幾何
三角形、圓、解析幾何與證明題。
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¿cuál de las siguientes afirmaciones debe ser verdadera según el diagra…
\(\overline{JL}\) is a segment bisector, \(\overline{JL}\) is an angle bisector, \(J\) is the vertex of two angles that are congruent to one another, \(L\) is the vertex of two an…
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k is the midpoint of \\(\\overline{gi}\\) and \\(\\overline{hj}\\). com…
- Statement 4 Reason: Definition of midpoint - Statement 6 Reason: SAS (Side - Angle - Side) Congruence Postulate - Statement 7 Reason: CPCTC (Corresponding Parts of Congruent Tri…
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in the coordinate plane, points a, b, and c have coordinates (1,2), (4,…
The figure formed by points \(A\), \(B\), and \(C\) is a right - angled triangle. ### Sub - question 2
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$\\angle r \\cong \\angle q$. complete the proof that $\\overline{pr} \…
1. Reason for $\angle R \cong \angle Q$: Given 2. Reason for $\overline{QR} \cong \overline{QR}$: Reflexive Property of Congruence 3. Reason for $\triangle PQR \cong \triangle PRQ…
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7. \\begin{cases} x - y = 1 \\\\ y = 5 \\end{cases}
The solution to the system of equations is \( x = 6 \), \( y = 5 \), and the point of intersection on the graph is \((6, 5)\).
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3. \\begin{cases} y = x - 1 \\\\ x - 4y = 16 \\end{cases}
The solution to the system is \( x = -4 \), \( y = -5 \) (or the ordered pair \((-4, -5)\))
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lesson 26: distance, area and perimeter on a coordinate plane 6.ns.8 2.…
c. 10
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given: r is the midpoint of \\(\\overline{qt}\\) and \\(\\overline{ps}\…
\( \triangle QRP \cong \triangle TRS \) (proven by SAS congruence postulate using midpoint properties and vertical angles)
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practice 1. solve -8m + 2 ≤ 50. then graph the solution.
The solution to the inequality \(-8m + 2 \leq 50\) is \( m \geq -6 \). The graph has a closed circle at \(-6\) and an arrow pointing to the right.
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model -0.2 + (-1.3) on the number line. -2 -1.9 -1.8 -1.7 -1.6 -1.5 -1.…
To model \(-0.2 + (-1.3)\) on the number line: 1. Start at \(-0.2\). 2. Move 1.3 units to the left (because we add \(-1.3\)). This lands at \(-1.5\) (since \(-0.2 - 1.3 = -1.5\)).…
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1. solve -8n + 2 ≤ 50. then graph the solution.
The solution to the inequality \(-8n + 2 \leq 50\) is \(n \geq -6\). For the graph, on a number line, draw a closed circle at \(-6\) (since the inequality includes equality) and s…
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use the tools to circumscribe a circle about the triangle.
To circumscribe a circle about the triangle, follow these steps: 1. Use the straight - edge to draw the perpendicular bisectors of two sides of the triangle. 2. Find the intersect…
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use the given information to prove that $\\triangle pqs \\cong \\triang…
The reason for \(\triangle PQS\cong\triangle RSQ\) is the Angle - Angle - Side (AAS) Congruence Criterion.
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find the volume of a cone with a base diameter of 12 in and a height of…
\(414.48\) cubic inches
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in the figure below, $m\\angle 3 = 144^{\\circ}$. find $m\\angle 1$, $m…
\(m\angle1 = 144^{\circ}\) \(m\angle2 = 36^{\circ}\) \(m\angle4 = 36^{\circ}\)
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use the graph to determine the behavior of the function between the ind…
- A and B: increasing - B and C: constant - C and D: decreasing - D and E: increasing
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in the figure below, ( m angle 4 = 98^circ ). find ( m angle 1 ), ( m a…
\(m\angle1 = 82^{\circ}\), \(m\angle2 = 98^{\circ}\), \(m\angle3 = 82^{\circ}\)
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in the figure below, m∠2 = 41°. find m∠1, m∠3, and m∠4
\(m\angle1 = 139^{\circ}\), \(m\angle3 = 139^{\circ}\), \(m\angle4 = 41^{\circ}\)
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3. a rectangular pool 6 meters by 8 meters is to be surrounded by a wal…
\( \frac{ -7 + \sqrt{97} }{2} \) (or approximately 1.42 meters)
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which of the following shapes have one line of symmetry but no rotation…
The third shape (the one with a small rectangle attached to the left of a larger rectangle, making a T - like shape) (or the fifth shape - trapezoid - like, or the last shape - ro…
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does the following figure have point symmetry? recycle symbol image opt…
No
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describe the rotational symmetry of the figure. image of a yellow diamo…
\( 90^\circ \), \( 180^\circ \), \( 270^\circ \) (the option with \( 90^\circ \), \( 180^\circ \), \( 270^\circ \))
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slo post-test how many lines of symmetry does the following shape have?…
2 (corresponding to the option "2" in the multiple - choice options)
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state if the triangles in each pair are similar. if so, state how you k…
$\triangle PFE$ (The triangles are similar by SAS similarity because $\angle FPE = \angle QPR$ and $\frac{FP}{QP} = \frac{EP}{RP} = \frac{1}{4}$)
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state if the triangles in each pair are similar. if so, state how you k…
$\triangle PEF$ ### Problem 2:
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which two triangles are congruent? complete the congruence statement. (…
$\triangle QPR \cong \triangle HFG$
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in the diagram, △abc below (black) is transformed to create △abc (red) …
First transformation: \( \triangle ABC \) was \(\boldsymbol{\text{translated 5 units right}}\) (or appropriate horizontal shift) to create \( \triangle A'B'C' \). Then, \( \triang…
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apply: finding unknown angle measures the five angles shown are formed …
The measure of \(\angle1\) is \(18^{\circ}\), the measure of \(\angle2\) is \(18^{\circ}\), the measure of \(\angle3\) is \(90^{\circ}\)
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the graph shows △abc and its image △abc. describe a sequence of transfo…
Reflection over the \(y\) - axis, then translated according to the rule \((x,y)\to(x - 2,y - 4)\) (the second option in the given choices, which is the one with the blue circle ne…
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what is the graph of the equation $y = -\frac{1}{4}x + 2$? the y-interc…
The \(y\) - intercept is \(2\), which means the line crosses the \(y\) - axis at the point \((0,2)\)
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△pqr is reflected across the line y = x to create △pqr. what are the co…
(6, -2) (assuming the fourth option, which is (6, -2))
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in the figure below, if you reflected △xyz over the y - axis, rotated 9…
The coordinate of the transformed \( Y \) is \( (4,-5) \)
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3. a rectangular pool 6 meters by 8 meters is to be surrounded by a wal…
168
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the diagram shows $\\triangle pqr$ after it has been rotated $90^{\\cir…
\((-7,4)\) (corresponding to the option \((-7,4)\))
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which of the following shows the figure after the transformation? (with…
The second graph (the one with the smiley in the first quadrant, positive x and positive y, with the smiling face)
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the figure in the coordinate plane below is reflected across the y - ax…
The figure after two reflections (first over \(y\) - axis, then over \(x\) - axis) will be in the first quadrant (with coordinates \((a,b)\) if original was \((-a,-b)\)).
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if $\\triangle abc$ is rotated $180^{\\circ}$ clockwise what is $b$? (o…
\(\boldsymbol{(-2, -3)}\) (corresponding to the option: \(\boldsymbol{(-2, -3)}\))
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if $\\triangle abc$ is rotated $180^\\circ$ clockwise, what is $a$? gri…
\((-2, - 3)\) (the option is \(\boldsymbol{(-2, - 3)}\))
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there are three geometric figures with related angle and side compariso…
\( m\angle ADB = m\angle CBD \)
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△rst is reflected across the line x = 2 to create △rst. what are the co…
\((-1, -3)\) (corresponding to the option \((-1, -3)\))
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what is the measurement of this angle? protractor image blank°
90
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drag the yellow point until an accurate \height\ of the triangle is dra…
The area of the triangle is \( \boxed{31.155} \) (or depending on the actual base and height, but following the calculation with base \( 9.3 \) and height \( 6.7 \), the area is \…
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what is the measurement of this angle?
70
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question 8 what is the x-intercept of the graph shown? a) (-5,0) b) (5,…
D) \((2,0)\)
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salma wants to lay carpeting over a certain area of her apartment. the …
The expression is \((2.5)^2 + (0.5)^2\) and the area is \(6.5\) square feet.
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nti day #1 - area of composite shapes due: december 12 at 3:00 pm grade…
Expression: \( 8^2 - 1^2 - 3^2 \) Evaluated: \( 54 \) square feet (Note: The exact dimensions depend on the diagram, but assuming the large square is 8x8, and unshaded squares 1x1…
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select the correct choice that completes the sentence below. the measur…
45
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if an angle measures ( x^circ ), how can its complement be represented?…
The measure of the complement of \( x^\circ \) is \( \boldsymbol{90 - x} \) degrees.
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question given the two rectangles below. find the area of the shaded re…
\( \boxed{72} \)
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find (a) the complement and (b) the supplement of an angle with the mea…
(a) \(70^\circ45'\) (b) \(160^\circ45'\)
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all of the quadrilaterals in the shape below are squares. find the area…
36
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question given the two rectangles below. find the area of the shaded re…
30
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question one rectangle is \framed\ within another. find the area of the…
\( 5 \)
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question one rectangle is \framed\ within another. find the area of the…
44
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the radius of a circle is 32 meters. what is the angle measure of an ar…
\( \frac{225}{2} \) (or \( 112.5 \))
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the radius of a circle is 9 inches. what is the length of a 102° arc? r…
\( \frac{51}{10}\pi \) (or \( 5.1\pi \), but as an exact form, \( \frac{51\pi}{10} \))
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all of the quadrilaterals in the shape below are squares. find the area…
45
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the radius of a circle is 9 inches. what is the length of a 102° arc? g…
\(\frac{51}{10}\pi\) inches
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the diameter of a circle is 8 inches. what is the angle measure of an a…
\(135\)
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the diameter of a circle is 10 kilometers. what is the angle measure of…
\(144\)
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the radius of a circle is 5 centimeters. what is the length of a 45° ar…
\(\frac{5\pi}{4}\)
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the diameter of a circle is 12 meters. what is the length of a 45° arc?…
\(\frac{3\pi}{2}\)
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the radius of a circle is 5 miles. what is the angle measure of an arc …
\(36\)
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the radius of a circle is 5 centimeters. what is the angle measure of a…
\(108\)
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the diameter of a circle is 16 centimeters. what is the angle measure o…
\(33.75\)
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certain positive angles are marked in the given figure. find the corres…
\(30^\circ=\boldsymbol{\frac{\pi}{6}}\) radians; \(\frac{\pi}{4}\) radians \(=\boldsymbol{45}\)°; \(60^\circ=\boldsymbol{\frac{\pi}{3}}\) radians; \(\frac{2\pi}{3}\) radians \(=\b…
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convert the following degree measure to radian measure. 240°
\( \frac{4\pi}{3} \)
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convert the following degree measure to radian measure. 270°
\( \frac{3\pi}{2} \)
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fill in the blank to correctly complete the sentence 76.45° written in …
\(76^\circ 27'\)
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convert the following radian measure to degree measure. \\(\frac{pi}{4}…
$45^\circ$
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given: \\(\\overline{ab} \\cong \\overline{bc}\\) and \\(\\angle abe \\…
To prove \(\triangle ABE \cong \triangle CBD\), we use the **SAS (Side - Angle - Side)** congruence criterion. ## Step 1: Identify the given congruent sides and angles We are give…
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10 \\(\\overline{de} \\cong \\overline{de}\\) reflexive property 11 \\(…
El tipo de enunciado es un **Enunciado de Congruencia Reflexiva de Segmentos** (o más precisamente, que utiliza la Propiedad Reflexiva de Congruencia de Segmentos), donde se afirm…
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1 $overline{ab} cong overline{bc}$ $angle abe cong angle cbd$ given 2 $…
Los enunciados (desde el 2 al 11) son enunciados que aplican la **Propiedad Reflexiva de Congruencia de Segmentos**, ya que afirman que un segmento es congruente consigo mismo (po…
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respuesta una rotación de 90° en el sentido de las agujas del reloj alr…
Una rotación de 180° en sentido antihorario alrededor del origen.
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traslada la figura 5 unidades a la derecha y 7 unidades hacia abajo. gr…
Los puntos traslados son \( (-3, 0) \), \( (0, 2) \), \( (-1, -3) \) (graficar estos puntos).
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traslada la figura 4 unidades a la izquierda y 2 unidades hacia arriba.…
Los puntos traslados son \( (-1, -5) \), \( (2, -2) \), y \( (3, -7) \). Al graficarlos, forman el triángulo trasladado 4 unidades a la izquierda y 2 unidades arriba. (Nota: La gr…
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step statements reason 1 \\(\\overline{ab} \\cong \\overline{bc}\\) \\(…
El error es que se intentó aplicar la propiedad reflexiva a $\overline{AD} \cong \overline{CE}$, pero la propiedad reflexiva se aplica a un segmento congruente consigo mismo, y $A…
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7 \\(\\overline{ae} \\cong \\overline{ae}\\) reflexive property 8 \\(\\…
La declaración es del tipo que usa la **Propiedad Reflexiva** para afirmar la congruencia de un segmento consigo mismo, por lo que el tipo de declaración se relaciona con la congr…
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given: \\(\\overline{ab} \\cong \\overline{bc}\\) and \\(\\angle abe \\…
Para probar \(\triangle ABE \cong \triangle CBD\) usando SAS: 1. \(\overline{AB} \cong \overline{BC}\) (Dado) 2. \(\angle ABE \cong \angle CBD\) (Dado) 3. \(\overline{BE} \cong \o…
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1 \\(\\overline{ab} \\cong \\overline{bc}\\)\\(\\angle abe \\cong \\ang…
Para la primera línea (número 1), el tipo de enunciado es "Given" (Dado), ya que son las hipótesis proporcionadas para la demostración. Para las líneas 2 a 11, el tipo de enunciad…
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respuesta intento 1 de 2 \\overline{tv} is a segment bisector. \\overli…
\(\overline{TV}\) is a segment bisector.
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utilice un compás y una regla para construir una bisectriz perpendicula…
linea (la herramienta "linea" para dibujar la línea azul que es la bisectriz perpendicular)
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¿cuál de las siguientes afirmaciones debe ser verdadera según el diagra…
# Explanation: ## Step1: Analizar \(\overline{KM}\) como bisectriz de segmento Un segmento bisectriz divide otro segmento en dos partes iguales. En el diagrama, \(M\) está en \(IJ…
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7 \\(\\overline{ae} \\cong \\overline{ae}\\) reflexive property\ 8 \\(\…
La congruencia correcta no es \( \triangle ABE \cong \triangle CBD \) con SAS. Debe ser otro par, por ejemplo, \( \triangle ABE \cong \triangle CDE \) por SAS (si \( AE = DE \), \…
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given: $ab \\cong \\overline{bc}$ and $\\angle abe \\cong \\angle cbd$.…
To prove \(\triangle ABE \cong \triangle CBD\), we need to identify the correct congruence criterion. Let's analyze the given information: 1. \(\overline{AB} \cong \overline{BC}\)…
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given: \\(\\overline{ab} \\cong \\overline{bc}\\) and \\(\\angle abe \\…
To prove \( \triangle ABE \cong \triangle CBD \), we can use the **SAS (Side - Angle - Side)** congruence criterion. Here are the steps: ## Step 1: Identify the given congruent si…
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13 \\(\\overline{ce} \\cong \\overline{ce}\\) reflexive property\ 14 \\…
$\overline{BD} \cong \overline{BD}$ (or other segment congruent to itself, but following the reflexive property rule)
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13 \\(\\overline{ce} \\cong \\overline{ce}\\) reflexive property 14 \\(…
The error is that \(\overline{AE}\cong\overline{AE}\) was already used in step 14, so we should use a different congruent pair (e.g., a side or angle not yet used) instead of repe…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
$\overline{BD} \cong \overline{BD}$ (or $\overline{AE} \cong \overline{AE}$ but since the incorrect one was $\overline{BD} \cong \overline{AE}$, the correct reflexive should be a …
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$\\overline{be} \\cong \\overline{be}$ reflexive property $\\overline{a…
The statement \(\overline{BD}\cong\overline{EA}\) cannot be justified by the Reflexive Property. The correct justification (if applicable) would depend on triangle congruence (e.g…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
El segmento \(\overline{BM}\) es inválido; en su lugar, un segmento válido (por ejemplo, \(\overline{BE} \cong \overline{DE}\)) debería usarse con CPCTC, pero la notificación indi…
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∠ead ≅ ∠eab reflexive property try type of statement a b e d c note: \\…
El tipo de enunciado es uno que utiliza la **Propiedad Reflexiva** (ya que un ángulo es congruente consigo mismo, $\angle EAB \cong \angle EAB$ se justifica por la Propiedad Refle…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
La declaración $\angle EAB \cong \angle EAB$ es una aplicación de la **Propiedad Reflexiva** (ya que un ángulo es congruente consigo mismo), y el tipo de declaración es una afirma…
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10 \\(\\overline{ab} \\cong \\overline{cd}\\) corresponding parts of co…
La razón correcta para $\overline{AB} \cong \overline{CD}$ es "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)" (no la propiedad reflexiva, ya que $\overline{AB}$…
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10 \\(\\overline{ab} \\cong \\overline{cd}\\) corresponding parts of co…
La declaración es un **afirmación de congruencia** (por ejemplo, en el menú, la opción correspondiente a declaraciones que establecen \(\cong\) entre segmentos o ángulos, como "Co…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
El triángulo \( \triangle BME \) no es válido. Debe elegir un triángulo válido en la figura, como por ejemplo \( \triangle ABE \) o \( \triangle CDE \) (dependiendo de la figura).…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (12…
La afirmación $\overline{AE} \cong \overline{DE}$ **no** puede justificarse con la Propiedad Reflexiva, ya que la reflexiva requiere que un segmento sea congruente consigo mismo (…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
El error es que se usa la razón "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)" para $\overline{AE}\cong\overline{DE}$ sin haber probado que existan triángulos …
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
El segmento \(\overline{BM}\) no es válido. Debe usar un segmento que exista en la figura, como \(\overline{AE} \cong \overline{DE}\) (o el correspondiente según la congruencia de…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
El segmento \( \overline{AM} \) no es válido; debe usar un segmento válido de la figura (por ejemplo, \( \overline{BM} \cong \overline{DM} \) si es el caso, o revisar la congruenc…