Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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determining angle relationships in right triangles triangle xyz is a ri…
Angle \(X\) must be acute. Angle \(Z\) must be acute. The sum of angles \(X\) and \(Z\) must be equal to \(90^{\circ}\).
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find a congruence transformation that maps \\( \\triangle zbd \\) to \\…
D. \(T_{(90,0)}\circ r_{(90^{\circ},O)}(\triangle ZBD)\)
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2. how do you show a point p(x,y) moved k right and l up? p(x - k,y + k…
\(P(x + K,y + L)\)
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1. △abc is translated 9 units to the left and 3 units up to create △abc…
\(8\)
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if triangle lmn has an obtuse angle at vertex m. which statements could…
- The angle at vertex \(N\) is acute. - Triangle \(LMN\) is an obtuse triangle. - The angle at vertex \(L\) is acute.
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find a congruence transformation that maps \\( \\triangle z b d \\) to …
B. \(T_{(-4,0)}\circ R_{x - axis}(\triangle ZBD)\) (Note: There was a miscalculation in the initial step - by reflection over \(x -\)axis \((x,y)\to(x,-y)\) and then translation \…
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the coordinates of the vertices of parallelogram rstu are r(0,0), s(2,3…
\(R'(0,0)\), \(S'(3,2)\), \(T'(3,6)\), \(U'(0,4)\)
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5. what is the image of a(3,-1) after a reflection, first across the li…
\((-5,7)\)
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4. in the graph below, what is the line of reflection for △xyz and △xyz…
\(x = 2\)
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3. what is true for an image and a preimage in a reflection? the image …
The image and the preimage have different orientations.
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in triangle abc, ( mangle bac = 50^{circ} ). if ( mangle acb = 30^{circ…
1. Obtuse - angled 2. Right - angled 3. \(4\) or \(6\)
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find a congruence transformation that maps \\( \\triangle n p b \\) to …
A. \(T_{(-10,-10)}\circ r_{(270^{\circ},O)}(\triangle NPB)\)
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2. the coordinates of the vertices of △cde are c(1,4), d(3,6), and e(7,…
\((3,0)\)
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1. in the graph below, what are the coordinates for d when we reflect a…
\((3,-1)\)
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find a congruence transformation that maps (\triangle mbw) to (\triangl…
D. \(T_{\langle - 6,0 angle}\circ R_{x - axis}(\triangle MBW)\)
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determine whether the pair of objects is congruent. if so, describe a c…
A. The objects are congruent. To map the object on the left to the object on the right, rotate it \(180^{\circ}\) around its center and reflect over a vertical line.
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the composition of transformations ( r_{y = - 5}circ r_{(90^{circ},a)} …
\(7\), \(9\), and \(10\)
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the composition of transformations ( r_{y = -5} circ r_{(90^{circ},a)} …
Reflections and rotations preserve length. The perimeter of \(\triangle ABC\) is equal to the perimeter of \(\triangle XYZ\). The perimeter of \(\triangle ABC\) is \(26\). A possi…
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are the pockets on this shirt congruent? if so, describe a composition …
A. The pockets on this shirt are congruent. To map the pocket on the left to the pocket on the right, translate the left pocket down and then reflect it across the row of buttons.
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find the exact value without a calculator. double - angle formulas: $\\…
\(\cos\frac{\pi}{8}=\frac{\sqrt{2+\sqrt{2}}}{2}\), so the green box is \(2\), the white box is \(2\), and the gray box is \(2\)
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use the given information to complete the proof of the following theore…
4. \(m\angle A+m\angle B + m\angle A+m\angle B = 360^{\circ}\) 5. \(2(m\angle A + m\angle B)=360^{\circ}\) 7. \(\angle A\) and \(\angle B\) 8. \(BC\); Consecutive - Interior Angle…
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use the compass and ruler to construct the line perpendicular to the li…
Follow the above three - step construction process using compass and ruler to get the line perpendicular to \( l \) through \( P \).
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consider a triangle ( abc ) like the one below. suppose that ( b = 71 )…
\(C = 20.0^{\circ},A = 131.0^{\circ},a = 110.5\)
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consider a triangle ( abc ) like the one below. suppose that ( c = 14 )…
\(B = 32.9^{\circ},A = 122.1^{\circ},a = 28.0\) or \(B = 147.1^{\circ},A = 7.9^{\circ},a = 4.5\)
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consider a triangle ( a b c ) like the one below. suppose that ( a = 53…
\(B = 42.0^{\circ},C = 106.0^{\circ},c = 96.1\) or \(B = 138.0^{\circ},C = 10.0^{\circ},c = 17.3\)
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practice 7 (from unit 3, lesson 3) the triangle abc is taken to triangl…
A. \(\frac{1}{2}\), B. \(\frac{5}{9}\)
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6 practice 6 (from unit 3, lesson 9) here are triangles abc and def. wh…
\(16\)
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consider a triangle ( abc ) like the one below. suppose that ( b = 72 )…
\(A = 36.8^{\circ},C = 97.2^{\circ},c = 99.2\)
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4 practice 4 (from unit 3, lesson 10) which of these statements is true…
C. To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
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katie wants to collect over 100 seashells. she already has 34 seashells…
The inequality is \(34 + 12d>100\), and the solution is \(d>5.5\). On the number - line, we have an open circle at \(d = 5.5\) (since \(d = 5.5\) is not included in the solution) …
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in the figure below, \\( \\overleftrightarrow { v p } \\) and \\( \\ove…
(a) slope of \(\overleftrightarrow{VP}\): \(\frac{VW}{WP}\); slope of \(\overleftrightarrow{PZ}\): \(-\frac{QZ}{PQ}\) (b) \(\frac{PQ}{QZ}\) (c) slope of \(\overleftrightarrow{VP}\…
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in the figure below, ( overleftrightarrow{pr} ) and ( overleftrightarro…
a. slope of \(\overleftrightarrow{PR}\): \(-\frac{PQ}{QR}\); slope of \(\overleftrightarrow{RT}\): \(\frac{ST}{RS}\) b. \(\frac{RS}{ST}\) c. slope of \(\overleftrightarrow{PR}\cdo…
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practice 2 here is a diagram. explain how you know that segment de is n…
Since \(\frac{AD}{DB}=\frac{4}{2} = 2\) and \(\frac{AE}{EC}=\frac{9}{5}=1.8\), and \(2 eq1.8\), by the converse of the basic proportionality theorem (Thales' theorem), segment \(…
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below are circles c, f, and j. a central angle of 135° is shown in each…
(a) Length of \(\overset{\frown}{AB}:\frac{9\pi}{4}\text{ m}\), Length of \(\overset{\frown}{DE}:\frac{3\pi}{4}\text{ m}\), Length of \(\overset{\frown}{GH}:\frac{3\pi}{2}\text{ m…
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practice 1 in the diagram, segment ( ab ) is parallel to segment ( ab )…
a. \(7.5\) units b. \(3.5\) units
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answer the following. when applicable, give the exact answer in terms o…
(a) Length of \(AB:\frac{\pi}{4}\) mm; Length of \(DE:\frac{3\pi}{4}\) mm; Length of \(GH:\frac{\pi}{2}\) mm. (b) \(\frac{\text{Length of }AB}{\text{Radius of }C}=\frac{\pi}{4}\);…
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below are circles c, f, and j. a central angle of 45° is shown in each.…
(a) Length of \(\overset{\frown}{AB}\): \(\frac{\pi}{4}\) mm Length of \(\overset{\frown}{DE}\): \(\frac{3\pi}{4}\) mm Length of \(\overset{\frown}{GH}\): \(\frac{\pi}{2}\) mm (b)…
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below are circles c, f, and j. a central angle of 45° is shown in each.…
- (a) Length of \(\overarc{AB}\): \(\frac{\pi}{4}\) mm; Length of \(\overarc{DE}\): \(\frac{3\pi}{4}\) mm; Length of \(\overarc{GH}\): \(\frac{\pi}{2}\) mm. - (b) \(\frac{\text{Le…
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below are circles ( c ), ( f ), and ( j ). a central angle of ( 150^{ci…
(a) Length of \(\overset{\frown}{AB}\): \(\frac{5\pi}{3}\text{ m}\), Length of \(\overset{\frown}{DE}\): \(\frac{5\pi}{2}\text{ m}\), Length of \(\overset{\frown}{GH}\): \(\frac{5…
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find the exact value without a calculator. double - angle formulas: $\\…
\(\frac{\sqrt{2+\sqrt{2}}}{2}\)
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activity 3: synonyms and antonyms instructions: for each vocabulary wor…
1. B. Seizure 2. B. Consent
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below are circles c, f, and j. a central angle of 60° is shown in each.…
(a) Length of \(\overset{\frown}{AB}\): \(\pi\) cm Length of \(\overset{\frown}{DE}\): \(\frac{\pi}{3}\) cm Length of \(\overset{\frown}{GH}\): \(\frac{2\pi}{3}\) cm (b) \(\frac{\…
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consider parallelogram pqrs below. note that pqrs has vertices p(-6, 6)…
(a) Slope of \(\overline{PS}\): \(\frac{-7}{5}\), Slope of side adjacent to \(\overline{PS}\): \(\frac{-5}{7}\) (b) Length of \(\overline{PS}\): \(\sqrt{74}\), Length of side adja…
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consider parallelogram g h j k below. note that g h j k has vertices g(…
(a) Slope of \( \overline{GH}:\frac{2}{7} \); Slope of side adjacent to \( \overline{GH}:\frac{5}{2} \) (b) Length of \( \overline{GH}:\sqrt{53} \); Length of side adjacent to \( …
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consider parallelogram ( wxyz ) below. note that ( wxyz ) has vertices …
A. \( WXYZ \) is a rectangle. B. \( WXYZ \) is a rhombus. C. \( WXYZ \) is a square.
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consider parallelogram wxyz below. note that wxyz has vertices w(-6, -2…
(a) Length of \(\overline{WX}\): \(\sqrt{89}\); Length of side adjacent to \(\overline{WX}\): \(\sqrt{89}\) (b) Slope of \(\overline{WX}\): \(\frac{8}{5}\); Slope of side adjacent…
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consider parallelogram j k l m below. note that j k l m has vertices j(…
(a) Length of \( \overline{JK}:3\sqrt{13} \), Length of side adjacent to \( \overline{JK}:\sqrt{13} \) (b) Slope of \( \overline{JK}:\frac{3}{2} \), Slope of side adjacent to \( \…
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consider parallelogram pqrs below. note that pqrs has vertices p(-2, 4)…
(a) Slope of \( \overline{QR}:\frac{4}{5} \), Slope of side adjacent to \( \overline{QR}:\frac{5}{4} \) (b) Length of \( \overline{QR}:\sqrt{41} \), Length of side adjacent to \( …
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consider a triangle ( abc ) like the one below. suppose that ( b = 72 )…
\(A = 36.8^{\circ}\), \(C = 97.2^{\circ}\), \(c = 99.0\)
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consider a triangle ( abc ) like the one below. suppose that ( b = 41 )…
\(A = 46.0^{\circ},C = 107.0^{\circ},c = 86.0\)
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what assumption contributes to the linear average - case efficiency of …
B. Points are randomly sorted in increasing \(x\) coordinates.
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answer the following questions. write your answers in terms of π. give …
- (a) The area of the cross - section of the square pyramid is \(\frac{16\pi}{121}\text{ mm}^2\), and the area of the cross - section of the cone is \(\frac{16\pi}{121}\text{ mm}^…
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try again your answer is incorrect. • (a): your answer is incorrect. an…
The area of the cross - section of the square pyramid is \(\frac{64\pi}{121}\) \(mm^{2}\), and the area of the cross - section of the cone is \(\frac{64\pi}{121}\) \(mm^{2}\).
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what operation can be performed in constant time using analytical geome…
C. Sorting points in the Cartesian plane.
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write the expression as the sine or cosine of an angle.\ \\cos 7y\\cos …
\(\cos(10y)\)
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write the expression as the sine or cosine of an angle. cos 94° cos 18°…
$\cos76^{\circ}$
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find all missing elements. a = 5 b = 2 c = 6 a = ?° b = ° c = ° round t…
\( A = 51.3^{\circ} \), \( B = 18.2^{\circ} \), \( C = 110.5^{\circ} \)
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find the measure of angle c. c b a c c = 20 a = 11 b = 12 c = ？°
\(120.7^{\circ}\)
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find the length of side b. a = 6 c = 7 b = 90°
\(9.2\)
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find the length of side a. b = 4 c = 10 a = 29° a = ? round to the near…
\(6.8\)
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in isosceles triangle abc, sides ab and ac are congruent. point d divid…
A. 6
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the perimeter of an isosceles right triangle is ( 62 + 62sqrt{2} ) inch…
C. 62
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consider what happens when you rotate line segment kl around two differ…
The top - left option.
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21 mark for review $(x - 6)^2+(y + 3)^2 = 25$ the given equation repres…
A. \((x - 9)^2+(y + 5)^2 = 100\)
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in right triangle abc, side bc has a length of √533. the hypotenuse, si…
\(\frac{14}{27}\)
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in the figure, ( overline{ab} ), ( overline{de} ), and ( overline{cf} )…
C. I and II
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the length of the base of a triangle is 6 inches, and the height of the…
B. 33
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2 mark for review note: figure not drawn to scale. in the triangle show…
C. 63
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for each pair of figures below, choose how they are related. none of th…
# Explicación: ## Paso 1: Comprender las transformaciones - **Traslación**: Desplazar una figura sin rotar ni reflejar. - **Rotación**: Girar una figura en torno a un punto. - **R…
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find the value of x.
\(99\)
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find the value of x.
\(x = 37\)
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in the xy - plane, circle m is the graph of the equation $(x - 5)^2+(y …
C. \((x - 5)^2+(y - 4)^2 = 36\)
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triangle a is similar to triangle b. the length of the base of triangle…
\(\frac{161}{6}\)
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22. two explorers on an expedition to the arctic circle have radioed th…
a. The linear distance between the two explorers is approximately \(53.08\) units. b. The mid - point between the two explorers is \((-6.5,3)\) c. The distance between the mid - p…
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18. (overline{jl}) has endpoints (j(8,10)) and (l(20,5)). point (k) has…
No, point \(K\) is not the mid - point of \(\overline{JL}\). ### 18b.
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15. determine the coordinates of the midpoint of the segment with endpo…
15. \((5,5)\) 16. \((3.5,7.35)\) 17a. \((8,-4)\) 17b. \(10\) 17c. \(5\)
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14. draw a scalene triangle on a coordinate plane, and use the distance…
A scalene triangle with vertices \(A(0,0)\), \(B(3,0)\), \(C(1,2)\) is drawn. Using the distance formula, \(d_{AB} = 3\), \(d_{BC}=2\sqrt{2}\), \(d_{AC}=\sqrt{5}\). Since all thre…
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13. use the distance formula to show that \\( \\triangle abc \\) is iso…
Since \(AB = BC=\sqrt{29}\), \(\triangle ABC\) is isosceles.
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for items 9 - 11, determine the length of each segment with the given e…
9. \(26\) 10. \(7\sqrt{5}\approx15.65\) 11. \(20\)
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8. on a map, a trailhead is located at (5,3) and a turnaround point is …
No, they will not make it to the trailhead in less than 2 hours. Since the time taken \(t\approx2.32\) h which is greater than 2 h.
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7. the distance from the origin to point p is 5 units. give the coordin…
\((0,5)\), \((0, - 5)\), \((5,0)\), \((-5,0)\)
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6. the vertices of \\( \\triangle lmn \\) are \\( l(7,4), m(7,16) \\), …
a. \(LM = 12\), \(LN = 35\), \(MN = 37\) b. \(84\) c. \(210\)
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5. (overline{jk}) has endpoints (j(-3, -1)) and (k(0, 3)). (overline{rs…
Since \( JK = 5\) and \( RS=3\sqrt{2}\approx4.24\), \( JK eq RS\), so \( \overline{JK} ot\cong\overline{RS}\)
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lesson 5 - 1 1. calculate the distance between the points a(-4,2) and b…
1. The distance between \(A(-4,2)\) and \(B(15,6)\) is \(\sqrt{377}\approx19.42\). 2. The distance between \(R(1.5,7)\) and \(S(-2.3,-8)\) is \(\sqrt{239.44}\approx15.47\). 3. For…
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lesson 5 - 1 1. calculate the distance between the points a(-4, 2) and …
# Explanation: ## Step1: Identify the coordinates For point \(F(-3,-4)\) and \(G(1,2)\), \(x_1=-3,y_1 = - 4,x_2=1,y_2=2\) ## Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^…
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show your answers on notebook paper. show your work. lesson 5 - 1 1. ca…
C. 8 units
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find the distance between the pair of points. (-8,3) and (1,-6) the dis…
\(9\sqrt{2}\)
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find the distance between the pair of points. (-2,2) and (2,-5) the exa…
The exact distance is \(\sqrt{65}\) units. The distance is approximately \(8.062\) units.
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7. look at triangle jkl. which expression can be used to find the measu…
D. $\sin^{-1}\frac{JK}{JL}$
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use triangle ltf to answer questions 4 - 6. 6. what is the measure of a…
$36.9^{\circ}$
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use triangle ltf to answer questions 4 - 6. 5. what is cos f? your answ…
$\frac{3}{5}$
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find the midpoint of the line segment whose endpoints are given. (1.1,9…
\((3.4,1.05)\)
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find the distance between the pair of points. (-2,1) and (1,-2) the dis…
\(3\sqrt{2}\)
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find the distance between the pair of points. give an exact answer and …
\(6.928\)
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find the distance between the pair of points. (-3,5) and (2,-2) the exa…
\(8.602\)
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find the distance between the pair of points. (-3,5) and (2,-2) the exa…
\(\sqrt{74}\)
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find the distance between the pair of points (2,2) and (8,10). the exac…
The approximate distance is \(10.000\) units.
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find the distance between the pair of points (2,2) and (8,10). the exac…
\(10\)
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using eulers formula, how many edges does a polyhedron with 20 faces an…
\(30\)
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how would the vertical cross section of this triangular prism look?
The vertical cross - section of the triangular prism is a rectangle.