kite, which statements must be true? Check all that apply.
QP ≅ QR PM ≅ MR ∠QPS ≅ ∠QRS
Given: AB ≅ CD and AD ≅ BC Prove: ABCD is a parallelogram. What is the missing reason in step 3?
SSS congruency theorem
How do the areas of the parallelograms compare?
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
What does CDE most specifically describe?
a major arc
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?
the negative part of the x-axis
Which statements are true of all squares? Check all that apply.
The diagonals are perpendicular. The diagonals are congruent to each other. The diagonals bisect the vertex angles. The diagonals bisect each other.
Which statement proves that parallelogram KLMN is a rhombus?
The slope of KM is 1 and the slope of NL is -1.
Line EF is tangent to circle G at point A. If the measure of angel CAE is 95°, what is the measure of CBA ?
190
Segments AC and BD are diameters of circle O. What is the measure ADE of ?
253
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?
96 sq. cm
In circle D, which is tangent to the circle?
AB
Points N, P, and R all lie on circle O. Arc PR measures 120°. How does the measure of angle RNQ relate to the measure of arc PR?
Angle RNQ is equal in measure to arc PR.
What is the area of triangle QRS?
7
Angle BCD is a circumscribed angle of circle A. What is the measure of minor arc BD?
100°
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?
12 units
SU and VT are chords that intersect at point R. What is the length of line segment VT?
13 units
What is the value of x?
130°
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
(x + 3)2 + (y + 2)2 = 42, so the center is (-3, -2).
If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?
1.6 units
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x - 1. What is the value of x?
10
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?
20
What is the area of parallelogram ABCD?
20 square units
TREC is a rectangle. What is the length of ET?
34 units
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
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?
4 units by 4 units
Line segment XY is tangent to circle Z at point U. If the measure of UV is 84°, what is the measure of ?
42
Figure ABCD is a parallelogram. What is the value of p?
6
Line segment BD is a diameter of circle E. What is the measure of BC ?
78
What is the value of x?
8
Which graph represents the equation y2 = -4x?
A
Which polygon has an interior angle sum of 1080°?
A
Which statements are true about the regular polygon? Check all that apply.
Each interior angle measures 108°. All of the angles are congruent. The sum of the measures of the interior angles is 180(5 - 2)°.
Which statements are true about polygons? Check all that apply.
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.
Given: JKLM is an isosceles trapezoid, KL ∥ JM Prove: KM ≅ JL What is the missing reason in step 4?
base angles theorem
What type of polygon is shown?
concave heptagon
What type of polygon is shown?
convex hexagon
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?
right
Consider kite ABCD. What are the values of x and y?
x = 5, y = 22
In parallelogram LMNO, what are the values of x and y?
x = 55, y = 14
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?
x2 = -8y
What is the length of line segment SV?
16 units
Kite WXYZ is graphed on a coordinate plane. What is the approximate perimeter of the kite? Round to the nearest tenth.
16.2 units
In circle V, r = 14ft. What is the area of circle V?
196
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?
324 r units
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. What is the measure of angel ABC ?
36
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?
47 square units
What is the area of the shaded sector of the circle?
B. 27 r units2
The perimeter of a rhombus is 28 centimeters. What is the length of each side of the rhombus?
7
A parabola is represented by the equation x2 = 4y. What are the coordinates of the focus of the parabola?
(0,1)
In parallelogram ABCD, what is DC?
13
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.
4.8 units
The area of the trapezoid is 40 square units. What is the height of the trapezoid?
5
If line segment RU is considered the base of parallelogram RSTU, what is the corresponding height of the parallelogram?
5.4 units
The figure is a square. Its diagonals meet to form four right angles. What is the approximate value of x?
5.7
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°
Which point is on the circle centered at the origin with a radius of 5 units? Distance formula: (x2 - x1)2 + (y2-y1)2
A. 2, 21
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 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure?
C.
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?
C. 3 square root 2 + 2 square root 5 units
What is the measure of angle COA?
160
Line segment QP is tangent to the circle. What is the length of line segment QP? Round to the nearest unit.
20 units
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
21 square units
Trapezoid ABCD is graphed in a coordinate plane. What is the area of the trapezoid?
24 square units
Point O is the center of the circle. What is the perimeter of quadrilateral DOBC
28 units
The measure of BAC is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?
2:1
The measure of central angle RST is radians. What is the area of the shaded sector?
8
What is the perimeter of △LMN?
8 + square root 10 units
Does the point (2,6 ) lie on the circle shown? Explain.
D. No, the distance from (0, 0) to (2,6 ) is not 3 units.
Which statements are true about circle Q? Check all that apply.
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.
Which equation represents the parabola shown on the graph?
x2 = 6y
What is the area of triangle GHJ?
6 square units
Figure ABCD is a parallelogram. What is the perimeter of ABCD?
44 unit
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?
24 feet, 24 feet, 30 feet
In circle D, which is a secant?
GH
The diagram shows quadrilateral MNPQ. What is the length of line segment MQ?
11 units
In circle V, angle WXZ measures 30°. Line segments WV, XV, ZV, and YV are radii of circle V. What is the measure of WUX in circle V?
120
Which quadrilateral is a kite?
B
Which equation can be used to find the measure of ?
m:EHG + 80 + 35 = 360
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?
substitution property
What is the area of triangle ABC?
3
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x + 3)2 + (y + 5)2 = 36
What is the sum of the measures of the interior angles of a 12-gon?
1800
Line segment ON is perpendicular to line segment ML. What is the length of chord ML?
24 units
In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?
30 square units
What is the area of triangle LMN?
4 square units
A kite is inscribed in a square with a side length of 9 units. What is the area of the kite?
40.5 square units
What is the measure of arc EF in circle H?
41
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?
68 feet
What is the area of triangle ABC?
7
What is the measure of circumscribed ∠X?
90
Which polygon has an interior angle sum of 900°?
D
Major arc JL measures 300°. Which describes triangle JLM?
equilateral
Angle X is a circumscribed angle of circle V. Which name best describes figure VWXY?
square
Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.
∠EFD ≅ ∠EGD ED = FD mFD = 120°
The perimeter of the rectangle is 146 units. What is the length of the longer side?
45 units
Right trapezoid WXYZ is shown. What is the measure of angle WXY?
107°
Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. What is the measure of angle DCU?
135o
Rhombus LMNO is shown with its diagonals. The length of LN is 28 centimeters. What is the length of LP?
14
In parallelogram PQSR, what is PQ?
9
Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?
The midpoint of both diagonals is 4 1/2 , 5 1/2 the slope
Which best explains if quadrilateral WXYZ can be a parallelogram?
WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
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.
a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches.
The diagonals of a parallelogram are congruent. Which could be the parallelogram?
rectangle
Given: RT ≅ TV and ST ≅ TU Prove: RSVU is a parallelogram.
△RTS ≅ △VTU and △RTU ≅ △VTS
What is the center of a circle whose equation is x2 + y2 + 4x - 8y + 11 = 0?
(-2, 4)
The center of a circle represented by the equation (x + 9)2 + (y − 6)2 = 102 is .
(-9,6)
A parabola can be represented by the equation x2 = -20y. What are the coordinates of the focus of the parabola?
(0,-5)
HIJK is a parallelogram because the midpoint of both diagonals is which means the diagonals bisect each other.
(1,0)
Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?
(x + 4)2 + (y - 9)2 = 25
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?
(x - h)2 + (y - k)2 = r2
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.
16.8 units
The measure of central angle XYZ is 1.25 radians. What is the area of the shaded sector?
40
What is the measure of angle L in parallelogram LMNO? m∠L =
40
Angle G is a circumscribed angle of circle E. Major arc FD measures 280°. What is the measure of angle GFD?
40°
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?
464
Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?
49
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?`
49
Which is a correct description of the polygon?
It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.
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.
The directrix will cross through the positive part of the y-axis. The equation of the parabola could be x2 = -1/2 y.
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?
up
Line segment BA is tangent to the circle. What is the length of line segment BA? Round to the nearest unit.
98
What is the perimeter of parallelogram WXYZ?
B. 2 square root 5 + 2 square root 17 units
What is the perimeter of square ABCD?
B. 4 square root 37
Figure ABCD is a parallelogram. What are the measures of angles B and D?
A. ∠B = 55°; ∠D = 55°
Figure ABCD is a parallelogram. What are the measures of angles B and C?
B. ∠B = 65°; ∠C = 115°
In the diagram, DG ∥ EF. What additional information would prove that DEFG is an isosceles trapezoid?
DE ≅ GF
The figure is a parallelogram. One diagonal measures 28 units.
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
Figure ABCD is a square. Prove BD ≅ AC. What is the missing reason in the proof?
all sides of a square are congruent
Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle What is the missing reason in Step 7?
consecutive ∠s in a ▱ are supplementary
What is the measure of angle O in parallelogram LMNO?
105
ABCD is a square. What is the length of line segment DC?
13
Figure ABCD is a parallelogram. If ABCD is also a rhombus, what must be the value of x?
13
In circle O, SU is a diameter. What is m:ST?
130
Kite ABCD represents a softball field that is being built. If AC = 48 meters, what is the perimeter of the field?
140 meters
What is the length of line segment XZ?
16
A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?
41 units
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?
42 feet
In circle O, RT and SU are diameters. If m:RV = m:VU, what is mVU?
64
Given: ABCD is a kite. Prove: BD bisects AC. What is the missing reason in step 5?
corresponding parts of congruent triangles are congruent
Given: Circle O with diameter LN and inscribed angle LMN Prove: LMN is a right angle. What is the missing reason in step 5?
inscribed angle theorem
Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is △STR?
isosceles triangle
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?
16 miles
