Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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question. the square on the right is a scaled copy of the square on the…
$\frac{3}{2}$
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point p has coordinates (-2.5, 3). point q is a reflection of point p a…
The coordinates of point $Q$ are $(-2.5,-3)$ and it is in the third quadrant.
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which statement is true about the prime polynomial 2x² + 3x + 3? it can…
It cannot be modeled with a rectangle.
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6. figure lmno is similar to figure tuvw. find the lengths of $overline…
$LM = 7.5$, $NO = 4.5$
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by the law of detachment, what can you conclude from the statement? if …
their intersection is a line
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5. in the diagram, △pqr is the image of △pqr under a dilation with cent…
4
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which statement is a valid conclusion based on the argument? if a polyg…
Therefore, the polygon has exactly five congruent angles.
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the water department for a city is deciding on which pipe configuration…
The one 8 - cm pipe can deliver more water to the residents because its cross - sectional area ($64\pi$ $cm^{2}$) is larger than the combined cross - sectional area of two 4 - cm …
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quadrilaterals that have two pairs of opposite equal sides are called p…
The first, fifth, and sixth quadrilaterals.
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choose the quadrilateral.
The orange - colored square
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which is a valid conclusion from these statements? if a quadrilateral i…
If a quadrilateral is a rhombus, then it is a parallelogram and its opposite angles are congruent.
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quadrilaterals that have one pair of parallel sides are called trapezoi…
The first, second and third quadrilaterals from the left in the yellow - colored section (as they have one pair of parallel sides).
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1 quadrilaterals that have one pair of parallel sides are called trapez…
Trapezoids
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12. the diagram shows triangle abc. which of the following statements w…
B. (Slope \(AB\)) times (slope \(BC\)) = - 1
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graph the image of trapezoid defg after a translation 8 units left and …
Graph the trapezoid with vertices \(D'(-4,-10)\), \(E'(0,-10)\), \(F'(-2,-2)\) and \(G'(-10,-2)\)
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the triangle stu is a dilation of the triangle stu. what is the scale f…
\(\frac{1}{2}\)
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the rectangle jklm is a dilation of the rectangle jklm. what is the sca…
\(\frac{1}{5}\)
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the parallelogram efgh is a dilation of the parallelogram efgh. what is…
$\frac{7}{2}$
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8. which of the following is enough to prove a rhombus? a. congruent si…
A. Congruent sides
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what is the value of x? s 2x + 50 t 78 r 5x - 22 78 u x =
24
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what is the value of x? s 78 2x+50 t r 78 5x-22 u
$24$
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what is the value of p? p =
$p = 20$
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if vw = vy = 38, wx = 5s - 90, and xy = 2s, what is wx?
60
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what is ad? ad =
48
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if $overline{ux}congoverline{wx}$, $uv = 2s - 3$, and $vw = s$, what is…
$3$
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10) practice: using visual cues fill in the blanks to explain the midpo…
midpoint \(=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\) where \((x_1,y_1)\) is the first point and \((x_2,y_2)\) is the second point. The \(x\) - coordinate of the mid - point is …
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solve 2x - 3 > 7. the solution is . graph the solution.
$x>5$; For the graph, you would choose the option with an open - circle at 5 and an arrow pointing to the right on the number line.
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what is gi? gi =
56
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if $overline{hk}congoverline{jk}$, $hi = 4w$, and $ij=w + 6$, what is t…
$2$
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3) practice: organizing information and summarizing fill in the blanks …
x; y
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if hi = ij = 60, hk = 2v, and jk = v + 20, what is hk? hk =
40
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if hi = ij = 60, hk = 2v, and jk = v + 20, what is hk?
$40$
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what is df? df =
$6$
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if gj = ij = 42, gh = v + 40, and hi = 6v, what is the value of v?
$8$
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6) practice: organizing information and summarizing. fill in the blanks…
x; y
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what is rs? q 99 r 81 p 81 s
99
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6) practice: organizing information and summarizing fill in the blanks …
\(y\), \(y\)
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what is rs? rs =
80
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9) practice: organizing information and summarizing fill in the blanks …
y; x
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9) practice: organizing information and summarizing. fill in the blanks…
x y
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1) practice: summarizing. fill in the blanks in the definition. the mid…
No blanks to fill as the definition is complete.
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3) practice: organizing information and summarizing fill in the blanks …
x; x; y
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which of the following sets of angles are not considered vertical angle…
# Explicación: ## Paso1: Recordar la definición de ángulos verticales. Los ángulos verticales son aquellos que se forman cuando dos rectas se intersectan y son opuestos por el vér…
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which describes the relationship between ∠1 & ∠5? alternate exterior co…
# Breve explicación: Los ángulos correspondientes son aquellos que se encuentran en la misma posición relativa con respecto a las líneas paralelas y la transversal. En este caso, …
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which of the following sets of angles are not considered alternate inte…
# Explicación: ## Paso 1: Definir ángulos alternos internos y exteriores Los ángulos alternos internos son aquellos que se encuentran entre las dos rectas cortadas por una transve…
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which of the following sets of angles are not considered alternate inte…
# Explicación: ## Paso 1: Definir ángulos alternos internos y exteriores Los ángulos alternos internos son aquellos que se encuentran entre las dos rectas paralelas y en lados opu…
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which of the following sets of angles are not considered vertical angle…
# Explicación: ## Paso 1: Definir ángulos verticales Los ángulos verticales son parejas de ángulos opuestos formados por la intersección de dos rectas. Tienen la misma medida. ## …
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6) practice: organizing information and summarizing. fill in the blanks…
- x - coordinate = x - coordinate of endpoints - y - coordinate = average of y - coordinates of endpoints
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a high - fountain of water is located at the center of a circular pool …
$6.11$ m
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which describes the relationship between ∠4 & ∠7? supplementary congrue…
# Breve explicación: Los ángulos verticales son formados por dos rectas que se cruzan y son opuestos por el vértice. Los ángulos verticales son congruentes. En la imagen, ∠4 y ∠7 …
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which of the following sets of angles are not considered corresponding …
# Explicación: ## Paso 1: Definir ángulos correspondientes Los ángulos correspondientes son aquellos que se encuentran en la misma posición relativa con respecto a las líneas para…
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which describes the relationship between ∠2 & ∠3? congruent and alterna…
# Explicación: ## Paso 1: Identificar ángulos adyacentes Los ángulos ∠2 y ∠3 son adyacentes y forman una línea recta. ## Paso 2: Recordar la definición de ángulos suplementarios D…
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cual es el perímetro, en pies, del polígono? a 105 b 185 c 192
105
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congruent and corresponding congruent and alternate interior congruent …
# Explicación: ## Paso 1: Identificar las propiedades de ángulos Los ángulos verticales son formados por dos rectas que se cruzan y son congruentes. Los ángulos suplementarios sum…
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which describes the relationship between ∠6 & ∠8? congruent and corresp…
# Explicación detallada: ## Paso 1: Identificar la relación entre ángulos Los ángulos verticales son formados por dos rectas que se cruzan y son congruentes. Los ángulos 6 y 8 son…
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if ∠1 = 34 which of the following is false? ∠7 = 146 ∠6 = 34 ∠4 = 34 ∠2…
# Explicación: ## Paso 1: Identificar ángulos correspondientes y opuestos por el vértice Los ángulos opuestos por el vértice son iguales y los ángulos correspondientes son iguales…
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if ∠1 = 34 which of the following is false? ∠2 = 146 ∠4 = 34 ∠6 = 34 ∠7…
# Explicación: ## Paso 1: Identificar ángulos opuestos y adyacentes Los ángulos opuestos por el vértice son iguales. Los ángulos adyacentes son suplementarios (suman 180°). Si $\a…
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congruent and alternate exterior congruent and vertical congruent and c…
# Explicación: ## Paso 1: Identificar relaciones de ángulos Los ángulos alternos externos son aquellos que se encuentran fuera de dos rectas paralelas y en lados opuestos de una t…
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which describes the relationship between ∠5 & ∠6? congruent and vertica…
supplementary
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which of the following sets of angles are not considered supplementary?…
# Explicación: ## Paso 1: Definir ángulos suplementarios Dos ángulos son suplementarios si la suma de sus medidas es 180°. ## Paso 2: Analizar cada par de ángulos - $\angle3$ y $\…
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which describes the relationship between ∠6 & ∠8? supplementary congrue…
# Explicación: ## Paso 1: Identificar el tipo de ángulos Los ángulos ∠6 y ∠8 son ángulos verticales. Los ángulos verticales son congruentes, es decir, tienen la misma medida. # Re…
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which of the following sets of angles are not considered supplementary?…
# Explicación: ## Paso 1: Definir ángulos suplementarios Dos ángulos son suplementarios si la suma de sus medidas es de 180°. ## Paso 2: Analizar cada par de ángulos - $\angle3$ y…
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8) practice: making mental images and summarizing diagonal segments the…
The mid - point of the segment with endpoints $(10,3)$ and $(20,17)$ is $(15,10)$. We can suspect it is a diagonal segment as its slope $\frac{7}{5}$ indicates it is not parallel …
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∠8 = 112 ∠6 = 68 ∠7 = 68 ∠4 = 68 if ∠5 = 112 which of the following is …
No se han proporcionado opciones, pero con los datos dados y las relaciones de ángulos, se pueden verificar cualesquiera afirmaciones que se hagan sobre los valores de los ángulos…
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if ∠5 = 112 which of the following is false? ∠8 = 112 ∠6 = 68 ∠7 = 68 ∠…
Ninguna de las opciones es falsa.
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11 match each number line to its inequality. -5x + 13 ≥ 29 -10x + 5 + 7…
First number line (closed - circle at $x = - 4$, arrow left): $-10x + 5+7x\geq17$ Second number line (closed - circle at $x=-10$, arrow right): $4x + 8+( - 5x)\leq18$ Third number…
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which of the following sets of angles are not considered corresponding …
# Explicación: ## Paso1: Definición de ángulos correspondientes Los ángulos correspondientes se encuentran en la misma posición relativa con respecto a las líneas paralelas y la t…
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solve the inequality. 4 - 2m > 7 - 3m solution: graph the solution.
$m>3$; The graph should have an open - circle at 3 and an arrow pointing to the right.
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the following is the graph of a function f = f(x). at what values of x …
$x = 1.5$ (smaller x - value) $x = 3.5$ (larger x - value)
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dean is exploring the formula for the circumference of a circle. he com…
(a) domain: \( x \geq 0 \) (b) range: \( y \geq 0 \)
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question quadrilateral mnop is similar to quadrilateral qrst. find the …
$57.2$
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11) practice: making mental images find the midpoint of each segment. s…
1. $(-4,3)$ 2. $(1,-3)$
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analyzing statements about tangents and secants. which statement is tru…
\(\overleftrightarrow{SR}\) is a secant of circle \(P\)
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dementia care: benefits of reminiscing. bobbys caregiver walks him to a…
Group reminiscing activity
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reflect the figure over the line y = -x - 1. plot all of the points of …
For each point $(x,y)$ of the original figure, the reflected point is $(-y - 1,-x - 1)$. Plot these reflected points.
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lucy wanted to study how the area of a rectangle changes with the lengt…
(a) range: 0 ≤ y ≤ 10 (b) domain: 0 ≤ x ≤ 5
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solve the inequality and graph the 57 - 16n ≥ 25. plot the endpoints. s…
$n\leq2$; On the number - line, place a closed - circle at 2 and draw a ray to the left.
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solve the inequality and graph the solution. $\frac{f}{4}+72 < 73$. plo…
The solution of the inequality is $f < 4$. On the number - line, we have an open - circle at 4 (since the inequality is strict, $f$ cannot equal 4) and the line extends to the lef…
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the diagram shows a regular polygon. what is the value of x? write your…
\(60\)
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determine a series of transformations that would map figure j onto figu…
A translation 4 units down and 2 units to the right.
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find the distance between the two points. round your answer to the near…
9.4
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solve the inequality and graph the solution on the line provided. $7x +…
Inequality Notation: \( x < 5 \) For the number line: We draw an open circle at 5 (since \( x \) is less than 5, not less than or equal to 5) and shade the region to the left of 5…
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find the distance between point c and point d.
4
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find the missing side length. assume that all intersecting sides meet a…
11 ft
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how many pairs of opposite sides are parallel? no pairs 1 pair 2 pairs
1 pair
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find the equation of the line. use exact numbers. for a negative y - in…
$y = 2x+12$
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find the missing side length. assume that all intersecting sides meet a…
4 cm
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find the measure of the missing angles.
e = 37°, f = 53°
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e is the midpoint of $overline{df}$. if $de = 3x - 4$ and $ef = x + 5$,…
$9\frac{1}{2}$
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what is the coordinate of the midpoint of $overline{ef}$? write your an…
$73$
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if $tu = 3x$, $uv=x + 8$, and $tv = 16$, what is $tu$? simplify your an…
6
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the rule $r_{y = x}circ t_{4,0}(x,y)$ is applied to trapezoid abcd to p…
$(-1,0),(1,1)$
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find the distance between the two points in simplest radical form. (8, …
\( 4\sqrt{5} \)
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solve the inequality. graph the solution. $\frac{x}{2}-5geq - 9$ soluti…
$x\geq - 8$; The graph has a closed - circle at $-8$ and an arrow pointing to the right.
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determine a series of transformations that would map figure s onto figu…
A series of transformations that maps Figure \( S \) onto Figure \( T \) is a horizontal translation (shift) of 9 units to the right. (Note: If there are other possible transforma…
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1) solve and graph the solution of $-\\frac{5}{3}x + 5 < -\\frac{1}{3}x…
$x>\frac{3}{2}$; On the number - line, an open circle at $\frac{3}{2}$ (or 1.5) and a line extending to the right.
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draw the angle in standard position. state the quadrant in which the an…
The angle \(\frac{4\pi}{3}\) lies in the third quadrant. Without seeing the actual details of the graphs (but based on the fact that for a third - quadrant angle, the terminal sid…
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which rule explains why these triangles are congruent? n q p t u s sas …
B. AAS
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what is the sum of the exterior angle measures, one at each vertex, of …
\( 360^\circ \)
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find the missing side length. assume that all intersecting sides meet a…
6 centimeters