Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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a thread is being pulled off a spool at the rate of 70.9 cm per sec. fi…
$5.29$
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abbey is getting new carpet in her living room and hallway. the followi…
C. 374 ft²
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question 1-9 state a counterexample to the definition below: a figure w…
# Explicación: ## Paso 1: Comprender la definición La definición dice que una figura con cuatro ángulos rectos es un cuadrado. Necesitamos un ejemplo que demuestre lo contrario. #…
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a smaller central angle of a circle corresponds to a smaller sector of …
1. sector 2. circumference 3. radius
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use an algebraic equation to find the measures of the two angles descri…
\(60\)
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line wg is perpendicular to line pq. line pq is represented by the equa…
The equation of line WG in slope - intercept form is $y=-4x - 17$
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bd bisects ∠abc. solve for x and find m∠abc. m∠abd = 7x - 6, m∠cbd = 4x…
x = 4, m∠ABC = 44
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a circle is a shape defined by a set of points equidistant from a the d…
1. Center 2. Radius 3. Circumference 4. Radius 5. Radians 6. Central angle 7. Sector
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line wg is perpendicular to line pq. line pq is represented by the equa…
The slope of line WG ($m_2$) is $\frac{1}{4}$ and the equation of line WG in slope - intercept form is $y=\frac{1}{4}x$
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abbey is getting new carpet in her living room and hallway. the followi…
None of the given options are correct. The area is \(544\) \(ft^2\).
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in the diagram, gh bisects ∠fgi. a. solve for x and find m∠fgh. b. find…
a. $x = 24$, $m\angle FGH=39^{\circ}$ b. $m\angle HGI = 39^{\circ}$ c. $m\angle FGI=78^{\circ}$
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∠efg and ∠gfh are a linear pair, m∠efg = 4n + 18, and m∠gfh = 3n + 22. …
$m\angle EFG = 98^{\circ}$ $m\angle GFH = 82^{\circ}$
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if the central angle of a sector is 2π/3 radians and the radius is 8 me…
1. A. $64\pi/3$ square meters 2. B. $10$ cm 3. B. $2\pi$ cm
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what additional information is needed to prove that the triangles are c…
$\angle LOA\cong\angle LMA$
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es una característica del cuadrilátero de la imagen. no tiene lados par…
Tiene dos pares de lados paralelos.
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if the central angle of a sector is 3 radians and the radius is 6 inche…
1. d. 54 square inches 2. b. $\frac{5\pi}{2}$ cm 3. a. $12\pi$ square cm
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prove #1 given: ∠m≅∠h, ∠mat≅∠hta prove: △mat≅△hta statements prove #2 g…
Proof 1: $\triangle MAT\cong\triangle HAT$ by ASA. Proof 2: $\triangle UVG\cong\triangle FHG$ by SAS.
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what is the central angle of a sector in radians if its area is half th…
1. d. $\pi$ radians 2. a. $\frac{\pi}{2}$ radians 3. d. Radians directly relate the arc length to the radius.
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a space vehicle is orbiting mars in a circular orbit. what radian measu…
(a) $7\pi$ (b) $\frac{5\pi}{3}$
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quadrilateral abcd is translated down and left to form quadrilateral ol…
6 units
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the area of a plane figure is a measure of the amount of surface of the…
$\frac{2}{49}$
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select whether the conjecture is true or false. if in △abc, (ab)^2 + (b…
True
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25. if △abc has sides 6, 8, 10 and △def has sides 12, 16, 20, what is t…
25. c. 2 26. b. They are similar by AA similarity. 27. d. They have proportional corresponding sides
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mark the picture state why the two triangles are congruent, then prove …
Proof #1: $\triangle MAT\cong\triangle HTA$ by AAS. Proof #2: $\triangle UVG\cong\triangle FHG$ by SAS.
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22. which point of concurrency divides each median into a 2:1 ratio? a.…
22. a. Centroid 23. c. \(XY\) corresponds to \(AB\), \(XZ\) corresponds to \(AC\), and \(YZ\) corresponds to \(BC\). 24. c. \(AB = DE\), \(BC=DF\), \(AC = EF\) where sides don't c…
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which statement proves that △xyz is an isosceles right triangle? the sl…
The slope of $\overline{XZ}$ is $\frac{3}{4}$, the slope of $\overline{XY}$ is $-\frac{4}{3}$, and $XZ = XY = 5$.
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select whether the conjecture is true or false. if you have three point…
False
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stu is laying brick down to make a patio. he plans for the patio to be …
Stu estimated correctly by rounding up. He ordered enough brick. The exact area is 228.75 square feet.
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19. which postulate or theorem is typically used to establish triangle …
19. d. SAS Postulate 20. c. ASA 21. b. To ensure that the scale factor between the triangles is consistent
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find an equation for the line below.
$y=\frac{1}{3}x+\frac{10}{3}$
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16. what does the “included angle” mean in triangle congruence? a. the …
16. B. The angle formed by the two given sides 17. D. $\triangle DEF$ with $DE = 7$ cm, $DF = 5$ cm, $\angle EDF = 50^{\circ}$ 18. D. It ensures stability by relying on fixed angl…
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13. if two triangles have one pair of congruent angles and the surround…
13. d. Yes, by SAS similarity 14. a. Centroid 15. c. Identify two pairs of corresponding angles
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for a project, carlos must provide one cut - out paper model of each ty…
13.5 square units
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10. what is the purpose of the sas similarity criterion? a. to identify…
10. B. To prove the similarity of two triangles 11. C. They are equal 12. A. $\frac{1}{3},\frac{2}{4},\frac{3}{5}$
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answer the following questions using the graph provided below: tell wha…
1. N 2. L 3. R 4. T 5. A 6. V 7. F 8. M 9. P 10. Z 11. $(0,5)$ 12. $(2,5)$ 13. $(0,0)$ 14. $(5,1)$ 15. $(0,7)$ 16. $(7,8)$ 17. $(3,2)$ 18. $(5,0)$ 19. $(2,2)$
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select whether the conjecture is true or false. if ∠2 and ∠3 are supple…
False
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rafael does a weekly exercise program consisting of cardiovascular work…
The shaded region is the intersection of the regions defined by $x + y\geq9$, $y\leq6$, $x\leq7$, $x\geq0$, and $y\geq0$. It is a polygon in the first - quadrant bounded by the in…
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8. this diagram was constructed with straightedge and compass tools. a …
AD = 2AC
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use the appropriate theorem(s) to find the measure of ∠1. m∠1 = □°
120
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line m and line n are parallel lines. which angles have the same measur…
C. $\angle6$, D. $\angle8$
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this diagram was created by starting with points c and d and using only…
Construct a circle centered at C. Construct a circle centered at D.
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what is the area of triangle lmn? 12 square units 24 square units 14 sq…
12 square units
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right triangle relationships and trigonometry which set of numbers can …
8, 10, 14; 8, 12, 15
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question 13 a dilation maps the point (8,12) to (4,6). what is the scal…
$\frac{1}{2}$
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solve for x and graph the solution on the number line below. -4 ≥ -2x a…
Inequality Notation: $x\geq 2$ Number - Line: Draw a number line. Mark a closed - circle at 2 (because $x$ can equal 2) and shade the line to the right of 2 to represent all value…
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consider the figure shown. classify each of the following statements as…
The statement \(m\angle2 + m\angle4 = 180\) is sometimes true. The statement \(\angle2\cong\angle3\) is sometimes true. The statement \(\angle2\cong\angle4\) is always true. The s…
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right triangle relationships and trigonometry what is the area of trian…
33 square units
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question 14 5 pts a triangle has vertices at (1, 2), (3, 4), and (5, 2)…
$(-3,2)$
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what is the volume of this cylinder in cubic inches? 6 in. 5 in. 30π 60…
C. $150\pi$
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7. what is required to use the asa method for constructing a triangle i…
7. a. The measures of two angles 8. d. Incenter 9. c. Angle Bisector Theorem
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6. this diagram was created by starting with points c and d and using c…
1. Start with points C and D. 2. Open compass to distance CD. 3. Draw arcs from C and D. 4. Use new - formed points for further arcs.
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what is the area of parallelogram rstu? 32 square units 21 square units…
28 square units
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a triangle has its vertices at (0,0), (2,0), and (0,3). if the triangle…
$(4,0)$
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4. given △abc≅△def, which of the following can be proven using cpctc? a…
4. c. Corresponding angles in $\triangle ABC$ and $\triangle DEF$ are equal. 5. b. They have corresponding angles and included sides that are equal. 6. d. The included angle betwe…
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find the gradient of the interval ab. a(0,2) b(3,7) $\frac{5}{2}$ $\fra…
$\frac{5}{3}$
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quadrilateral lmno is dilated with center at the origin by a scale fact…
$(x,y)\to(2x,2y)$
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1. which of the following is an example of a correct proportion for sim…
1. A. \(AB/DE = AC/DF\) 2. C. Prove that the triangles are congruent 3. D. \(\triangle JKL\sim\triangle MNO\)
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question 12 a rectangle has a length of 6 units and a width of 4 units.…
3 units by 2 units
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right - triangle relationships and trigonometry. what is the area of tr…
33 square units
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find the gradient of the interval ab. a(1,2) b(4,6) ○ $\frac{3}{4}$ ○ -…
$\frac{4}{3}$
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a right triangle has one angle that measures 33°. what is the measure o…
$57^{\circ}$
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triangle congruence. two rigid transformations are used to map △abc to …
a rotation about point C
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right triangle relationships and trigonometry. javier is asked to creat…
0
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question 10 5 pts which rule describes a rotation of 270 degrees counte…
For the first question: $(x,y)\to(y, - x)$ For the second question: $(-4,-1)$
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right triangle relationships and trigonometry the hypotenuse of a 45 - …
7 units
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the diameter of a circle is 22cm. what is the area of the circle?
$121\pi$ $cm^{2}$ (or approximately $379.94$ $cm^{2}$)
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13. which of the following is not a postulate used to prove triangle co…
13. c. AA 14. a. Incenter 15. c. SAS
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right triangle relationships and trigonometry. the hypotenuse of a 45 -…
$5\sqrt{10}$
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9. given two triangles with two pairs of corresponding angles congruent…
9. a. The triangles are similar. 10. c. The included angle defines the shape of the triangle. 11. a. Similar
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triangle congruence could △jkl be congruent to △xyz? explain. yes, if (…
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
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5. why is the sas method common in bridge design? a. it only uses angle…
5. c. It ensures stability by relying on fixed angles and sides. 6. d. Both corresponding sides and angles are equal 7. d. Incenter
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the perimeter of the triangle below is 52 units. fill in the missing bl…
Blank 1: 7 Blank 2: 52 Blank 3: 10 Blank 4: 23 Blank 5: 2
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triangle rst is reflected across the line y = -x. what are the coordina…
R'(2, - 8), S'(2, - 1), T'(0, - 8)
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1. what type of information is required to construct a triangle using t…
1. c. Two sides and the included angle 2. d. Circumcenter 3. d. The measures of two angles
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question 8 5 pts what is the image of the point (2,3) after a rotation …
(-3,2)
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complete the proof to show that abcd is a parallelogram. b(-3,4) c(2,2)…
slopes of opposite sides are equal
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if ∠rqt = 155, what are m∠rqs and m∠tqs? (4x - 20)° (3x + 14)°
$m\angle RQS = 72^{\circ}$, $m\angle TQS = 83^{\circ}$
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decide which transformation was used on each pair of shapes below. matc…
1. c. reflection 2. a. translation 3. b. rotation 4. b. rotation
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fall 2025 geometry b wvva right triangle relationships and trigonometry…
$\frac{1}{2}$
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sometimes, a motion appears to be a reflection when it really isnt. con…
A. The heart - shaped figure shows a rotation instead of a reflection.
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right triangle relationships and trigonometry. the equation tan(55°) = …
10.5 cm
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triangle congruence in the diagram, sr = 4√2 and qr = √10. what is the …
\(8\sqrt{2}+2\sqrt{10}\text{ units}\)
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sometimes, a motion appears to be a reflection when it really isnt. con…
b
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example 2: os is the perpendicular bisector of mp. which segments are e…
# Explicación: ## Paso 1: Identificar segmentos iguales Como $\overrightarrow{OS}$ es la bisectriz perpendicular de $\overline{MP}$, entonces $MO = OP$ porque una bisectriz perpen…
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sometimes, a motion appears to be a reflection when it really isnt. con…
b
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triangle congruence. the triangles are congruent by the sss congruence …
translation, then rotation
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2025 geometry e wwa right triangle relationships and trigonometry given…
$\frac{5}{13}$
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q is the midpoint of pr. what are pq, qr, and pr? 6x - 7 5x + 1
$PQ = 41$, $QR = 41$, $PR = 82$
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fall 2025 geometry b wwva right triangle relationships and trigonometry…
\(27.7^{\circ}\)
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what is the vertical change from point a to point b? 1 what is the hori…
0.3
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the rectangle shown in frame 1 is rotated to a new position shown in fr…
B. 40 degrees counterclockwise
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fall 2025 geometry b wwva right triangle relationships and trigonometry…
\(7^{2}=8^{2}+11^{2}-2(8)(11)\cos(P)\)
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how does the area of triangle abc compare to the area of parallelogram …
The area of $\triangle ABC$ is equal to the area of parallelogram $GHJK$.
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the measure of angle abc is 120°. the measure of angle dbc is 75°. the …
$45$
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fall 2025 geometry b wwva right triangle relationships and trigonometry…
$\frac{\sin(76^{\circ})}{2.6}=\frac{\sin(51^{\circ})}{z}$
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these two shapes are similar. find a. a = □ inches 3 in. 9 in. 2 in. a
6
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9. find the midpoint of the segment below. (2 pts) 11. rachel lives at …
# Explicación: ## Paso 1: Recordar la fórmula del punto medio La fórmula para el punto medio entre dos puntos $(x_1,y_1)$ y $(x_2,y_2)$ es $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2…
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4. starting with 2 marked points, a and b, precisely describe the strai…
1. Open the compass to the length of the line segment AB. 2. Place the compass point at A and draw an arc. 3. Without changing the compass width, place the compass point at B and …
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record your matches in the table. $10 + 5xleq - 10$ $-x + 11geq6$ $9<-\…
Match the inequalities with the graphs as follows: $10 + 5x\leq - 10$ with the graph having a closed - circle at - 4 and shading to the left. $-x + 11\geq6$ with the graph having …
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what is the area of parallelogram rstu? 38 square units 24 square units…
24 square units