Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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no additional details were added for this assignment. which frieze patt…
pattern 5: 180 - degree rotational symmetry and translational symmetry
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details no additional details were added for this assignment. sunspire/…
D. reflection and translation
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details no additional details were added for this assignment. rodina ol…
B. translation
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details no additional details were added for this assignment. majeczka/…
81.25 m by 41.63 m by 41.63 m
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details no additional details were added for this assignment. question …
reflection
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an arch at a new amusement park is constructed with two vertical walls …
$60$
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read the sentences below, filling in the blanks with items from this li…
1. central 2. inscribed 3. Inscribed Angle Theorem 4. inscribed 5. diameter 6. chord 7. radius 8. circumscribed
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which pair of coordinates would have the longest distance between them …
1. D. $(1,1)$ and $(3,4)$ 2. C. Plot the points and form a right triangle 3. A. Calculating the distances between celestial bodies 4. A. (assuming correct form of $x_2 - x_1$)
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what variable represents the horizontal difference between two points i…
1. c. \(\Delta x\) 2. d. \(\Delta y\) 3. a. Delivery routes 4. d. Object positioning 5. d. 5 units 6. a. 10 units
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the form of a quadratic equation is used in geometry to derive the dist…
1. Pythagorean theorem 2. Algebraic 3. Urban planning 4. Coordinates
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the distance formula is derived from the theorem. to find the distance …
1. Pythagorean 2. $x$, $y$ 3. Cartesian 4. hypotenuse 5. stability 6. movement 7. relationships 8. square 9. standard 10. algebraic 11. urban planning 12. location
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a dartboard consists of a circle inscribed in a square. the area of the…
22%
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complete the two - columns proof. given: x||y prove: ∠3≅∠5 1) m∠3 + m∠5…
Since \(m\angle3 + m\angle5=m\angle3 + m\angle7\), by the Subtraction Property of Equality, \(m\angle5=m\angle7\). If the lines are parallel, \(\angle2\) and \(\angle7\) are corre…
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which graph represents the solution set of the compound inequality - 5 …
The number line with an open - circle at 10, an open - circle at 17, and the line segment between them shaded.
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complete the two - column proof. given x||y prove ∠3≅∠5 1) x||y 1) give…
$m\angle3=m\angle5$
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complete the two - column proof. given: x||y prove: ∠3≅∠5. statements: …
The reason for statement 2 (\(m\angle3 + m\angle5 = 180\)) should be "Same - Side Interior Angle Postulate" instead of "Transitive Property of Equality".
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complete the two - column proof. given: x||y. prove: ∠3≅∠5. statements:…
The reason for \(m\angle3 + m\angle8 = 180\) should be "Same - Side Interior Angles Postulate". Then, since \(\angle5\) and \(\angle8\) are vertical angles (\(m\angle5 = m\angle8\…
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complete the two - column proof. given x||y. prove ∠1≅∠5. statements: 1…
2) Linear - pair postulate; To prove $\angle1\cong\angle5$: Statements: 1) $x\parallel y$ (Given); 2) $m\angle1 + m\angle2 = 180^{\circ}$ (Linear - pair postulate); 3) $\angle1\co…
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in the figure to the right, line m and line n are parallel. determine w…
congruent angles
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in the figure to the right, a||t. use the figure to answer the followin…
alternate interior angles
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in the figure to the right, s||t. use the figure to answer the followin…
alternate interior angles
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for each pair of triangles, determine what additional information is ne…
19. Need $\angle LKM=\angle GIH$, $\triangle LKM\cong\triangle GIH$. 20. Need $DX = ZY$, $\triangle DXZ\cong\triangle ZYX$. 21. Need $\angle WUV=\angle KVM$, $\triangle WUV\cong\t…
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in the figure to the right, s || t. use the figure to answer the follow…
corresponding angles
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read the sentences below, filling in the blanks with items from this li…
1. central 2. inscribed 3. Inscribed Angle Theorem 4. inscribed 5. diameter 6. chord 7. radius 8. circumscribed
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read the sentences below, filling in the blanks with items from this li…
1. central 2. inscribed 3. Inscribed Angle Theorem 4. inscribed 5. diameter 6. chord 7. radius 8. circumscribed
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what is the sum of opposite angles in any quadrilateral inscribed in a …
1. d. 180 degrees 2. b. 220° 3. b. 75 degrees
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what must be the measure of the arc that angle c intercepts if angle c …
1. b. 160 degrees 2. a. 360 degrees 3. b. Arc $BCD$ 4. d. 60 degrees 5. d. 50 degrees 6. b. The Inscribed Angle Theorem 7. a. 50 degrees
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5. 84° x + 59 x + 51 6. (2x - 2)° (x + 5)° 9. 36° (2 - 3x)° 46°
1. For the first triangle with angles \(84^{\circ}\), \(x + 59\), and \(x+51\): - \(x=-17\) 2. For the right - angled triangle with angles \(90^{\circ}\), \(2x - 2\), and \(x + 5\…
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parallel lines in a coordinate plane will never the of a line is calcul…
1. intersect 2. slope 3. negative 4. intercept 5. \(y = mx + b\) 6. undefined 7. parallel 8. point - slope 9. intercept 10. equal 11. slope 12. slope - intercept 13. perpendicular…
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∠3≅∠4 by the alternate exterior angles theorem. error analysis describe…
The error is that ∠3 and ∠4 are misidentified as alternate - exterior angles. They are actually vertical angles, and ∠3≅∠4 by the Vertical Angles Theorem.
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example 12 in the diagram, p, q, r and s are points on the circle. ∠qpr…
i) $35^{\circ}$ ii) $128^{\circ}$
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name lesson 3 homework practice solve equations with variables on each …
$m=-2,x = 4,d = 5,p=13,h = 1,f = 2,y = 3,x = 6,a=-20,v = 2.4,x = 7,x=-3,x = 8,x = 1.4$
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12. in aerospace engineering, what is the primary reason honeycombs are…
12. a. To maximize strength while minimizing weight 13. d. Mid - points of diagonals are equal 14. a. Yes 15. a. The product of their slopes is - 1
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8. where do the angle bisectors of a triangle intersect? a. circumcente…
1. b. Incenter 2. c. Opposite sides are parallel and all angles are right angles 3. b. \(2r^{2}\) 4. d. 10.6 units
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8. where do the angle bisectors of a triangle intersect? a. circumcente…
1. b. In - center 2. c. Opposite sides are parallel and all angles are right angles 3. b. \(2r^{2}\) 4. d. 10.6 units
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8. when do the angle bisectors of a triangle intersect? a. circumcenter…
b. Incenter ### 9.
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1. if a circle has a radius r and an inscribed regular hexagon, what is…
1. d. $P = 6r$ 2. c. By dividing the circle into equal arcs using the central angles. 3. b. Compass 4. b. They efficiently cover surfaces without gaps. 5. d. $(3,6)$ 6. b. Structu…
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the diagram shows the universal set u = {parallelograms}. set a represe…
26
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identify the sequence of transformations that will carry △abc→△abc. giv…
\((x,y) ightarrow(x + 4,-y)\)
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use the image to answer the question. identify a sequence of rigid tran…
\((x,y)\to(-x - 4,y)\)
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a boy is cycling along a square field at the speed of 18 km/hr. in how …
$392\ s$
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unit 4 transformations > lesson 9 compositions of transformations deter…
$\triangle ABC$ was rotated $- 180^{\circ}$ (clockwise) or $180^{\circ}$ (counter - clockwise), then shifted 2 units to the right and 2 units up.
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11. using the diagram below, classify the angle pairs as corresponding,…
a. Consecutive interior b. Alternate exterior c. Corresponding d. Alternate interior e. Consecutive exterior f. None g. None h. Consecutive interior i. None j. None k. None l. Non…
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unit 4 transformations > compositions of transformations assess paralle…
Yes, \(ADCB\cong EHGF\) since parallelogram \(ADCB\) was translated.
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compositions of transformations practice. complete this assessment to r…
Option #1: $(x,y)\to(x,-y - 3)$
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refer to the trapezoid in the diagram. identify a line of reflection th…
$x = 0$
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examine the polygon in the figure shown. identify a line of symmetry th…
$x = 3$
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which of the following summarizes the reflections that carry a parallel…
B. A parallelogram does not have any lines of reflection.
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classify ∠1 and ∠2 on the diagram as corresponding, alternate interior,…
3. Consecutive (same - side) interior angles 4. Alternate interior angles 5. Alternate exterior angles 6. Consecutive (same - side) exterior angles 7. Corresponding angles 8. Cons…
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2. using the diagram below, describe the relationship as parallel, inte…
a) Intersecting b) Parallel c) Parallel d) Intersecting e) Parallel
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point p(-5,2) is transformed using the rule (x+3, y-1). what type of tr…
a translation 3 units right and 1 unit down
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question 3 0 pts what transformation trnasforms (p,q) to (q,p)? a refle…
C. a reflection over y=x
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given quadrilateral pqrs in the diagram, find a line of reflection that…
$y=-2.5$
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identify the transformation that maps abcd to abcd. dilation translatio…
rotation
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the polygon shown has a line of reflection that will cause the figure t…
$x=-3$
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what transformation transforms (a,b) to (a,-b)? a reflection over the y…
Question 1: a reflection over the x - axis Question 2: \(\angle Z\cong\angle Z\), \(XY\cong XY\)
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1. use the diagram below to answer the following questions. a) name all…
a) $\overline{SU}$, $\overline{TV}$, $\overline{ZW}$ b) $\overline{TX}$, $\overline{SV}$, $\overline{UW}$ c) $\overline{UW}$, $\overline{TX}$, $\overline{ZY}$ d) Plane $VWZ$ e) Pl…
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the midpoint m of $overline{st}$ has coordinates (-6.75, 10.5). point t…
$(-4.2,10.5)$
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the midpoint of $overline{gh}$ is $m(-6.05, 8.8)$. one endpoint is $g(-…
$(6.6,8.9)$
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the midpoint m of $overline{uv}$ has coordinates (2.7, 5.8). point v ha…
$(13.7,4.2)$
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a gardener is planning a circular garden with a square flower bed. she …
the square's diagonal is equal to the circle's diameter
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vw has a midpoint at m(20.5, 43). point w is at (13, 15). find the coor…
$(28,71)$
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you are tasked to inscribe a square in circle o using a compass and str…
Draw a perpendicular diameter using the center of the circle as the intersection point
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list the angle measures of △qrs in order from smallest to largest. assu…
\(m\angle Q<m\angle S<m\angle R\)
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tu has a midpoint at m(-26, 33). point u is at (-78, 71). find the coor…
$(26,-5)$
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gh has a midpoint at m(-2.5, 25). point h is at (8, 35). find the coord…
$(-13,15)$
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kl has a midpoint at m(40, 42). point k is at (68, 12). find the coordi…
$(12,72)$
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find the largest angle of △ijk. assume that a is a positive number.
\(\angle K\)
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the midpoint m of st has coordinates (64.5, 39). point t has coordinate…
$(60,44)$
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if square abcd is inscribed in the circle, which of the following state…
C. Its length is equal to the side of the square.
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fg has a mid - point at m(12, 12.5). point f is at (10, 18). find the c…
$(14,7)$
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what part of the construction ensures that the vertices of the square i…
A. Drawing two perpendicular diameters of the circle
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find the shortest side of △wxy.
$\overline{XY}$
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gh has a midpoint at m(3, 10). point h is at (4, 17). find the coordina…
$(2,3)$
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the midpoint m of qr has coordinates (1.5, -2.5). point q has coordinat…
$(-7,-14)$
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what is the next step to complete the construction of the square? const…
Construct another diameter perpendicular to $\overline{GH}$.
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the midpoint m of $overline{pq}$ has coordinates (5, -7). point q has c…
$(5,-13)$
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suppose you have drawn a circle using a compass and marked its center. …
Draw a diameter across the circle using a straightedge
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the midpoint m of $overline{gh}$ has coordinates (-8.5, -3.5). point h …
$(-11,0)$
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find the smallest angle of △xyz.
$\angle Y$
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find the largest angle of △rst.
$\angle{S}$
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for exercises 2 and 3, circle the correct answer. choose all that apply…
2. b. $\frac{32}{10}$, d. $\frac{80}{25}$ 3. d.
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st has a mid - point at m(-4.5, 0). point s is at (-4, -4). find the co…
$(-5,4)$
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uv has a mid - point at m(8.5, 1.5). point u is at (8, 16). find the co…
$(9,-13)$
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find the shortest side of △uvw.
\(UW\)
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find the smallest angle of δwxy.
$\angle Y\approx18.3^{\circ}$
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the midpoint of $overline{jk}$ is $m(4, 9)$. one endpoint is $k(0, 10)$…
$(8,8)$
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find the largest angle of △vwx.
$\angle V$
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find the smallest angle of △hij.
$\angle J\approx67.6^{\circ}$
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rs has a midpoint at m(4, 9). point s is at (3, 8). find the coordinate…
$(5,10)$
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find the shortest side of δvwx.
\(VW\)
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find the shortest side of △vwx.
\(VW\)
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14. a poster is 15 inches wide by 24 inches tall. a smaller version of …
160 square inches
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graph the trigonometric function. y = cos x+3 plot all points correspon…
Graph the points $(0,4),(\frac{\pi}{2},3),(\pi,2),(\frac{3\pi}{2},3),(2\pi,4)$ and draw a smooth cosine - like curve through them.
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f(8.1, 1.7) and g(-8.6, 0.4) are the endpoints of a line segment. what …
$(-0.25,1.05)$
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example 6 two points a and c, are on the same level ground as the foot …
i) Approximately $19.0$ m ii) Approximately $60.1$ m
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pq has endpoints at p(15.2, 7.8) and q(9.3, 9.6). find the midpoint m o…
$(12.25,8.7)$
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f(2.6, -5.3) and g(9.1, 6.3) are the endpoints of a line segment. what …
$(5.85,0.5)$
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find the value of x, y, and z in the parallelogram below.
$x = 91$, $y=\frac{88}{7}$, $z = 87$
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example 8 a pole and a stick stand vertically on a level ground. the st…
The height of the pole is $6.25$ m.