SOL / JLAB answers
A trapezoid is located entirely in quadrant II. If this trapezoid is reflected across the x-axis, in which quadrant will the new trapezoid be located?
III
Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other?
Rhombus
Which point lies on the line perpendicular to AB that bisects AB?
S
Given: ABCD is a parallelogram. Prove: △ABD≅△CDB ∠A≅∠C ↔ Opposite angles of a parallelogram are congruent. AD≅BC ↔ Opposite sides of a parallelogram are congruent. AB≅CD ↔ Opposite sides of a parallelogram are congruent. Therefore, △ABD≅△CDB▵ABD≅▵CDB by which postulate/theorem?
SAS
Given: M is the midpoint of LN and KP. The given information is sufficient to prove △KML ≅ △PMN by which postulate/theorem?
Side-Angle-Side
Three lookout towers are located at points A, B, and C on the section of a national forest shown in the drawing. Which of the following statements is true concerning △ABC formed by the towers?
The measure of angle A is greatest.
In the design, a hexagon is inscribed in a circle. Which point shows the location of Point Q after a 240° clockwise rotation around the center?
U
Which point apparently lies on the perpendicular to l from A?
X
If triangle XYZ is similar to triangle XLM, then -
XM : XZ = XL : XY
The drawing shows the arcs used to construct -
an angle congruent to a given angle
Jennifer made these measurements on △ABC. BC must be -
between 10 and 12 inches
The locations of three water pumping stations form a triangle on a map of the area. The distance from station A to station B is 650 meters. The distance from station B to station C is 558 meters. The distance from station A to station C is -
between 92 m and 1,208 m
Which statement would be sufficient to prove that line l is parallel to line m?
line AB ⊥ l
Use this figure to answer the following. AB is parallel to CD if -
m∠1 + m∠2 = m∠3 + m∠4
Line p is a transversal. For lines q, r, s, and t, which is not parallel to the other three?
s
A construction engineer needs to make sure a ceiling beam is parallel to its corresponding floor beam. Using the drawing as a guide, which pair of measurements is sufficient to show the beams are parallel?
x = y
Rectangle ABCD is placed in a coordinate plane as shown. Which equation describes a line of symmetry for rectangle ABCD?
y = 5
A gardener rested his hoe against a shed. The hoe made a 50° angle with the ground as shown in the diagram below. Which represents the supplement to the 50° angle?
z
To mark the end of a race, a finish-line banner is stretched across the road as shown in the drawing. Which is closest to the length of the support rope designated by x in the drawing?
10.6 ft
The two adjacent figures are a regular hexagon and a regular octagon. What is the measure of ∠PQR?
105°
Joseph is standing 12 feet from a mirror lying on the ground, and his eyes are 5 feet above the ground. The line-of-sight reflection on the mirror makes ∠1 congruent to ∠2. If the building is 264 feet from the mirror, which is closest to the height of the building?
110 ft
Chords WP and KZ intersect at point LL in the circle shown. What is the length of KZ?
12
In the drawing, A, C and D are collinear and AB is tangent to the circle at B. Using the values shown, what is the measure of CD?
12
The ratio of the perimeter of △U to the perimeter of △V is 1:2. If the triangles are similar, what is the value of x + y?
12
In parallelogram ABCD, the measure of ∠C is -
120.0°
In the figure drawn below, LM and QR are parallel and m∠M = m∠L = 60°. What is m∠QNP?
120°
The distance between the points (-2, -4) and (3, 8) is -
13
A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus?
13 ft
Gene's horse corral, labeled ABCD in the drawing, is shaped as a parallelogram and is adjacent to the shed, labeled ZAD. If a gate, labeled CF, opens all the way to the corral fence, position labeled CG, through how many degrees does the gate swing?
130°
TW is a diameter of circle X, and TW is parallel to UV. If the measure of TU is 25°, what is the degree measure of UV?
130°
Which of the following is the measure of the supplement of ∠CAB?
132°
The figure represents the pattern for a quilt. What is the measure of ∠DCE?
140°
What is the value of x in the pentagon above?
155°
What is the length of a diagonal brace that could be used for a wall 9 feet high and 12 feet long?
15ft
The floor plan for a modern home is modeled by the composite of the regular nonagon and triangle shown. What is the measure of ∠JKL?
160°
In relation to one figure, the other figure is apparently a -
180° rotation about the origin
The volumes of two spheres are in a ratio of 1:8. What is the ratio of their radii?
1:2
Each interior angle of a regular polygon has a measure of 162°. The polygon has a total of -
20 sides
The diagram shows the locations of Noah and Ben after swimming in different directions from a dock. Let d be the distance from Noah to Ben, in yards. Which represents all the possible values, in yards, of d?
21 < d < 147
A concrete pillar shaped as a rectangular prism is designed as follows. Which is closest to the volume of concrete needed to fill the pillar?
21.4 m^3
What is the volume in cubic feet of a refrigerator whose interior is 4.5 feet tall, 2.5 feet wide, and 2 feet deep?
22.5 cu ft
If m∠AOB = 45° in circle O, what is m∠ACB?
22.5°
Quadrilateral ABCD is a parallelogram. The measure of ∠C is -
22°
Triangle ABC is a right triangle with the measures shown. The length of BC is -
24 in
A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?
27 ft
Mr. Ammons is constructing a walkway through his rectangular garden. The walkway runs diagonally as shown in the diagram. Which is closest to the length of the walkway?
28.3 ft
The graph of line j is shown. Which ratio represents the slope of a line parallel to line j?
3/7
This figure shows a pattern of triangles and regular hexagons. What is the value of x?
30
The angle from a point on the ground to the top of a 168-foot tower is 30°. About how long is a wire that reaches from the top of the tower to the point on the ground? sin 30° = 0.5, cos 30° ≈ 0.866, tan 30° ≈ 0.577
336 ft
Line BD is tangent to the circle at B and the measure of AC is 108°. What is the measure of ∠CBD?
36°
Two vehicles, each moving from a point in a straight line away from each other at an angle, are 150 feet apart after 6 second. Both are moving at a constant rate, vehicle A at 50 feet per second and vehicle B at 40 feet per second. How far apart are they after 15 seconds?
375 ft
How many different lines of symmetry does a square have?
4
Which set of lengths could not be the lengths of the sides of a triangle?
4 cm, 5 cm, 9 cm
Given quadrilateral KLMN, what is the value of x?
40
A circle has a radius of 8 centimeters. The measure of the arc of the shaded section is 72°. Which is closest to the area of the shaded section of the circle?
40.2 cm^2
If m∠CAB=40°, what is m∠CDB?
40°
Rectangular flowerbeds are built on each side of a fishpond in the shape of a regular octagon. What is the measure of the angle, x, between two consecutive flowerbeds?
45°
To the nearest gallon, what is the volume of a cylindrical water heater 1.4 feet in diameter and 4 feet tall? (1 cubic foot = 7.48 gallons)
46 gal
What is the value of z?
4√2
In the drawing, a regular polygon is partially covered by the trapezoid. How many sides does the covered polygon have?
5
In the diagram, m∠1=(6x+12)° and m∠2=(9x−4)°. Which is closest to the value of x?
5.3
Parallelogram ABCD is placed on a coordinate grid as shown. What is the approximate length of diagonal AC?
5.4 units
A cylinder has a diameter of 10 inches and a height four times its radius. What is its volume?
500π cu in.
George used a decorative fencing to enclose his deck. Using the information on the diagram and assuming the top and bottom are parallel, the measure of ∠x is -
50°
Which is the closest to the measure of a central angle x in this regular polygon?
50°
Which angle measure below is not a possible measure of an exterior angle of a regular polygon?
54°
An airplane leaves a runway heading due east then turns 35° to the right as shown in the figure. How much more will the airplane have to turn to be heading due south?
55°
Triangle ABC is an equilateral triangle with side lengths of 10 inches. What is the length, in inches, of AD?
5√3
Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the length of the remaining side?
6 in
If lines a and b are parallel, what is the value of x?
60
The figure has angle measures as shown. What is the measure of ∠BCD?
60 degrees
What is the volume of a right square pyramid with a height of 3 centimeters and a base that measures 8 centimeters by 8 centimeters?
64 cm3 (cubed)
Sally is using strings to mark parallel rows for a vegetable garden behind her house. If the measure of ∠1 is 115°, what should be the measure of ∠2?
65°
What is the value of x in trapezoid ABCD?
7
ABCD is a rhombus. What is the measure of ∠CBD?
70°
AB || DE AB= 6 ; AC = 9 ; BC = 10 ; CE = 12 What is DE?
8
The logo of an airline is a circle inscribed in a triangle. If AF = 3 and AB =11 , then BD =?
8
The radius of Sphere A is 2 inches, and the radius of Sphere B is 4 inches. How many times larger is the volume of Sphere B compared to the volume of Sphere A?
8
Two chords intersect with the measures shown in the drawing. What is the value of x?
8.0
In the figure, △ABC is a right triangle. AD is perpendicular to BC, and the measure of BD=2 meters and DC=8 meters. What is the measure of AC?
8.9 m
The parallelogram has the measurements shown. Which is closest to the length of the altitude, h?
8.91
In circle O, the degree measure of PSR is 280°. What is the degree measure of =∠POR?
80°
Given: B, C, and D are collinear; m∠ACD=85°. What value of x will ensure that A, C, and E are also collinear?
85
Parallel lines l and m are cut by transversal t, m∠4 = m∠5m, and m∠6 = m∠7. What is the measure of ∠8?
90°
A baseball diamond is in the shape of a square, 90 feet on a side. What is the direct distance from home plate to second base?
90√2 ft
The quadrilateral ABCD is a parallelogram. Which of the following pieces of information would suffice to prove that ABCD is a rectangle?
AC = BD
Which segment is apparently congruent to AB?
AZ
Three towns form a triangle on a map. The angle formed at the point designating Afton is 48°, at Badenton 60°, and at Capeton 72°. Which lists the distances between towns in order, greatest to least?
Afton to Badenton, Afton to Capeton, Badenton to Capeton
In the figure, line t is a transversal for lines l and m. Which of the following best describes the relationship between ∠1 and ∠2?
Alternate exterior angles
Which lists the sides of △BCD in order from shortest to longest?
BC, CD, BD
What is most likely the slope of the line graphed above?
1/3
If parallelogram ABCD is translated so that the new location of point D is (-1, 2), what would be the new location of point B?
(-3, 4)
Circle O has a center at (-2, -2) and a diameter of 10 units. Which point lies on circle O?
(-6, -5)
The town plaza in a certain town is a parallelogram. The town's planning committee has decided to build a fountain at the center of the plaza. This sketch shows the corner points when placed on a coordinate grid. Which coordinates show where the fountain will be located?
(2, 0.5)
Coordinates A(2, 5), B(6, 4), and C(6, 0) are connected to form △ABC. If △CDA is congruent to △ABC, what are the coordinates of D?
(2, 1)
What are the most likely coordinates of R' if R'S' is a reflection of RS across the y-axis?
(4, 3)
Triangle ABC is placed on a grid as shown. The apparent midpoint of AB is -
(4.5, 4.5)
Given: Circle P with center at (-4, 1) Which equation could represent circle P?
(x + 4)^2 + ( y − 1 )^2 = 41
What is the apparent slope of line QV?
-1/2
Given: P(5, 7) and T(-3, 3) What is the slope of line PT?
1/2