Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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solve each problem. 21. in triangle def, m∠e is three times m∠d, and m∠…
\( m\angle D = 27^\circ \), \( m\angle E = 81^\circ \), \( m\angle F = 72^\circ \) ### Problem 22:
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circumference match each radius or diameter with the circumference of t…
- Diameter = 4 cm → \( C \approx 12.56 \) cm - Radius = 4 cm → \( C \approx 25.12 \) cm - Radius = 8 cm → \( C \approx 50.24 \) cm
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in the figure below, two congruent (identical) circles with centers a a…
\( 30\pi \)
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which of the following statements must be true about this diagram? chec…
The correct statements are \(x + y = w\), \(w>x\), \(w>y\) (corresponding to the options with these expressions). So if we assume the options are labeled as follows (based on the …
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which pairs of figures are congruent? which pairs are similar? (there a…
- Top - Left: Congruent? No; Similar? Yes - Top - Right: Congruent? No; Similar? Yes - Bottom - Left: Congruent? Yes; Similar? Yes - Bottom - Right: Congruent? No; Similar? No
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constructed response a boy climbed a tree that was next to his outdoor …
The boy traveled a distance of 22 feet.
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for the following right triangle, find the side length x.
26
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which of the following are remote interior angles of ∠1? check all that…
$\angle4$, $\angle6$ (and maybe $\angle5$? Wait, no, according to the exterior angle theorem, the two remote interior angles are the two non - adjacent interior angles. So from th…
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what is the greatest number of acute angles that a triangle can contain…
D. 3
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for the following right triangle, find the side length x.
\( \sqrt{161} \) (or approximately \( 12.69 \))
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19. write a two - column proof of corollary 5.1 given: ∠r is a right an…
The two - column proof is as shown above, proving that \(\angle S\) and \(\angle T\) are complementary.
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for the following right triangle, find the side length x.
\( \sqrt{161} \) (or approximately \( 12.69 \))
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what is the value of x? a. 45° b. 57° c. 38° d. 28°
C. \(38^\circ\)
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draw a circle with the given center point that has a circumference of a…
First, find the radius using \( C = 2\pi r \). With \( C\approx43.98 \) and \( \pi\approx3.14 \), \( r = 7 \). Then, identify the center point (from the grid, e.g., (16, 14)) and …
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3. write a rule for the translation of $\\triangle abc$ to $\\triangle …
$(x, y) \to (x + 5, y - 5)$
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what is the value of y? triangle with angles 2y°, y + 10°, and 90° a. 3…
D. \(40^\circ\)
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for the following right triangle, find the side length x.
41
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alicia is running around a circular track. the radius of the track is 2…
The distance she has traveled is 65.9 meters.
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a circle has a diameter of 16 units. what is the circumference? use 3.1…
50.24
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which angles are complementary to each other? select all that apply. ∠3…
\(\angle 3\) and \(\angle 6\), \(\angle 5\) and \(\angle 6\), \(\angle 4\) and \(\angle 3\) (i.e., the options: \(\boldsymbol{\angle 3}\) and \(\boldsymbol{\angle 6}\), \(\boldsym…
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circumference danielle is baking cookies. she uses a circular cookie cu…
\( 9.4 \)
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2. find the component form of the vector that translates a(-4, 8) to a(…
$\langle 11, -17 angle$
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what is the value of n? 121° n° 144° a. 95° b. 59° c. 23° d. 38°
A. 85°
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which angles are adjacent to ∠8? select all that apply. ∠7 ∠12 ∠11 ∠6
$\angle 7$ (and also $\angle 5$ if it were an option, but among the given options, $\angle 7$ is adjacent. Also, maybe $\angle 6$ is a mistake, but based on the definition, $\angl…
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which angles are vertical to ∠6? select all that apply. ∠1 ∠5 ∠2
\( \angle 2 \)
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which angles are adjacent to each other? select all that apply. ∠2 and …
∠2 and ∠3, ∠1 and ∠2, ∠1 and ∠4, ∠3 and ∠4
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which angles are adjacent to each other? select all that apply. (image …
\(\angle2\) and \(\angle1\), \(\angle5\) and \(\angle4\), \(\angle2\) and \(\angle3\), \(\angle2\) and \(\angle4\)
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which angles are complementary to ∠5? select all that apply. ∠6 ∠4 ∠1 ∠3
\(\angle 4\), \(\angle 1\)
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1. the vertices of $\\triangle fgh$ are $f(-2, -6)$, $g(3, 0)$, and $h(…
Original vertices: $F(-2,-6)$, $G(3,0)$, $H(1,-4)$ Image vertices: $F'(-4,1)$, $G'(1,7)$, $H'(-1,3)$ To graph: Plot original points and connect them; plot image points and connect…
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in the figure below, ( l parallel m ). find ( x ).
\( 60 \)
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adjacent to each other? select all that apply. ∠10 and ∠11 ∠13 and ∠14 …
∠10 and ∠11, ∠13 and ∠14, ∠11 and ∠12, ∠15 and ∠16 (all the given pairs are adjacent as they meet the criteria of adjacent angles: common vertex, common side, and non - common sid…
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in the figure below, ( l parallel m ). find ( x ).
\(80\)
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warm-up what percentage of each figure is shaded? be prepared to explai…
Figure A: \(20\%\), Figure B: \(50\%\), Figure C: \(75\%\)
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in the figure below, ( l parallel m ). find ( x ).
\(x = 132\)
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in the figure below, ( l parallel m ). find ( x ).
\(48\)
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in the figure below, ( l parallel m ). find ( x ).
\( \boxed{50} \)
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read the story. bats alive is a bat rescue group that works with fruit …
119
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find the value of x. the quadrilateral has angles 78°, 125°, 70°, and x…
\(87\)
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read the story. the sixth graders at elmtree middle school made spring …
120
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gideon is filling a container with sand. how much sand will fit in the …
418 cubic centimeters
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find the value of x. the figure is a quadrilateral with angles 89°, 99°…
\(120\)
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find the value of x. (there is a quadrilateral with angles 74°, 122°, 1…
\(x = 41\)
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the star - spangled banner was influenced by the events of the bombing …
A. McHenry
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a maintenance crew wants to build a shed at a location that is the same…
A. The point of intersection of the angle bisectors is equidistant from the sides of the triangle, which represent the paths. The shed should be built at this intersection point
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what combination of transformations is shown below? reflection, then ro…
reflection, then rotation
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which angles are vertical to ∠7? select all that apply. ∠3 ∠2 ∠1 ∠10
(Assuming the correct vertical angle to ∠7 is ∠5, but since it's not an option, there might be a mistake. However, if we consider the options, maybe the intended answer is ∠5, but…
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what combination of transformations is shown below? reflection, then ro…
rotation, then translation
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if $\\angle xyz$ and $\\angle zyc$ form a linear pair and the measure o…
C. \(144^\circ\)
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21 which of the following types of statement cannot be used to explain …
C. Guess, D. Conjecture
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graph the inequality 4b > 125. four number lines with options and an i …
The second graph (the one with the open circle and the arrow pointing to the right, among the first three graphs)
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in the diagram below, lines \\( \\overleftrightarrow{ab} \\) and \\( \\…
C. perpendicular
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which of the following are accepted without proof in a logical system? …
B. Postulates, D. Axioms
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for each pair of figures below, choose how they are related. chart with…
1. First Pair: \(\boldsymbol{\text{Reflection}}\) (correct option, not Translation) 2. Second Pair: \(\boldsymbol{\text{Rotation}}\) 3. Third Pair: \(\boldsymbol{\text{Rotation}}\…
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other than itself, which angle is congruent to ∠ech?
\(\angle FCG\)
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the diagram shows two parallel lines and a transversal. if the measure …
C. 40°
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for each pair of figures below, choose how they are related. four rows …
Reflection ### Second Pair (Arrow - Shaped Figures):
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an angle measuring between 90° and 180° is called ______. a. acute b. s…
D. obtuse
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for each pair of figures below, choose how they are related. (images of…
1. First pair: None of these 2. Second pair: Translation 3. Third pair: Rotation 4. Fourth pair: Translation
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graph the inequality $4b > 125$. options are number lines (with some ma…
The third graph (the one with the blue dot and shading to the right, open circle)
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two angles are said to be congruent if: a. they have the same angle mea…
A. they have the same angle measure.
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for each pair of figures below, choose how they are related. (images of…
1. Translation 2. Translation 3. Reflection 4. Rotation
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a precise statement of the qualities of an idea, object, or process is …
C. definition
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line ( t ) is the perpendicular bisector of ( overline{fg} ). if line (…
- Line \( t \) is perpendicular to \( \overline{FG} \) - Point \( H \) is the midpoint of \( \overline{FG} \) - Line \( t \) intersects \( \overline{FG} \) at a right angle
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find the value of x. 121° 65° x° x =
\(x = 56\)
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13 what is the measure of ∠bad ? a. 38° b. 128° c. 52° d. 60° reset next
C. 52°
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find the value of x. x = \\boxed{}
\(x = 123\)
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17.5 the arabic language 12. for muslims, arabic was the language of __…
12. d. Religion 13. b. False 14. c. Rectangular 15. c. Geometric
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<1 and <2 are... complementary angles supplementary angles vertical ang…
adjacent angles
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find the value of x.
\(69\)
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determine a series of transformations that would map figure i onto figu…
A reflection over the \(x\) - axis, a translation \(6\) units up and \(7\) units left.
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what is the measure of $\\angle bvd?$ a. $105^\\circ$ b. $95^\\circ$ c.…
C. 75°
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which shows the graph of $x < \\frac{1}{3}$? \ a) blue arrow from below…
B) The graph with an open circle at \(\frac{1}{3}\) (or the appropriate position on the number line) and the arrow pointing to the left.
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graph the inequality 15v > 65. options include number lines and \i dont…
The third graph (the one with the open circle near 5 and the arrow pointing to the right)
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which pairs of figures below are congruent? (there are four groups of f…
First pair (circles): Yes Second pair (complex shapes): No Third pair (triangles): No Fourth pair (rectangles): No
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17.4 an emphasis on education 10. timbuktu was famous for its community…
10. a. True 11. a. Qur'an
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find the value of x
145
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are the figures below congruent? (four sets of figures with congruent? …
Top - Right: Yes; Top - Left: No; Bottom - Right: No; Bottom - Left: Yes
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graph the inequality $15v > 65$. options include number lines and \i do…
The bottom - most number line (the fourth option) with an open circle at 5 and the line shaded to the right.
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the 30 degree angle + the 150 degree angle form what kind of angle supp…
supplementary angle
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graph the image of \\( \\triangle qrs \\) after a rotation \\( 180^\\ci…
The image of $\triangle QRS$ after 180° counterclockwise rotation around the origin has vertices at $(4,6)$, $(3,3)$, and $(1,7)$. (Plot these points to form the rotated triangle.)
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find the value of x. triangle with angles 38°, 99°, and x° x = blank box
\(43\)
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a harpsichord case has the dimensions shown. a find the area of the top…
a. The area of the top and bottom surfaces is \(35478\space cm^{2}\) b. The area of front - back sides is \(14892\space cm^{2}\) and the area of left - right sides is \(5508\space…
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10 true or false? to begin an indirect proof, you assume the inverse of…
A. True
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if ∠acd and ∠bac are alternate interior angles and ( mangle acd = 101^c…
A. \(79^\circ\)
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angle abc is a right angle. the measure of angle abd is 40°. the measur…
\( 50 \)
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16 trouve lexpression algébrique qui représente le périmètre des polygo…
a) \(38\) mètres b) \(54\) mètres
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which of the following describes an angle with a vertex at y? a. ∠xzy b…
B. \( \angle XYZ \)
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angle abc is a straight angle. the measure of angle dbc is 55°. the mea…
\( x = 125 \)
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question what is the image point of (1, 2) after the transformation $d_…
\((-4,2)\)
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which angles are corresponding angles? check all that apply. image of t…
7 and 3, 1 and 5
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angle fgh is a right angle. the measure of angle jgh is 65°. the measur…
\( 25 \)
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graph the image of \\( \\triangle qrs \\) after a rotation \\( 180^\\ci…
The image of △QRS after rotation has vertices at (4,6), (3,3), and (1,7) (plot these points to form the triangle).
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4. when did muslims from the north, the almoravids, capture kumbi? (cir…
4. (Assuming the correct option is among the choices, but the image's question 4 options are partially unclear; if the intended answer is 1076, then A. 1076) 5. 1,000 (common appr…
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graph the inequality $2u \\geq 140$. \\bigcirc i dont know yet \\bigcir…
The second graph (the one with a closed dot at 70 and the line going to the right)
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what is the image point of (7, 3) after the transformation $r_{y\\text{…
\((-2,4)\)
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solve the inequality. then graph the solution. 1. $\\frac{c}{3} > -13$ …
2. $x > -0.019$ 4. $k \leq 98$ 5. $b < 72$ 6. $r \geq -48$ 7. $s \geq -330$ 8. $i < -102$ 9. $c < -20$ (Graphs for each solution: Open circle at boundary for >/<, closed circle fo…
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the influence of islam on west africa directions: while you read chapte…
1. c. Middle East and North Africa 2. b. Between 639 and 708 3. b. False
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4 a lipstick container has a diameter of 12 millimeters (mm) and a heig…
\(2487\) \(mm^{2}\)
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which statement about parallel lines is true? a. parallel lines have op…
B. Parallel lines have the same slope.
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which part of the angle is the vertex? a. \\(overrightarrow{ab}\\) b. \…
C. Point A