Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
Reflexive Property (el enunciado $\overline{CE} \cong \overline{CE}$ se justifica por la Propiedad Reflexiva, ya que un segmento es congruente consigo mismo)
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
La justificación correcta para $\overline{CE} \cong \overline{CE}$ es la **Reflexive Property** (Propiedad Reflexiva).
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15. determine side c . 15. in an obtuse triangle the measurement of two…
The length of side \( c \) is approximately \( 6.98 \) centimeters.
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
Reflexive Property (la justificación para $\overline{CE} \cong \overline{CE}$ es la Propiedad Reflexiva, por lo que la opción seleccionada es correcta).
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
Reflexive Property (y la justificación para \(\overline{CE} \cong \overline{CE}\) es la Propiedad Reflexiva, no CPCTC como estaba marcado incorrectamente antes)
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
La razón correcta para \( \angle D \cong \angle B \) es "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)" (ya que los ángulos son correspondientes de triángulos c…
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11 ∠a ≅ ∠c corresponding parts of congruent triangles are congruent (cp…
$\angle D \cong \angle B$ (o en la casilla, primera caja: $D$, segunda caja: $B$)
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9 \\(\\overline{ba} \\cong \\overline{ba}\\) reflexive property 10 \\(\…
El error es que $\angle A\cong\angle C$ no se justifica con la Propiedad Reflexiva, sino con CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
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given: \\(\\overline{df} \\parallel \\overline{hg}\\), \\(f\\) is the m…
The completed two - column proof is as shown above. The key steps are using given information, properties of midpoints, corresponding angles from parallel lines, and SAS congruenc…
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5 \\(\\overline{bd} \\cong \\overline{bd}\\) reflexive property 6 \\(\\…
La razón correcta para \( \triangle ABE \cong \triangle CDE \) es **SAS** (Side - Angle - Side), ya que se tienen \( \overline{AB} \cong \overline{CD} \) (lado), \( \angle A \cong…
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5 $overline{bd} cong overline{bd}$ reflexive property 6 $overline{de} c…
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
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5. $overline{bd} cong overline{bd}$ reflexive property 6. $overline{de}…
Geometría (subcampo de Matemáticas)
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prove: \\(\\overline{ac}\\) bisects \\(\\overline{bd}\\). note: quadril…
$\overline{AC}$ bisecta $\overline{BD}$ se demuestra porque $\triangle ABE \cong \triangle CDE$ implica $\overline{BE} \cong \overline{DE}$ (CPCTC), lo que significa que $E$ es el…
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7 \\(\\overline{be} \\cong \\overline{be}\\) reflexive property 8 \\(\\…
El tipo de enunciado para $\overline{CE} \cong \overline{CE}$ es uno que utiliza la **Propiedad Reflexiva** (Reflexive Property), ya que un segmento es congruente consigo mismo.
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7 \\(\\overline{be} \\cong \\overline{be}\\) reflexive property 8 \\(\\…
El segmento correcto es \( \overline{DE} \cong \overline{DE} \) (o otro segmento válido como \( \overline{CE} \cong \overline{CE} \)), así que la corrección es reemplazar \( ME \)…
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7 be ≅ be reflexive property 8 \\(\\overline{ac} \\cong \\overline{ac}\…
La razón correcta para \( \overline{ME} \cong \overline{ME} \) es la **Propiedad Reflexiva** (Reflexive Property), no Sustitución.
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3 ∠aeb ≅ ∠ced corresponding parts of congruent triangles are congruent …
La subdisciplina que mejor se aplica es **Geometría** (subcampo de Matemáticas), ya que el problema trata sobre congruencia de segmentos, ángulos y triángulos, utilizando propieda…
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13. determine side x. 13. in a scalene triangle the measurement of two …
The length of side $x$ is approximately $\boldsymbol{51.48}$ mm (or depending on the precision of the sine values, it can be calculated more accurately. If we use a calculator for…
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given: $\\triangle abe \\cong \\triangle cde$. prove: $\\overline{ac}$ …
Para probar que \( \overline{AC} \) bisecta \( \overline{BD} \), usamos la congruencia de triángulos \( \triangle ABE \cong \triangle CDE \) (dado). Por el Teorema de Partes Corre…
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determine whether each function shown in the coordinate plane is linear…
The function with the curved graph (the one below the two boxes) should be placed in the "Non - Linear Function" box.
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input (x) output (y) (x,y) -1 -3 (-1,-3) 0 -1 (0,-1) 1 1 (1,1) 2 3 (2,3…
The points \((-1, -3)\), \((0, -1)\), \((1, 1)\), \((2, 3)\) are graphed on the coordinate plane as per the steps (visual marking of these points on the given grid).
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which graph represents a function?
The first graph (the left - most graph)
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8. determine side a. 13.006 cm 63.7° 27.9° a
Approximately $6.79$ cm (or more precise $6.786$ cm)
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given \\( \\mathbf{u} = \\langle 4, -4 \ angle \\) and \\( \\mathbf{v} …
\(-32\)
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find the value of x. x = (there is a triangle with an exterior angle of…
\(55\)
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which equation can be used to find the value of x? x = 45 + 40 find the…
\(x = 85\)
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parallel lines e and f are cut by transversal b. what is the value of y…
130
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which equation can be used to find the value of x? x = 45 − 40 x + 45 +…
\(x = 45 + 40\) (the fourth option: \(x = 45 + 40\))
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which equation can be used to find the value of x? x = 45 - 40 x + 45 +…
\(x = 45+40\) (the fourth option: \(x = 45 + 40\))
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which equation can be used to find the value of x? x = 45 - 40; x + 45 …
\(x = 45 + 40\) (the fourth option: \(x = 45 + 40\))
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which equation shows the relationship between the exterior angle and th…
\(m\angle4 = m\angle1 + m\angle2\) (the third option: \(m\angle4 = m\angle1 + m\angle2\))
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which equation can be used to find the value of x? x + 68 + 72 = 180 fi…
\(40\)
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which equation can be used to find the value of x? x + 68 + 72 = 360 x …
\(x + 68 + 72 = 180\) (the last option)
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graph. x > -60 plot the endpoints. select an endpoint to change it from…
To graph \( x > -60 \): 1. Place an **open circle** at \( -60 \) (since \( x eq -60 \)). 2. Draw a **ray** starting from the open circle at \( -60 \) and extending to the **righ…
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which equation shows the relationship between the angles in the triangl…
\( \boldsymbol{m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ} \) (the first option)
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graph. x ≤ -805 plot the endpoints. select an endpoint to change it fro…
To graph \( x \leq -805 \): 1. Place a **closed circle** (filled dot) at \( -805 \) (the tick mark for \( -805 \) on the number line). 2. Draw a **ray** extending to the **left** …
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solving oblique triangle problems using the law of sines solve these pr…
\(a\approx5.680\) cm (if we take angle opposite \(a\) as \(33^\circ\)) or if angle opposite \(a\) is \(30^\circ\), \(a\approx5.214\) cm. But based on the diagram with 70 and 33, t…
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value: 3 solve and graph. select all answers that -3(4n + 2) < -78 mark…
B. $n > 6$, E. (the graph with an open circle at 6 and extending to the right)
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question 21 find the length of side x. round to the nearest tenth. tria…
\(7.3\)
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find the common ratio and write out the first four terms of the geometr…
Common ratio is \( g \) \( a_1=\frac{1}{6g^{2}} \), \( a_2=\frac{1}{6g} \), \( a_3=\frac{1}{6} \), \( a_4=\frac{g}{6} \)
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use the following information to answer the next question. a surveyor m…
D. \( 47^\circ \) ### Question 6 (Triangle \( \triangle RST \))
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given: ∠1 ≅ ∠2 prove: p || q statements 1. ∠1 ≅ ∠2 2. ∠1 and ∠3 are ver…
The missing statement is $\boldsymbol{\angle3\cong\angle2}$ (obtained by transitive property from $\angle1\cong\angle2$ and $\angle1\cong\angle3$).
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what is the value of x? x = exterior angle = non - adjacent interior an…
\(30\)
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which equation can you use to find the value of x? x = 120 + 35 what is…
\( x = 155 \)
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which equation can you use to find the value of x? x = 120 + 35 x = 120…
\(x = 120+35\) (the first option: \(x = 120 + 35\))
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which equation can you use to find the value of x? $x = 120 + 35$ $x = …
\(x + 120 + 35 = 180\)
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the exterior angle is ∠4. the non - adjacent interior angles are ∠1 and…
\( m\angle1 + m\angle2 \)
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use the figure below to help. first identify the types of angles in the…
\(180\)
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using the conjugate to rationalize the denominator use the work shown t…
\(\frac{3+\sqrt{3x}}{3 - x}\) (corresponding to the first option among the given choices, likely the right - most option in the image with \(\frac{3+\sqrt{3x}}{3 - x}\))
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show that the measure of an exterior angle is always equal to the sum o…
The exterior angle is $\boldsymbol{\angle2}$. The non - adjacent interior angles are $\boldsymbol{\angle1}$ and $\boldsymbol{\angle3}$.
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first identify the types of angles in the figure. the exterior angle is…
The exterior angle is $\boldsymbol{2}$. The non - adjacent interior angles are $\boldsymbol{1}$ and $\boldsymbol{3}$.
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proving parallel lines with alternate exterior angles given: ∠1 ≅ ∠2 pr…
To complete the two - column proof: - **Statement 2**: $\angle 1\cong\angle 3$; **Reason 2**: Vertical Angles Theorem. - **Statement 3**: $\angle 2\cong\angle 3$; **Reason 3**: Tr…
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the measure of the exterior angle equals the sum of the measures of the…
Yes, because $50^{\circ}+60^{\circ}=110^{\circ}$.
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complete the statement. the measure of the exterior angle equals the su…
\(110\)
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complete the statement. the measure of the exterior angle equals the? o…
sum
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write the first six terms of of the geometric sequence with the first t…
\(-800\)
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write the first six terms of of the geometric sequence with the first t…
\(1600\)
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write the first six terms of of the geometric sequence with the first t…
\(-200\)
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6. triangle a is an isosceles triangle with two angles of measure x deg…
(for part a): Three combinations are \((x = 50,y = 80)\), \((x = 60,y = 60)\), \((x = 80,y = 20)\) (answers may vary as long as \(2x + y=180\) and \(x>0,y>0\)) ### Part b
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quiz - special triangles 1 triangle with right angle, 60° angle, hypote…
D. \(m=\frac{7\sqrt{3}}{2},n = \frac{7}{2}\)
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a triangle with a right angle, one side labeled 4, another side labeled…
C. \(x = 4\sqrt{2},y = 4\)
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a right triangle with one angle 45°, one leg is $3\\sqrt{2}$, hypotenus…
C. \(x = 6\), \(y=3\sqrt{2}\)
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a) $m = \\frac{3\\sqrt{2}}{4}$, $n = \\frac{3\\sqrt{2}}{4}$ b) $m = 3\\…
D) \(m = \frac{3\sqrt{2}}{2}\), \(n=\frac{3\sqrt{2}}{2}\)
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quiz - special triangles 8 x 45° 45° 8√2 a) 4√2 b) 16√2 c) 16√6 d) 32 a…
A) \(4\sqrt{2}\)
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quiz - special triangles 1 a) $16\\sqrt{2}$ b) $\\frac{4\\sqrt{3}}{3}$ …
D) 4
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quiz - special triangles (figure of a triangle with angles and side len…
B) 10
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quiz - special triangles 1 a) \\(\\frac{7}{2}\\) b) \\(\\frac{7\\sqrt{2…
C. \(\frac{7\sqrt{3}}{3}\)
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the graph shows quadrilaterals bcde and qrst. is bcde congruent to qrst…
Yes, BCDE is congruent to QRST. We can justify it by showing that there exists a rigid transformation (such as translation, rotation, or reflection) that maps one quadrilateral on…
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the graph shows quadrilaterals defg and pqrs. is defg congruent to pqrs…
No, \(DEFG\) is not congruent to \(PQRS\). The side lengths (e.g., \(DE = 2\sqrt{2}\) vs. \(PQ = 3\sqrt{2}\)) and vertical/horizontal distances (e.g., \(EG = 4\) vs. \(RP = 5\)) d…
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solve. steve and kim have put in a new tile entryway in their house. th…
\(40\frac{1}{2}\text{ in}\)
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7) a) $x = 9$, $y = \\frac{27}{4}$ b) $x = 9$, $y = \\frac{9\\sqrt{3}}{…
7) B. \(x = 9,y=\frac{9\sqrt{3}}{2}\) 8) A. \(x = 7,y = 7\) 9) D. \(x = 5\sqrt{2},y = 5\) 10) A. \(x=\frac{14\sqrt{3}}{3},y=\frac{7\sqrt{3}}{3}\) 11) C. \(9\sqrt{6}\) 12) D. \(16\…
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special right triangles date______ find the missing side lengths. leave…
1) B; 2) B; 3) D; 4) A; 5) D; 6) A
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find the distance between the points (4, -3) and (4, 7). distance:
10
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triangle similarity: aa proving triangle similarity given: $overline{fh…
- Step 4 Reason: all right angles are congruent - Step 6 Statement: \(\angle FGH\cong\angle KGJ\) - Step 7 Reason: AA (Angle - Angle) similarity criterion
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elige el par o pares ordenados que son soluciones del sistema. (puede h…
# Explanation: ## Step1: Analizar la región solución La región solución es la intersección de las regiones de cada desigualdad. Observamos la gráfica: la línea sólida y la línea p…
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find the length of ef in the trapezoid shown below. 8x 7x - 1 16
48
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15. compute the length of piece ab of the roof truss in figure 35–74. f…
\(\approx 3.13\) meters (or more precise value based on calculator steps)
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find the length of ef in the trapezoid shown below. ef=
55
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15. compute the length of piece ab of the roof truss in figure 35-74. f…
The length of \(AB\) is approximately \(\boldsymbol{3.13}\) meters (or more precise value around \(3.13\) - \(3.14\) m depending on calculation precision).
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what is the slope of a line that passes through the points (5,-4) and (…
The option with \(-\frac{3}{2}\) (assuming it's the second option, e.g., B. \(-\frac{3}{2}\))
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what is the slope of the line graphed in the given coordinate plane?
\(\frac{2}{3}\)
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find the value of x and y in the isosceles trapezoid shown below. 63° (…
\(x = 11\), \(y = 117\)
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Question was provided via image upload.
The equation of the line is \(y =-\frac{3}{10}x\) (or \(y=-0.3x\))
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what is the slope of the line graphed in the given coordinate plane?
\(-\frac{1}{5}\)
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7 for the rhombus, find the of x. (7x - 17)° (5x + 9)°
13
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three students attempt to define the geometric object called an angle. …
- Ivy's definition: Your definition is incorrect, and its precise meaning is unclear. - Ethan's definition: Excellent! You have a razor sharp intellect! - Ebuka's definition: Angl…
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three students attempt to define what it means for two lines to be para…
- Daniela's definition ↔ "Nice definition! Hip, hip, hurrah!" - Ori's definition ↔ "Part of your definition is correct, but the other part is not. Parallel lines don't have to be …
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elige el par o pares ordenados que son soluciones del sistema. (puede h…
# Explanation: ## Step1: Analizar la región solucion Observar la región sombreada (solución del sistema de desigualdades). La región es la intersección de las dos semirrectas somb…
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three students attempt to define what a circle is. can you match the te…
- Duru's definition: Stupendous! Well done. - Oliver's definition: You seem to be confusing a circle with a sphere. - Carlos's definition: Your definition needs to be much more pr…
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three students attempt to define what a line segment is. can you match …
- Ruby's definition ↔ "Wunderbar! Well done." - Shriya's definition ↔ "Your definition is kind of correct, but it lacks mathematical precision." - Abhishek's definition ↔ "Were yo…
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select the most precise and correct statement about perpendicular lines…
B. \( \overleftrightarrow{AB} \) is perpendicular to \( \overleftrightarrow{CD} \) if the two lines intersect such that \( \angle AOD \) is a right angle.
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pqrs is a rectangle. find the value of x and the length of each diagona…
\( x = 3 \), \( PR = SQ = 26 \)
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find the value of each variable in the rhombus below. (image of a rhomb…
\( x = 28 \), \( y = 90 \), \( z = 90 \)
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find the value of the variables in the rectangle shown below. image of …
\( x = 9 \), \( y = 17 \)
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2 find the value of the variables in the parallelogram shown below. ima…
\( x = 25 \), \( y = 105 \)
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1 find the missing angle measures of the parallelogram. m∠b=_________ m…
\( m\angle B = 82^\circ \), \( m\angle C = 98^\circ \), \( m\angle D = 82^\circ \)
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7 for the rhombus, find the value of x. (7x - 17)° (5x + 9)° 7x - 17 = …
13
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question 19 of 50 if $\\triangle rsu \\sim \\triangle vst$, then the tr…
the SAS similarity theorem.
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question 18 of 50 the value of k is: diagram with parallel lines, trans…
48 (and the option corresponding to 48, which is "48" among the given options)
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question 17 of 50 the triangles are similar by: diagram of triangles wi…
the SSS similarity theorem