Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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find ( mangle a ). the diagram is not to scale. 73 63 117 107
\(73\)
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directions: study the figures, read the question, and choose the best a…
D. 157
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find ( mangle a ). the diagram is not to scale. 73 63 117 107
73
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figure b is the result of a transformation on figure a. which transform…
A translation 4 units to the left and 4 units up
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∠dfg and ∠jkl are complementary angles. ( m angle dfg = x + 2 ), and ( …
\(\angle DFG = 48\), \(\angle JKL=42\) (corresponding to the option \(\angle DFG = 48,\angle JKL = 42\))
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directions: study the information and figure, read the question, and ch…
A. 160
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directions: study the information and figure, read each question, and c…
A. \(12.5m^{2}\) ### Question 4
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the rectangle below has an area of $35x^{3}$ square meters and a width …
\(7x^{2}\) meters
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directions: study the information and figure, read each question, and c…
A. \(12.5\space m^{2}\)
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in the diagram, polygon ( abcdcong ) polygon ( pqrs ). find the value o…
\(x = 38\)
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fix the one word that is used incorrectly. in one famous optical allusi…
Change "allusion" to "illusion".
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find the value of x. in the diagram, polygon abcd ≅ polygon pqrs.
\(x = 38\)
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find the value of x. the diagram is not to scale. 90 145 45 35
\(45\)
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a lake near the arctic circle is covered by a 2 - meter - thick sheet o…
E. \(y\)-intercept and a point that is not an intercept
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fatoumata spots an airplane on radar that is currently approaching in a…
\(14300\) feet
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15. in \\( \\triangle a b c \\), if \\( m \\angle a \\) is thirteen les…
\( m\angle A = 21^{\circ} \) \( m\angle B = 125^{\circ} \) \( m\angle C = 34^{\circ} \)
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directions: read the question, and choose the best answer. 2. kirsten s…
D. 59.625
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11. what is the perimeter of the polygon? 12. a parallelogram has an ar…
A. 55 cm
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find the surface area of the cone below. leave your answer in terms of …
\(24\pi\)
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a wooden cane is 3 feet tall. its shadow is 4 feet long. close by, ther…
12
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find the surface area of the cone below. leave your answer in terms of …
\(18\pi\)
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a shadow 16 meters long is cast by a redwood tree that is 30 meters tal…
\(60\)
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find the surface area of the cone below. leave your answer in terms of …
\(270\pi\)
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if a street sign is 3 meters tall and casts a shadow 4 meters long, the…
\(12\)
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find the surface area of the cone below. leave your answer in terms of …
\(864\pi\)
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directions: read each question, and choose the best answer. 11. what is…
A. \(55\mathrm{cm}\)
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a water tower is 45 meters tall and its shadow is 24 meters long. nearb…
15
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10. △yvh ~ △yba
\(x = 23.375\)
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a radio tower that is 60 meters tall casts a shadow 32 meters long. if …
$24$
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an ash tree is 8 meters tall and its shadow is 15 meters long. a nearby…
60
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each pair of polygons are similar. find the missing side length. 9. △ab…
\(x = 18\)
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jack found that a jungle gym that is 3 meters tall casts a shadow 4 met…
12
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in the diagram below, \\( \\triangle nml \\sim \\triangle kmj \\). find…
\(y = 69\)
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find u. write your answer as a whole number or a decimal. do not round.…
\(u = 0.4\) yards
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find d. write your answer as a whole number or a decimal. do not round.…
\(d = 45\) yards
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find d. write your answer as a whole number or a decimal. do not round.…
\(69\)
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in the diagram below, ( \triangle nju sim \triangle kil ). find ( n ). …
\(100\)
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developing proof state which postulate or theorem you can use to prove …
Use the AAS (Angle - Angle - Side) theorem. When \(\triangle KJL\cong\triangle MNL\) (by AAS), \(KL = NL\) because corresponding parts of congruent triangles are equal.
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in the diagram below, \\( \\triangle cde \\sim \\triangle cfg \\). find…
\(j = 6\) meters
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each pair of polygons are similar. find the missing side le 3. \\( \\tr…
\(x = \frac{16}{3}\)
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11. twin oaks soccer field is a rectangle. the longer side of the field…
\(328\) yards
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13 enter the correct answer in the box simplify the expression $(6^{4})…
\(1679616\)
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directions: study the figure, read each question, and choose the best a…
B. \(25\) cm
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what is the slope of this line? simplify your answer and write it as a …
\(\frac{3}{2}\)
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4. scale factor from a to b is 2:3. find x.
\(15\)
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\america at play\ by susan reyburn as major league baseball prepared to…
Baseball did not originate where baseball officials originally claimed.
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directions: study the figure, read each question and choose the best an…
B. \(30\) ft
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2. show that the two triangles △abc∼△def are similar by comparing the r…
Since \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}=\frac{5}{8}\), by the Side - Side - Side (SSS) similarity criterion, \(\triangle ABC\sim\triangle DEF\).
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11) a table in the shape of a trapezoid has vertices: a(3,3), b(5,3), c…
For problem 11: The new coordinates are \(A'(3,-3)\), \(B'(3,-5)\), \(C'(0,-6)\), \(D'(0,-2)\) and the rule is \((x,y)\to(y, - x)\). For problem 12: The new coordinates are \(A'(6…
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america at play by susan reybum what is the central idea of this excerp…
Baseball did not originate where baseball officials originally claimed.
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\america at play\ by susan reyburn what is the claim in the excerpt fro…
If they checked the Library of Congress, they would see that baseball originated in England.
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find the area of a sector of a circle with radius 12 inches subtended b…
\(96\pi\)
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find the length of the arc of a circle of radius 36 inches subtended by…
\(6\pi\)
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for #s 9 and 10, find the coordinates of the given vertices and the rul…
For the \(90^{\circ}\) clockwise rotation: - \(R(-7,-5)\) rotates to \((-5,7)\) - \(S(-1,-2)\) rotates to \((-2,1)\) - \(T(-1,-5)\) rotates to \((-5,1)\) The rule is \((x,y)\to(y,…
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solve the inequality and graph the solution. 12 + 7g ≥ 5 to draw a ray,…
The solution of the inequality \(12 + 7g\geq5\) is \(g\geq - 1\). On the number - line, there is a closed circle at \(-1\) and an arrow extending to the right.
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solve the inequality and graph the solution. 18 ≤ 12f - 18 to draw a ra…
The solution of the inequality is \(f\geq3\). On the number - line, we plot a closed circle at \(3\) (because the inequality is \(\geq\), so \(3\) is included in the solution set)…
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solve the inequality and graph the solution. 14 - g < 20 to draw a ray,…
The solution of the inequality \(14 - g < 20\) is \(g>-6\). On the number - line, there is an open circle at \(-6\) and the ray extends to the right.
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solve the inequality and graph the solution. - 12 ≥ 6(u + 6) to draw a …
The solution of the inequality is \(u\leq - 8\). On the number - line, we have a closed circle at \(-8\) and a ray extending to the left.
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a figure has rotational symmetry if a rotation of 180° or less produces…
7) The figure has rotational symmetry. When rotated by \(60^{\circ}\) (as \(360\div6=60\)), the image matches the original. 8) The figure has rotational symmetry. When rotated by …
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9 all horizontal lines are parallel to the ____________. a quadrant b o…
D. \(x-\)axis
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2 all vertical lines are parallel to the a quadrant b y - axis c x - ax…
B. \(y -\)axis
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1 which of the following is not true about vertical lines? a vertical l…
D. Vertical lines have equations of the form \(y = b\).
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determine the reference angle ( \theta ). | ( \theta ) | quadrant | + c…
For \(\theta=-135^{\circ}\): Quadrant \(QIII\), Coterminal Angle \(225^{\circ}\), Ref. Angle \(45^{\circ}\) For \(\theta = 480^{\circ}\): Quadrant \(QII\), Coterminal Angle \(120^…
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question 4 convert the angle in radians to degrees. \\( \\frac { 13 \\p…
$260^{\circ}$
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developing proof state which postulate or theorem you can use to prove …
We use the AAS postulate to prove \(\triangle MLN\cong\triangle QLP\). Then, by CPCTC, \(ML\cong QL\) as they are corresponding parts of the congruent triangles.
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32. triangle abc has vertices a(-2,2), b(-1,-3), and c(4,0). find the c…
The coordinates of the vertices of \(\triangle A'B'C'\) are \(A'(-2,-2)\), \(B'(-1,3)\) and \(C'(4,0)\)
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find the reference angle, the quadrant of the terminal side, and the si…
Reference angle: \(45^{\circ}\) Quadrant: II \(\sin(135^{\circ})=\frac{\sqrt{2}}{2}\) \(\cos(135^{\circ})=-\frac{\sqrt{2}}{2}\)
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fill in the missing statement and reason the proof below. given: \\( \\…
The missing statement in step 3 is \(\overline{BE}\cong\overline{ED}\) and the reason is "Definition of bisecting segments"
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23.) a hiker stands 80 ft from a giant redwood tree and sights the top …
\(299\) ft
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31. which transformation of the line ( x = 3 ) results in an image that…
C. \(r_{y=x}\)
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prove: \\( \\triangle abe \\cong \\triangle cde \\). note: quadrilatera…
\(\triangle ABE\cong\triangle CDE\) by the AAS (Angle - Angle - Side) congruence criterion.
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12. the rectangle abcd shown in the diagram below will be reflected acr…
A. slope of \(\overline{AB}\)
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annie is expanding the flowerbed in her backyard. currently there is a …
\(21.0\) square feet
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annie is expanding the flowerbed in her backyard. currently there is a …
\(21.0\) square feet.
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1. use similar right triangles to determine the slope of each line.
The slopes of the lines are \(-3\) and \(\frac{3}{8}\)
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5. if segment ab was dilated by a scale factor of 3/2, what is the leng…
The length of the image \(A'B'\) is \(12\).
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determine the relationship between the two triangles and whether or not…
The two triangles are related by **not being in the correct SAS (the angle is not included)** and **cannot be proven congruent** as the given information does not satisfy any of t…
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1. find the measure of the indicated angle a. 78° b. 54° c. 111° d. 107…
1. B. \(54^{\circ}\) 2. B. \(9\)
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the perimeter of the rectangle below is 148 units. find the length of s…
\(34\)
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△abc∼△def. resuelve para y y x.
\( y = 30 \), \( x = 5 \)
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△qrs ~ △tuv. resolver para y y z. s 3 9 t 6 r 21 у u
$y = 18$, $z = 7$
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$\\triangle ghi\\sim\\triangle jkl$. resuelve para $y$ y $x$.
\( y = 10 \), \( x = 11 \)
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determine the relationship between the two triangles and whether or not…
The two triangles are related by **AAS (Angle - Angle - Side)**, so the triangles **are congruent**.
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1. if segment ab was dilated by a scale factor of 1.5, what is the leng…
1. \(12\) 2. \(\frac{1}{3}\) 3. \(20\) 4. \(3\)
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determine the relationship between the two triangles and whether or not…
The two triangles are related by **Hypotenuse - Leg (HL)**, so the triangles **are congruent**.
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△abc∼△def. resuelve para y y x. y = x =
\(y = 27\), \(x = 4\)
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question △ckm can be mapped onto △rnl by a reflection. if m∠c = 120°, f…
cannot
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the perimeter of a rectangle is 40 inches. find the length and width if…
Length \(=6\) inches, Width \(=14\) inches
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diagram below, ( overline{ab} cong overline{bd} cong overline{bc} ), an…
\(65^{\circ}\)
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determine the relationship between the two triangles and whether or not…
The two triangles are not congruent. There is no congruence criterion (like SSS, SAS, ASA, AAS, HL) that can be applied to prove their congruence.
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in the diagram below, ( overline{ad} ) bisects ( angle cab ), ( mangle …
\(m\angle B = 50^{\circ}\)
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n the diagram below, \\( \\overline { b e } \\perp \\overline { e d } ,…
\(69\)
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the points l(2, -2), m(9, 0), and n(4, 3) form a triangle. plot the poi…
slope of \(\overline{LM}=\frac{2}{7}\), slope of \(\overline{MN}=-\frac{3}{5}\), slope of \(\overline{NL}=\frac{5}{2}\), length of \(\overline{LM}=\sqrt{53}\), length of \(\overli…
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the library of a contemporary elementary school is circular. the floor …
\(2068.00\)
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question in △nop, \\overline{op} \\cong \\overline{no} and m∠o = 57°. f…
\(m\angle N = 61.5^{\circ}\)
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question in \\( \\triangle w x y, \\overline{w x} \\cong \\overline{y w…
\(m\angle Y = 58^{\circ}\)
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the length of a rectangle is three times its width. if the area of the …
\(56\space m\)
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question in $\triangle mno$, $overline{om}congoverline{no}$ and $mangle…
\(m\angle M = 81.5^{\circ}\)
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the perimeter of a rectangle is 110 feet. find the length and width if …
Length = \(13\) feet, Width = \(42\) feet
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question in \\( \\triangle w x y, \\overline{x y} \\cong \\overline{w x…
\(m\angle X = 58^{\circ}\)