Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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if quadrilateral pqrs is a kite, which statements must be true? select …
\(\overline{QP}=\overline{QR}\), \(\overline{PM}=\overline{MR}\), \(\angle PQR=\angle PSR\)
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quadrilateral stuv is a kite. what is rt? 48 80 rt =
$64$
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name angles of a triangle the sum of the angles in a triangle = 180 deg…
(a) $x = 50$ (b) $x = 50$ (c) $x = 18$ (d) $x = 44$ (e) $x = 12$
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the figure is a kite. what is the length of the kites longer diagonal? …
40 units
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a town planner wants to build two new streets, elm street and garden ro…
$72^{\circ}$
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quadrilateral ghij is a kite. what is fg? fg =
$36$
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quadrilateral tuvw is a kite. what is st? st =
21
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quadrilateral tuvw is a kite. what is m∠v? m∠v =
$95$
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quadrilateral efgh is a kite. what is m∠e? m∠e = °
$128$
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quadrilateral tuvw is a kite. what is m∠w? m∠w = °
$116$
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quadrilateral stuv is a kite. what is m∠v? s 119° u 97° m∠v = □°
$72$
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quadrilateral abcd is a kite. what is m∠d? a 61° c 77° m∠d = □ °
$111$
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quadrilateral cdef is a kite. what is m∠c? m∠c = °
$80$
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use each of these terms or phrases once to complete the sentences. prop…
1. slope 2. proportional relationship 3. run 4. rise 5. $y_2 - y_1$, $x_2 - x_1$
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what is the volume of this figure? 4 m 2 m 8 m 5 m 9 m cubic meters
$228$
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if (wx = 3s), (vy=-2s + 19), and (uz = 5s+2), what is the value of (s?)
\(s = - 1\)
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quadrilateral defg is an isosceles trapezoid and m∠g = w + 72°. what is…
$55$
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sv is the midsegment of the trapezoid tuwx. if wx = z - 15, sv = z, and…
$76$
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ux is the midsegment of the trapezoid stvw. if st = y, ux = -y + 100, a…
$40$
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quadrilateral hijk is an isosceles trapezoid, hj = 2a + 24, and ik = 8a…
$8$
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adage decree evolve preclude servile citadel discordant hover rubble wr…
1. discordant 2. decree 3. evolved 4. wrangle 5. adage 6. servile 7. hovered 8. citadel 9. rubble 10. precludes
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quadrilateral qrst is an isosceles trapezoid and (mangle r = 4u - 84^{c…
$55$
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ux is the midsegment of the trapezoid stvw. if vw = 4z, ux = 6z + 2, an…
$z = 1$
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quadrilateral pqrs is an isosceles trapezoid and m∠s = 4a + 100°. what …
$-8$
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set b choosing the right word select the boldface word that better comp…
1. wrangled 2. decreed 3. servile 4. hovered 5. citadels 6. discordant 7. evolved 8. hover 9. rubble 10. adage 11. preclude 12. wrangling
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sv is the midsegment of the trapezoid tuwx. if tu = -2z + 14, sv = 3z -…
$4$
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s and v are the midpoints of the legs, $overline{rt}$ and $overline{qu}…
$50$
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29) based on the information in the diagram, which triangle congruence …
# Explicación: ## Paso 1: Identificar los elementos congruentes Observamos que en los triángulos $\triangle ABC$ y $\triangle FGH$ hay dos ángulos de $42^{\circ}$ congruentes y lo…
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name angles of a triangle the sum of the angles in a triangle = 180 deg…
(a) $x = 50$ (b) $x = 50$ (c) $x = 18$
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quadrilateral stuv is an isosceles trapezoid, su = 3y - 68, and tv = y …
$84$
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if ij is not parallel to hk, what is ij?
53
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tw is the midsegment of the trapezoid rsuv. if uv = 29 and tw = 50, wha…
$71$
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if $overline{ij}$ is not parallel to $overline{hk}$, what is $hk? hk = …
$49$
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if ux = 55 and vw = 66, what is st? st =
$110$
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29) based on the information in the diagram, which triangle congruence …
# Explicación: ## Paso 1: Identificar las partes congruentes Observamos en el diagrama que hay dos ángulos de $42^{\circ}$ congruentes y un lado congruente (las barritas indican l…
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30) triangle abc has coordinates a(0,6), b(3,0), and c(4,3). triangle a…
$(4, - 3)$
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28) which single transformation is shown below? dilation translation re…
# Explicación: ## Paso 1: Comprender las transformaciones Una dilatación cambia el tamaño de una figura, una rotación gira una figura alrededor de un punto, una reflexión es un es…
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what is the volume of this figure? 10 m 8 m 5 m 2 m 6 m 4 m cubic meters
428 m³
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29) based on the information in the diagram, which triangle - congruenc…
# Explicación: ## Paso 1: Identificar los elementos congruentes En el diagrama, vemos que hay dos ángulos de $42^{\circ}$ congruentes y un lado entre ellos (el lado común a los do…
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what is the volume of this figure? 3 in. 5 in. 10 in. 6 in. 12 in. cubi…
570 pulgadas cúbicas
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26) for the circle below, which expression can be used to find the area…
# Explicación: ## Paso 1: Formula del área de un círculo El área de un círculo completo es $A = \pi r^{2}$, donde $r$ es el radio. Aquí, $r = 8$ cm, entonces $A_{círculo}=\pi(8)^{…
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what is the volume of this figure? 5 m 11 m 19 m 3 m 8 m cubic meters
# Explicación: ## Paso 1: Dividir la figura en dos cuboides Podemos dividir la figura en dos cuboides. Uno con dimensiones 5 m × 3 m × 19 m y otro con dimensiones (8 - 5)m×3 m×(19…
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28) which single transformation is shown below? dilation translation re…
# Explicación: ## Paso 1: Analizar la transformación Observamos que la figura se mueve hacia abajo en el plano cartesiano sin cambiar su tamaño, orientación o forma. ## Paso 2: Id…
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what is the volume of this figure? 12 m 3 m 4 m 3 m 2 m 9 m cubic meters
# Explicación: ## Paso 1: Encontrar el volumen del primer prisma rectangular El primer prisma rectangular tiene dimensiones 12 m × 3 m × 4 m. El volumen de un prisma rectangular s…
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what is the volume of this figure? 2 m 4 m 2 m 4 m 15 m 3 m cubic meters
# Explicación: ## Paso1: Calcular volumen del primer cubo $V_1 = 2\times4\times2= 16\ m^3$ ## Paso2: Calcular volumen del segundo cuboide $V_2=15\times3\times4 = 180\ m^3$ ## Paso…
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25) a circle has its center at (4, -2) and has a radius of 3. what is t…
$(x - 4)^2+(y + 2)^2=9$
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26) for the circle below, which expression can be used to find the area…
# Explicación: ## Paso 1: Encontrar el área total del círculo La fórmula para el área de un círculo es $A = \pi r^{2}$, donde $r = 8$ cm. Entonces $A=\pi(8)^{2}=64\pi$ cm². ## Pas…
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27) the radius of the circle is 5 centimeters. line segment ab is a dia…
# Explicación: ## Paso 1: Aplicar el teorema del ángulo inscrito Como AB es el diámetro del círculo, el ángulo inscrito en la semi - circunferencia es un ángulo recto. Entonces, e…
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24) in the right triangle below, m is the mid - point of hypotenuse qr.…
1. **Explanation**: - **Step 1: Record the coordinates of the endpoints of the hypotenuse** - Los puntos \(Q(a,d)\) y \(R(c,b)\) son los extremos de la hipotenusa \(QR\). - **Step…
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27) the radius of the circle is 5 centimeters. line segment ab is a dia…
2.2
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26) for the circle below, which expression can be used to find the area…
# Explicación: ## Paso 1: Recordar la fórmula del área de un sector circular La fórmula del área de un sector circular es $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, donde $\th…
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find the midpoint of the line segment between the points (7, 13) and (-…
D. $(-3.5, 16)$
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26) for the circle below, which expression can be used to find the area…
# Explicación: ## Paso1: Usar fórmula de área de sector El área de un sector de un círculo se da por $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, donde $\theta$ es el ángulo cen…
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determine the equation of a circle with radius 6 and its center at the …
B. $x^{2}+y^{2}=36$
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what is the area of this figure? square kilometers
48
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in △abc, m∠a = 65, m∠b = 45, and m∠c = 70. which side of the triangle i…
B. $\overline{AB}$
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20) a scientist has two similar cylindrical beakers. beaker a has radiu…
# Explicación: ## Paso 1: Fórmula del volumen de un cilindro El volumen de un cilindro se calcula con la fórmula $V = \pi r^{2}h$. Supongamos que las alturas de los dos cilindros …
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b is the midpoint of line segment $overline{ac}$. the coordinates of b …
D. (8, 28)
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what is the area of the trapezoid? square meters
14
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in circle o, m\\(widehat{ac}\\) = m\\(widehat{bc}\\) = 160. what is m\\…
C. 40
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find the distance between points g and v. -2\\frac{1}{2}\t-1\\frac{1}{2…
2
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what is m\\(\\stackrel{\\frown}{bc}\\)? (not drawn to scale) a 76 b 284…
D. 152
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select the correct choice that completes the sentence below. when repre…
not
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what is the area of this figure? square inches
26
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what is the area of the triangle? 5 mm 5 mm 4 mm 6 mm square millimeters
12
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you are writing a story about lily, who is in study hall. choose the be…
Lily could see that Pedro didn't understand his homework. She went over to him and said, "Here, let me show you a trick."
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20) a scientist has two similar cylindrical beakers. beaker a has radiu…
# Explicación: ## Paso 1: Recordar la fórmula del volumen de un cilindro El volumen de un cilindro se calcula con la fórmula $V = \pi r^{2}h$. Supongamos que las alturas de los ci…
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a classroom board is 36 inches wide and 24 inches tall. cheryl is putti…
B. 120 inches
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the diagonals of this rhombus are 8 kilometers and 10 kilometers. what …
40
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20) a scientist has two similar cylindrical beakers. beaker a has radiu…
# Explicación: ## Paso 1: Fórmula del volumen de un cilindro El volumen de un cilindro se calcula con la fórmula $V = \pi r^{2}h$. Supongamos que las alturas de los cilindros A y …
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what is the area of the parallelogram? 10 mm 5 mm 10 mm square millimet…
50
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19) the volume of a cone is given by the formula v = 1/3πr²h. what is t…
# Explicación: ## Paso 1: Identificar el radio y la altura El radio $r$ del cono es de 6 pulgadas y la altura $h$ es de 8 pulgadas. ## Paso 2: Aplicar la fórmula del volumen del c…
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18) a plane intersects a right cylinder parallel to one of the cylinder…
C. círculo
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point n is on line segment $overline{mo}$. given $no = 2x - 3$, $mo = 3…
$20$
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point v is on line segment $overline{uw}$. given $vw=x + 7$, $uw = 3x-9…
$27$
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find the value of the variables in the diagrams below:
For the first diagram, $x = 12$. For the second diagram, $x = 20$.
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17) for the right triangle shown below, what is the tangent of ∠a? o ta…
# Explicación: ## Paso 1: Recordar la definición de tangente En un triángulo rectángulo, $\tan(A)=\frac{\text{cateto opuesto}}{\text{cateto adyacente}}$ respecto al ángulo $A$. ##…
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16) a triangle undergoes an enlargement as shown in the diagram. what i…
# Explicación: ## Paso 1: Identificar triángulos semejantes Los triángulos son semejantes, entonces las razones de los lados correspondientes son iguales. ## Paso 2: Establecer la…
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point k is on line segment $overline{jl}$. given $jl = x + 10$, $kl = 4…
8
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1. find the measures of the interior angles of the triangle. the measur…
30°, 60°, 90°
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point s is on line segment $overline{rt}$. given $rt = 2x$, $rs = 3x - …
$4$
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21. which diagram(s) show adjacent angles? __________ 22. which diagram…
21. C, F 22. B, D, F 23. A, C 24. E 25. E
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point s is on line segment $overline{rt}$. given $st = 3x - 8$, $rt = 4…
$20$
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20. ∠3 and ∠4 are supplementary angles. find the measures of the angles…
\(m\angle3 = 149^{\circ}\), \(m\angle4 = 31^{\circ}\)
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point d is on line segment $overline{ce}$. given $cd = x, de = 7$, and …
$7$
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point u is on line segment $overline{tv}$. given $uv = 2$, $tu = 5x$, a…
$12$
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3. find the measures of the interior angles of the triangle. the measur…
\(25^{\circ},45^{\circ},110^{\circ}\)
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solve the inequality and graph the solution on the line provided. 3 + 5…
Inequality Notation: $x\geq4$ Number Line: Plot a closed - circle at 4 (because the inequality is $\geq$) and draw a line to the right of 4.
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solve the inequality and graph the solution on the line provided. -2x +…
Inequality Notation: $x\leq - 2$ Number Line: Plot a closed - circle at - 2 and draw a line to the left.
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solve the inequality and graph the solution on the line provided. -13 +…
Inequality Notation: $x\geq - 1$ Number Line: Plot a closed - circle at $-1$ and draw a line to the right.
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20. ∠3 and ∠4 are supplementary angles. find the measures of the angles…
\(m\angle3 = 149^{\circ}\), \(m\angle4 = 31^{\circ}\)
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solve and write interval - notation for the solution set. then graph th…
The solution set in interval notation is $(-\infty,-\frac{7}{2})$. For the graph, it would be a number - line with an open circle at $-\frac{7}{2}$ and an arrow pointing to the le…
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20. ∠3 and ∠4 are supplementary angles. find the measures of the angles…
$m\angle3 = 149^{\circ}$, $m\angle4 = 31^{\circ}$
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solve the inequality and graph the solution on the line provided. -5x -…
$\geq$, $x\geq - 7$ On the number - line, we would place a closed circle at - 7 (because the inequality is $\geq$) and shade to the right.
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7) the table below shows the sum of the interior angle measures of cert…
# Explicación: ## Paso1: Identificar la fórmula La fórmula para el cálculo de la suma de los ángulos interiores de un polígono es $S=(n - 2)\times180^{\circ}$, donde $n$ es el núm…
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finding scale factor scale factor is a ratio between the side - length …
For #1: New side lengths are 18 ft and 24 ft. For #2: New side lengths are 1 cm and 5 cm. For #3: New side lengths are 4 in and 6 in.
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6) the table below shows the number of diagonals in certain polygons. w…
$\frac{n(n - 3)}{2}$
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19. ∠1 and ∠2 are complementary angles. find the measures of the angles…
$m\angle1 = 48^{\circ}$ $m\angle2 = 42^{\circ}$
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∠3 and ∠4 are supplementary angles. given the measure of ∠3, find m∠4. …
17. \(105^{\circ}\) 18. \(64^{\circ}\)
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x = ________ y = ________ z = ________
# Explicación: ## Paso 1: Usar la proporcionalidad de triángulos semejantes Como los triángulos son semejantes, se tiene $\frac{4z}{4z + 20}=\frac{x}{x + y}=\frac{24 - x}{24}$. To…