Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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fall 2025 geometry b wwva solving for side lengths of right triangles t…
$AC = 29.9$, $AB = 30.9$
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which undefined term is used to define an angle? line plane point ray
D. ray
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which pair of undefined terms is used to define the term parallel lines…
plane and line
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reflect the figure over the line y = -5. plot all of the points of the …
# Explanation: ## Step1: Recall reflection rule For a point $(x,y)$ reflected over the horizontal line $y = k$, the $x$-coordinate remains the same and the new $y$-coordinate is g…
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which pair of undefined terms is used to define a ray? line and plane p…
D. point and line
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solving for side lengths of right triangles using trigonometric ratios …
\(XY=\frac{22}{\cos(41^{\circ})}\)
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which defines a circle? two rays with a common endpoint a piece of a li…
all coplanar points equidistant from a given point
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which lines below appear to be parallel?
B. The two horizontal lines in option B
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given a triangle with the vertices a(1, 3), b(4, 8), and c(5, 2). deter…
a. $A'(1,-3)$, $B'(4,-8)$, $C'(5,-2)$ b. $A'(-1,3)$, $B'(-4,8)$, $C'(-5,2)$
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find the cylinder.
C. Cylinder
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geometry here is a figure that looks like the letter a, along with seve…
Figure 1, Figure 2, and Figure 4 are scaled copies of the original A because their corresponding side - lengths are in proportion and they have the same shape as the original figu…
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parallelogram defg with coordinates d(0, 2), e(1, 5), f(6, 5), and g(5,…
D: (-7, 2) E': (-6, 5) F': (-1, 5) G': (-2, 2)
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write the coordinates of the vertices after a translation 3 units right…
B. (5, - 6), C. (5,-16), D. (11,-6)
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exercise 16 quiz circle the correct answer. 1. two weeks ago, i — a new…
1. a) bought 2. a) stopped 3. b) last 4. b) took 5. a) was 6. a) decided 7. a) ago 8. b) caught 9. a) Did you finish 10. b) were 11. a) tried 12. a) didn't go
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translations determine the coordinates of the image following each give…
$A'(6,4)$ $B'(7,6)$ $C'(9,1)$
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3. consider the ratios 3:5 and 21:d. what must c and d be for the ratio…
3. $D = 35$ 4a. 22 4b. Made: 18, Missed: 15
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9) graph the image of the figure using the transformation function: (x,…
The figure is reflected over the y - axis.
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solve the inequality - 2(w + 6)+8 < - 16. graph the solution. choose th…
The solution of the inequality is $w > 6$. The graph has an open circle at 6 and an arrow pointing to the right.
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6. a ball travels following the bold line from the top left corner, and…
9
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the diagram below shows a nearly completed construction of the perpendi…
Draw the line passing through points C and D.
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7) function: (x,y)→(−x,y) a (-5,-3), c (-3,2), t (1,-2)
$A'(5,-3),C'(3,2),T'(-1,-2)$
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rotations triangle hop has coordinates h(2,1), o(-3,4), and p(5,7). det…
a. 90 - degree clockwise: $H'(1,-2)$ $O'(4,3)$ $P'(7,-5)$ 90 - degree counter - clockwise: $H'(-1,2)$ $O'(-4,-3)$ $P'(-7,5)$ 180 - degree: $H'(-2,-1)$ $O'(3,-4)$ $P'(-5,-7)$
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2 matching 2 points match the coordinates of the original point (x,y) w…
Rotation about the origin 90 degrees counterclockwise: $(-y,x)$ Rotation about the origin 90 degrees clockwise: $(y, - x)$ Rotation about the origin 180 degrees: $(-x,-y)$
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in the figure below, (mangle abd = 66^{circ}), and (mangle2) is two tim…
$22$
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a triangle has side lengths of (q + r) centimeters, (5q - 10s) centimet…
C. $6q - 6r - 5s$
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22. draw all of the lines of symmetry in the figure shown below.
Draw a vertical line passing through the mid - points of the longer sides and a horizontal line passing through the mid - points of the shorter sides of the rectangle.
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a triangle has side lengths of (5h - 4k) centimeters, (10h + 7m) centim…
$15h - 6k + 12m$
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transformations make a conjecture about which figures are congruent to …
Figure C is congruent to Figure A. Figure A can be translated onto Figure C.
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3. (a) to modify something is to (b) set it free. (c) to extricate some…
3. d. make changes to it 4. d. a collection of writings 5. c. is one made without previous thought 6. d. make changes to it 7. b. A pivotal event is one that is of great importanc…
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the width of a rectangle measures (9x - 2) centimeters, and its length …
$8 + 26x$
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a triangle has side lengths of (7m - 2) centimeters, (9m - 5) centimete…
D. $16m + 6n - 8$
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for #1 - 4, find the perimeter of the polygon with the given vertices. …
22
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reflection + independent cer 1. what makes a strong cer different from …
1. Clear claim, relevant evidence, logical reasoning. 2. Validates claim from different angles. 3. Varies per individual. 4. Practice linking evidence - claim.
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7) function: (x,y)→(1.5x, 1.5y) verbal description: ______________
A dilation with a scale factor of 1.5.
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draw all of the lines of symmetry in the figure shown below.
Draw a vertical line through the mid - points of the longer sides and a horizontal line through the mid - points of the shorter sides of the rectangle.
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2. draw all of the lines of symmetry in the figure shown below.
Draw a vertical line passing through the mid - points of the longer sides and a horizontal line passing through the mid - points of the shorter sides of the rectangle.
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left and right, up and down lets explore how you know whether a transla…
1. a. $(x + c,y)$ b. If $c>0$, move right; if $c < 0$, move left. 2. a. $(x,y + d)$ b. If $d>0$, move up; if $d < 0$, move down. 3. Yes, the point remains on a straight - line. Th…
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if ef = x + 8, fg = 19, and eg = 10x - 18, what is ef? simplify your an…
13
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if st = 16, tu = x + 14, and su = 2x + 17, what is su? simplify your an…
43
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practice: using midpoint formula assessment a listen 4. complete the fo…
The line passing through point \(M\) is the segment bisector of \(\overline{RS}\).
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in exercises 7 and 8, identify the segment bisector of (overline{jk}). …
$JM = 40$
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1. name the angle in the scaled copy that corresponds to angle abc. 2. …
1. Angle PQR 2. Segment PS 3. Cannot be determined without side - lengths (ratio of corresponding side - lengths)
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△cde is a translation of △cde. write the translation rule. (x,y)↦(x+□,y…
$(x,y)\to(x - 10,y - 8)$
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in exercises 27 - 30, the mid - point m and one endpoint of $overline{g…
27. \((3,12)\) 28. \((-1,3)\) 29. \((12,-9)\) 30. \((-9,-13)\)
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in exercises 23 - 26, the endpoints of $overline{cd}$ are given. find t…
23. $M(5,2)$ 24. $M(-2,2)$ 25. $M(1,4.5)$ 26. $M(-6,2)$
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if (jk = 10x), (kl=5x + 14), and (jl = 20x-6), what is (jk)? simplify y…
40
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if (jk = 7x), (kl=x + 1), and (jl = 9), what is (jk)? simplify your ans…
7
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if (kl = 14) and (lm = 9), what is (km)? write your answer as a decimal…
23
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if ef = 9 and fg = 20, what is eg? write your answer as a decimal or in…
29
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reflect the figure over the line y = 2. plot all of the points of the r…
To plot the reflected figure, find the new $y$ - coordinates of all vertices of the original figure using the rule $(x,y)\to(x,4 - y)$ and then plot these new points. The $x$ - co…
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if rs = 4 and rt = 14, what is st? write your answer as a decimal or in…
10
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in exercises 9 and 10, identify the segment bisector of $overline{xy}$.…
The segment bisector of $\overline{XY}$ is $\overrightarrow{MN}$, and $XY = 32$.
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reflect the figure over the line y = 2. plot all of the points of the r…
Plot the points $(3,0)$, $(4,-5)$, $(6,-2)$, $(4,0)$ to form the reflected figure.
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△wxy is a translation of △wxy. write the translation rule. (x,y)→(x+□,y…
$(x,y)\to(x - 9,y - 6)$
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△ijk is a translation of △ijk. write the translation rule. (x,y)→(x - □…
\((x,y)\to(x - 10,y + 8)\)
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graph the point (-7, -8) on the coordinate plane.
Plot the point 7 units left and 8 units down from the origin.
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you move left 2 units and up 1 unit. you end at (-2, 5). where did you …
(0, 4)
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you move right 3 units and down 3 units. you end at (4, 0). where did y…
(1, 3)
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you start at (-5, 1). you move right 8 units. where do you end?
$(3,1)$
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you start at (4, -2). you move right 1 unit. where do you end?
$(5, - 2)$
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you move right 6 units and up 2 units. you end at (5, 3). where did you…
$(-1,1)$
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you start at (3, -1). you move left 4 units and down 1 unit. where do y…
$(-1,-2)$
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5) function: (x,y)→(1/2 x, 1/2 y) verbal description: ________
The function represents a reduction with a scale factor of $\frac{1}{2}$.
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you move up 1 unit and right 1 unit. you end at (-1, 5). where did you …
(-2, 4)
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football 2 continued. the wide receiver is a little over 25 yards down …
25 yards
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you start at (4, -4). you move right 1 unit and left 9 units. where do …
$(-4,-4)$
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solve for x. (3x + 17)° (4x + 2)°
23
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you start at (1, -1). you move down 3 units and right 1 unit. where do …
(2, - 4)
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solve for x. t (4x + 7)° a (5x - 13)° s m h
20
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you move down 1 unit and left 4 units. you end at (-5, -1). where did y…
$(-1,0)$
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you start at (-5, 0). you move up 5 units and right 2 units. where do y…
$(-3,5)$
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you move up 2 units and down 9 units. you end at (3, -5). where did you…
$(3,2)$
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you start at (4, 0). you move up 5 units and left 2 units. where do you…
$(2,5)$
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find the width of the tv. the number you enter in for w will measure th…
32
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you start at (0, -3). you move right 2 units and left 3 units. where do…
$(-1,-3)$
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you move right 3 units and left 2 units. you end at (-4, -1). where did…
(-5, -1)
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you start at (5, 3). you move left 5 units and up 2 units. where do you…
$(0,5)$
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the midpoint of $overline{jk}$ is $m(6,3)$. one endpoint is $j(14,9)$. …
$(-2,-3)$
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1 - 85. calculate the area of the shaded region at right. use the appro…
68 square - inches
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you start at (-3, -2). you move right 5 units and up 3 units. where do …
$(2,1)$
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you move right 7 units and left 1 unit. you end at (4, -4). where did y…
$(-2,-4)$
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you start at (4, 1). you move up 2 units and down 3 units. where do you…
$(4,0)$
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you start at (1, 3). you move right 4 units and down 7 units. where do …
$(5,-4)$
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you start at (4, -3). you move right 1 unit. where do you end?
(5, - 3)
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3. trapezoid abcd find side lengths first! ab = 3 ad = 5 dc = 6 bc=\\sq…
$22.5$
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you start at (5, -2). you move up 4 units and down 2 units. where do yo…
(5, 0)
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you start at (-1, -1). you move up 4 units. where do you end?
$(-1,3)$
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you start at (-2, 4). you move right 6 units. where do you end?
(4, 4)
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3. trapezoid abcd find side lengths first! ab = 3 ad = 5 dc = 6 bc=\\sq…
$19.8$
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true or false: all squares are similar to one another, as are all circl…
A. True
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true or false: similar and congruent mean the same thing. choose one op…
B. False
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describe the difference between the following problems. how much fencin…
C. To find how much fencing is needed, find the perimeter of the garden, measured in linear units. To find how much fertilizer is needed, find the area of the garden, measured in …
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quiz question 2 of 5 two figures are similar if they are ________. choo…
C. the same shape but not the same size
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which measurements of two similar triangles are the same? choose one op…
A. The angles
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24. carlos bought a cube - shaped aquarium. write an expression to repr…
$27s^3$
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what is the main idea of \the man who made the myth\? people are fascin…
C. The Bermuda Triangle is a popular myth because it was spread by stories that fascinated readers.
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reflection is another kind of rigid transformation in which a figure is…
A. acts as the line of symmetry between the figure and its reflection
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procedures and problem s using slope in exercises 7 and has the indicat…
(a) $L_2$, (b) $L_3$, (c) $L_1$
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how would you rotate triangle jkf so that it maps onto triangle hcz? a …
D. (0, 0), 180°
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which of the following is true about translations? a they are a useful …
C. They can help you see if two figures are congruent.