Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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pretest: foundations of geometry given: ( mangle 1 = 110^circ ) ( mangl…
1. $m\angle1 = 110^\circ$: $\boldsymbol{\text{given}}$ 2. $m\angle2 = 70^\circ$: $\boldsymbol{\text{given}}$ 3. $\angle1$ is supplementary to $\angle2$: $\boldsymbol{\text{definit…
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jonathan is standing near a fountain (f) that is located at the center …
D. The distance from F to G is equal to the distance from F to B.
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by which angle must \\(\\overline{ab}\\) turn about point \\(a\\) in th…
B. $180^\circ$
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select the correct answer. which example is the best application of geo…
C. designing the layout of the structure
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drag the tiles to the correct boxes to complete the pairs. not all tile…
1. If two figures are congruent, then their corresponding sides are equal. → If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. 2. If t…
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2. what is the scale factor of the dilation from triangle a to triangle…
$\frac{1}{2}$
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drag the tiles to the correct boxes to complete the pairs. match each d…
- circle → the set of all points in a plane that are equidistant from a given point - line segment → a part of a line that begins at one point and ends at another point - angle → …
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which greek mathematician is known as the father of geometry? a. pythag…
C. Euclid
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select the correct answer. which statement is a converse of ( p )? ( p …
A. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade.
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nd the area of the figure. (sides meet at right angles.)
$21$ $\text{cm}^2$
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select the correct answer from each drop - down menu. given: ( cd = ef …
## Statement: $CE = DF$ ## Reason: transitive property of equality
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find the area of the figure. (sides meet at right angles.)
$50$ $\text{m}^2$
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what is the slope of the line that goes through points a and b? whats a…
The slope of the line through A and B is $-\frac{1}{4}$. Another way to write the slope is $\frac{3-1}{-3-5}$ (or any equivalent fraction simplifying to $-\frac{1}{4}$).
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2. what is the scale factor of the dilation from triangle a to triangle…
1. $\frac{1}{2}$ 2. a. Enlargement; b. Reduction 3. a. $\frac{2}{3}$; b. Reduction
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what is the slope of the line that goes through points a and b? subtrac…
$\frac{-1}{4}$
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draw a polygon with 3 angles and 2 equal sides.
An isosceles triangle can be drawn on the dot - grid. For example, by connecting three points such that two of the sides have the same length (e.g., choosing three appropriate poi…
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choose 1 answer: a translation b rotation c reflection d dilation
D. Dilation
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line m goes through points a and b. what is the slope of line m? start …
First, fill the fraction as $\frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}$. The slope of line $m$ is $\frac{3}{5}$.
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what is another way to write the slope of line d? slope = \\(\\frac{\\t…
$-\frac{5}{4}$ (corresponding to the option $-\frac{5}{4}$)
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in her lifeguarding class, summer swam a loop from point a to point b, …
C. 360 meters (go to J)
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4, use the coordinates to write an expression you could use to find the…
$\frac{3 - 8}{6 - 2}$
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start by writing an expression that would represent the slope of line d…
Slope = $\boldsymbol{\frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}} = \frac{-5}{4}}$
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which side of figure jklm corresponds with ab? jk kl lm mj
\(JK\) (the option with \(JK\) as the text, so the first option: \(JK\))
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is parallelogram uvwx a rectangle? yes no
no
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quadrilateral abcd is a square. what is bd? bd = submit
74
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quadrilateral bcde is a rectangle, ab = 12a + 41, and ae = 19a + 27. wh…
$2$
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quadrilateral uvwx is a square. what is ( mangle xwy )?( mangle xwy = s…
$45$
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quadrilateral vwxy is a square. what is vy? x 5w - 86 y 4w - 52 w v vy …
84
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quadrilateral tuvw is a rectangle, sv = 2v + 30, and sw = 20v + 12. wha…
$v = 1$
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is parallelogram fghi a square? yes no
no
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98. the rectangle has a perimeter of 86 yards. which is its area? a 210…
C. 420 sq yd
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quadrilateral fghi is a rectangle, fj = 10w - 5, and ij = 14w - 29. wha…
$w = 6$
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3. quelle expression représente le volume de ce prisme? 4. quelle expre…
Le volume du prisme est représenté par l'expression \( \boldsymbol{10x(2x - 3)(x - 8)} \) (ou sa forme développée \( 20x^{3}-190x^{2}+240x \)).
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quadrilateral stuv is a square. what is ( mangle tsw )?( mangle tsw = s…
$45$
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is parallelogram stuv a square? yes no
no
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q and t are the midpoints of the legs, \\(\\overline{rv}\\) and \\(\\ov…
$y=48$
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quadrilateral ghij is an isosceles trapezoid, gi = 3a + 72, and hj = 4a…
\( a = 15 \)
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complementary and supplementary angles (visual) what is the measure of …
\( 74 \)
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1 multiple choice 1 point find the value of x. round to the nearest deg…
53 (corresponding to the option with 53, e.g., the second option: 53)
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start by writing an expression that would represent the slope of line d…
$\boldsymbol{\frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}}$ (or calculated as $\boldsymbol{\frac{3 - 8}{6 - 2} = -\frac{5}{4}}$)
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10. higher order thinking an art class is planning to paint a rectangul…
10 feet, 12 feet, 15 feet
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similar right triangles 1. identify the similar triangles in the diagra…
1. Similarity statement: $\triangle STU \sim \triangle TVU \sim \triangle STV$. Sketches: - Triangle 1: Right angle at top, vertices labeled $S$, $T$, $U$ (right at $T$) - Triangl…
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write the equation of the line in fully simplified slope - intercept fo…
$y = -x - 6$
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find the equation of a line perpendicular to $y = -4x - 1$ that passes …
$-x + 4y = 16$
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solve. round to the nearest whole number if nee 18. the “welcome home, …
72 square feet
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home work - determine if each graph shows a function and explain how yo…
1. Graph 44: Is a function. It passes the vertical line test (no vertical line intersects the graph more than once). 2. Graph 48: Is NOT a function. It fails the vertical line tes…
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1. nikolas is constructing a skyscraper with walls made of only glass t…
$116735\ \text{square meters}$
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this expression shows point bs y - value minus point as y - value in th…
No, $-\frac{3}{4}$ is not the same as the slope of line $p$. The correct slope is $\frac{3}{4}$, and the error came from inconsistent subtraction order of x and y coordinates.
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parallel/perpendicular line through a point (mc) question find the equa…
$y = x - 11$
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what is the area of this figure? 16 mm 9 mm 5 mm 4 mm 2 mm 2 mm 7 mm 2 …
122 square millimeters
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you just found that the slope is \\(\frac{3}{4}\\). how can you rewrite…
$\boldsymbol{\frac{-3}{-4}}$
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determine the answer to the following. * 11 points \\( \\triangle mdh \…
15.549
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subtract in the numerator and denominator to find the slope of line p. …
$\frac{3}{4}$
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find the geometric mean of each pair of numbers. 1. 12 and 50 2. 24 and…
1. $10\sqrt{6}$ (or ~24.49) 2. $6\sqrt{30}$ (or ~32.86) 3. $\sqrt{105}$ (or ~10.25) 4. $\frac{50}{3}$ (or ~16.67) 5. $4\sqrt{6}$ (or ~9.80) 6. 32
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the measure of $\\angle baw$ can be calculated. $m\\angle baw = \\squar…
\(160\)
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keep going. subtract in the numerator and denominator to find the slope…
$\frac{3}{4}$
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find the common ratio of the geometric sequence -10, 20, -40, ...
$-2$
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are these triangles similar? write a similarity statement. $\\triangle …
yes $\triangle DFE \sim \triangle STU$
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fix any punctuation or capitalization errors below. click \submit answe…
The tourists asked Richard Watterson for directions: "We've been walking in circles for an hour."
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write an expression you could use to find the horizontal distance, or t…
$7 - 3$
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find the common ratio of the geometric sequence 19, 152, 1216, ...
8
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are these triangles similar? f 56° e u 56° t g s yes no
yes
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to find the change in vertical distance, we can find the change in the …
The expression for vertical change is $\boldsymbol{5 - 2}$
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7. one side of the flower garden is 3 times as long as the other. what …
The dimensions of the flower garden are 4 meters and 12 meters.
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12 points\ $\\triangle lbz$ is a right triangle where $m\\angle bzl = 9…
$\boldsymbol{61.928}$
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$\\triangle pqr \\sim \\triangle wvx$. find $wx$.
1.5
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3. quadrilateral abcd was translated 4 units to the left and 2 units up…
B. \((x,y)\to(x - 4,y + 2)\)
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this time, the expression shows point as coordinates minus point bs coo…
First blank: $-3$; Final slope: $\frac{1}{2}$
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△lbz is a right triangle where ( mangle bzl = 90^circ ), ( bz = 24 ), a…
$\boldsymbol{45}$ (matches the unmarked option; note: the pre-selected 56.134 is incorrect. The correct calculation gives 45, which is listed as an option)
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the area of a rectangular rug is given by the trinomial ( r^2 - 4r - 77…
$r - 11$, $r + 7$
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△rst is translated so that point r (-2, 1) is mapped to point r′ (2, -4…
B. $(x, y) \to (x + 4, y - 5)$
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this expression shows point bs coordinates minus point as coordinates i…
$\frac{1}{2}$ (the denominator of the final fraction is 6, and the simplified slope is $\frac{1}{2}$)
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the figure on the right is a scaled copy of the figure on the left. ans…
- The side corresponding to \( OM \) is \( GF \). - The scale factor is \( 3 \).
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this expression shows point b’s coordinates minus point a’s coordinates…
The slope of line $t$ is $\frac{1}{2}$ (the value for the blank in the numerator is $3$)
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rstuv ~ fghij. what are ( mangle s ) and ( mangle f )? ( mangle s = squ…
$m\angle S = 131^\circ$, $m\angle F = 129^\circ$
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what is the slope of line t? you can use the slope triangle to help you…
$\frac{1}{2}$
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rstuv ~ dcbfe. find rv.
10
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uvwxy ~ defbc. what is ( mangle w )? ( mangle w = square^circ )
123°
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stuvw ~ iefgh. find hi.
20
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6. what is the area of a square with a perimeter of 28 feet?
49 square feet
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$\\triangle pqr \\sim \\triangle hji$. what are $m\\angle i$ and $m\\an…
$m\angle I = 89^\circ$, $m\angle P = 55^\circ$
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qrstu ~ bcdea. what are ( mangle c ) and ( mangle u )? ( mangle c = squ…
$m\angle C = 83^\circ$, $m\angle U = 95^\circ$
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10. $-x + y = -2$; $2x - y = 6$
The solution to the system of equations is \( x = 4 \), \( y = 2 \) (the point \((4, 2)\) is the solution as it satisfies both equations).
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stuv ~ wzyx. what is ( mangle v )? ( mangle v = square^circ )
$66^\circ$
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uvwxy ~ efbcd. what is ( mangle b )? ( mangle b = square^circ )
$92^\circ$
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△xpm is a right triangle where ( mangle xpm = 90^circ ), ( xp = 16 ), a…
12
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qrstu ~ cgfed. find qr. qr = \\boxed{}
16
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m∠e = \\square° m∠t = \\square° submit
$m\angle E = 105^\circ$ $m\angle T = 86^\circ$
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toni is testing her new model airplane. she starts its descent at an el…
-200
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10. $-x + y = -2$ $2x - y = 6$
The solution to the system of equations \(\begin{cases}-x + y=-2\\2x - y = 6\end{cases}\) is \(x = 4\), \(y = 2\) or the ordered pair \((4,2)\)
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m∠x = \\square°
$72$
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unfamiliar word excerpt from jane eyre, chapter 5 by charlotte bronte t…
"Ignominious" means causing public shame, humiliation, or disgrace; it describes an action or situation that is demeaning and embarrassing, especially when done in front of others.
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uvwxy ~ tpqrs. what is ( mangle s )?( mangle s = square^circ )
$118$
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$\\triangle xyz \\sim \\triangle jhi$. what is $m\\angle i$? $m\\angle …
$47$
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two sides of $\\triangle abc$ have lengths of 4 inches and 7 inches.\ a…
1. For $\triangle ABC$: a. $3 < x < 11$ inches b. 4, 5, 6, 7, 8, 9, 10 inches 2. For $\triangle XYZ$: a. $4 < y < 24$ cm b. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, …
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ghijk ~ tuvwx. find uv and gk. write your answers as decimals or whole …
UV = 9.3 GK = 4.5
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bcde ~ vstu. what are ( mangle b ), ( mangle s ), and ( mangle t )?
$m\angle B = 129^\circ$ $m\angle S = 51^\circ$ $m\angle T = 129^\circ$
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review the passage. the allusion is shown in bold. the engineer had lis…
It highlights the project's extreme difficulty.
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uvwx ~ adcb. find cd and uv. write your answers as decimals or whole nu…
$CD = 48$ $UV = 1.5$
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select the allusion in the passage. the engineer had listened to the en…
"was a Herculean task"