Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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use reference angles to find the exact value of the following expressio…
The reference angle is $30^{\circ}$ and $\sin(-210^{\circ})=\frac{1}{2}$
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refer to the number line. find the coordinate of q on (overline{fl}) su…
\(-\frac{45}{19}\)
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problem 4 constructing the angle bisector got it? draw obtuse ∠xyz. the…
13. ruler 14. protractor 15. compass 16. straightedge
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activity 3: triangle square dance first, we will work in pairs for this…
From 1 to 2: El triángulo se mueve hacia arriba. From 2 to 3: Los dos cuadrados y el triángulo se mueven hacia la derecha. From 3 to 4: Los dos cuadrados se mantienen en su lugar …
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in triangle abc, \\(\\overline{cd}\\) is an altitude and \\(\\overline{…
| Statement | Reason | |--|--| | $\overline{AD}\cong\overline{BD}$ | Given | | $\angle ADC\cong\angle BDC$ | Right - angles are congruent | | $\overline{CD}\cong\overline{CD}$ | R…
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refer to the number line. the ratio of fx to xk is 1:1. which point is …
C) H
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problem 4 constructing the angle bisector got it? draw obtuse ∠xyz. the…
Ray YP is the bisector of obtuse ∠XYZ.
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refer to the number line. the ratio of fx to xk is 1:1. which point is …
B. G
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the vertices of quadrilateral pqrs are listed. p(3,7), q(6,-2), r(0,-4)…
B. Quadrilateral PQRS is a square.
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use your calculator to find the angle, to the nearest hundredth of a de…
$18.43^{\circ}$
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refer to the number line. point x is what fractional distance from e to…
\(\frac{2}{3}\)
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select the correct answer. jenna attempted to construct equilateral tri…
B. When Jenna drew the arc centered at point E, she should have changed the width of the compass to be less than the radius length.
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problem 4 constructing the angle bisector got it? draw obtuse ∠xyz. the…
The two tools used for constructions are compass and straight - edge. 13. measure lines - ruler 14. measure angles - protractor 15. construct arcs - compass 16. construct lines - …
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refer to the number line. which point on $overline{ae}$ is $\frac{2}{3}…
B. Y
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the coordinate plane shows the floor plan for a swimming pool. what is …
C. 80 square meters
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3. following the steps below, what is the next step in constructing a l…
Using the straight - edge, draw a line from K to where the arcs cross.
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which of the following could be trigonometric functions of the same ang…
$\cot Y=\frac{2}{5},\tan Y=\frac{5}{2},\cos Y=\frac{2}{\sqrt{29}}$ (the third - option values are consistent with trigonometric identities)
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refer to the number line. find the coordinate of point y on $overline{a…
The distance from A to C is 4 and the coordinate of point Y is - 4.
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what are sin d and cos d? sin d = 9/41 and cos d = 40/41 sin d = 9/41 a…
$\sin D=\frac{9}{41}$ and $\cos D=\frac{40}{41}$
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what is the equation of the circle? a. (x + 3)^2+(y - 2)^2 = 8 b. (x - …
D. $(x - 3)^2+(y + 2)^2 = 16$
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which statement is true? the side opposite angle a and adjacent to angl…
The side opposite angle A and adjacent to angle C is BC.
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use reference angles to find the exact value of the following expressio…
$-\frac{2\sqrt{3}}{3}$
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in the image, point a marks the center of the circle. which two lengths…
C. EF:AI
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refer to the number line. find the coordinate of point x on $overline{a…
- 2
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3. following the steps below, what is the next step in constructing an …
Without changing the compass's width, repeat from the point B so that the two arcs cross each other, creating the point A.
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use reference angles to find the exact value of the following expressio…
$\frac{\pi}{3}$
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a perpendicular bisector of a segment is a line, segment, or ray that i…
The student likely did not use equal radii for the arcs drawn from \(S\) and \(T\). The correct construction involves using a compass to draw arcs of equal radius from both \(S\) …
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use your calculator to find the angle, to the nearest hundredth of a de…
$19.47^{\circ}$
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4. what is the name of the point where a segment bisector intersects a …
Midpoint
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3. a ____ divides a segment or angle in half. bisector straight line sl…
A. bisector
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which of the following could be trigonometric functions of the same ang…
$\cos Y=\frac{8}{17}$, $\cot Y=\frac{8}{15}$, $\sec Y=\frac{17}{15}$
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2. what geometric construction is in progress in the image? bisecting a…
D. Bisecting a segment
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what are the values of cos y and cot x in the triangle below? cos y = 3…
$\cos Y=\frac{3}{\sqrt{34}},\cot X=\frac{5}{3}$
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1. which construction tool would be the best substitute for a straighte…
A. Ruler
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use reference angles to find the exact value of the following expressio…
The reference angle is $\frac{\pi}{6}$ and $\cos\frac{11\pi}{6}=\frac{\sqrt{3}}{2}$
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the midpoint m of rs has coordinates (1, 16). point r has coordinates (…
$(-10,19)$
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refer to the number line. find the coordinate of point x such that the …
-1
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what is the measure of central angle aob to the nearest tenth of a degr…
$98.2$
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use reference angles to find the exact value of the following expressio…
The reference angle is 45°. The value of $\tan765^{\circ}=1$.
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select the correct answer. the endpoints of wx are w(2,-7) and x(5,-4).…
E. $3\sqrt{2}$
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4. if quadrilateral abcd was rotated 270 degrees counterclockwise about…
(0, - 1)
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gh has a midpoint at m(-13.5, -5). point g is at (-16, -12). find the c…
$(-11,2)$
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3. describe the translation of triangle abc to triangle abc.
Translate 6 units left and 5 units down.
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what is the area of this figure? 3 mi 5 mi 9 mi 6 mi 11 mi 15 mi
$151.5$ square miles
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2. if triangle abc was reflected over the y - axis, what would be the c…
$(3,4)$
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slices were made parallel to and perpendicular to the base of a 3 - dim…
triangular prism
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name the figure below in two different ways. symbol: je and ef answer a…
$\overline{JF}$ and $\overline{FJ}$
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st has a midpoint at m(3, -14.5). point s is at (5, -10). find the coor…
$(1,-19)$
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3. if the carpet in this den is 4 by 6, what is its perimeter?
$20$ feet
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a perpendicular bisector of a segment is a line, segment, or ray that i…
The student's error is that the arcs drawn from \(S\) and \(T\) to construct the perpendicular bisector are of unequal radii. The correct construction involves drawing arcs of equ…
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tu has a mid - point at m(6, 27). point t is at (17, 29). find the coor…
$(-5,25)$
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what is the area of this figure? write your answer using decimals, if n…
71
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1. the pizzas crust has cheese in it. how many inches around is the cru…
50.27 in
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a perpendicular bisector of a segment is a line, segment, or ray that i…
9. The first drawing (where a line EF is perpendicular to segment AB at what appears to be the mid - point of AB). 10. Without seeing the full construction details, if the constru…
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figures pqrs and pnms are congruent. select all of the sequences of tra…
A. A reflection of $PQRS$ across side $SR$ followed by a $90^{\circ}$ counter - clockwise rotation around point $S$. C. A rotation of $PQRS$ by $90^{\circ}$ counter - clockwise ar…
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the midpoint of jk is m(24.5, 55). one endpoint is k(-80, 52). find the…
$(129,58)$
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the mid - point of tu is m(2, 15). one endpoint is t(6, 12). find the c…
$(-2,18)$
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4. which is not a pair of congruent angles in the diagram below? ∠aeb≅∠…
A. $\angle AEB\cong\angle DCB$
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the midpoint m of kl has coordinates (0.5, 11). point l has coordinates…
$(18,16)$
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3. triangle abc is similar to triangle dbe. ac:de is 3:2 and the length…
28
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writing converses write the converse of the statement. 19. if ∠2 measur…
If ∠2 is acute, then ∠2 measures 38°.
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3. triangle abc is similar to triangle dbe. ac : de is 3:2 and the leng…
$13.125$
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select the correct answer. point e is the mid - point of rv. point e is…
A. $(22,-32)$
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2. if rectangle abcd is similar to rectangle mnop, which of the followi…
\(\angle C\cong\angle O\)
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the midpoint m of $overline{uv}$ has coordinates (0.5, -2.5). point v h…
$(19,-5)$
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select the correct answer from each drop - down menu. a quadrilateral h…
rhombus with nonperpendicular adjacent sides
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1. which statement is not true based on the figures below? o ae≅jn o ab…
$CD\cong JK$ is not true.
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name the figure below in two different ways. symbol: and
$\overleftrightarrow{WL}$, $\overleftrightarrow{LT}$
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the midpoint of $overline{uv}$ is $m(5.5, 9.5)$. one endpoint is $u(8, …
$(3,18)$
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cd has a mid - point at m(16.5, 10.5). point c is at (20, 7). find the …
$(13,14)$
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refer to the number line. find the coordinate of point x such that the …
-4
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question name the figure below in two different ways. symbol: and answe…
$\overleftrightarrow{NX}$, $\overleftrightarrow{XN}$
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refer to the number line. find the coordinate of point x such that the …
- 4
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name the figure below in two different ways. answer attempt 1 out of 2 …
$\overrightarrow{EI}$, $\overrightarrow{EO}$
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for questions #10 - 14, refer to the diagram at the right, where ∠abc i…
$x=\frac{192}{29}$
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what is the approximate value of x in the diagram below? (hint: you wil…
C. 31.64
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the midpoint m of $overline{kl}$ has coordinates (-10, -5). point k has…
$L=(-12,-10)$
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question 9 of 10 the ____ of an angle is the ratio of the opposite leg …
C. sine
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9. plot the following points on the coordinate plane below: 1) p(5, 5) …
The points are plotted on the given coordinate - plane according to the above steps.
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question 8 of 10 the _____ of an angle is the ratio of the adjacent leg…
A. cosine
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refer to the number line. find the coordinate of point h that is ⅕ of t…
$-2.2$
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what is sin 60°? a. $\frac{1}{sqrt{2}}$ b. $sqrt{3}$ c. 1 d. $\frac{1}{…
F. $\frac{\sqrt{3}}{2}$
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the midpoint m of jk has coordinates (9, 7.5). point k has coordinates …
$(3,14)$
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which is not a correct description of the graph below? o the graph of y…
The option "the graph of $y=\sin\theta$ shifted to the left by $\frac{\pi}{2}$ units" is not a correct description if it is presented in a wrong - context way (assuming the incorr…
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question 6 of 10 according to this diagram, what is cos 16°? a. $\frac{…
D. $\frac{24}{25}$
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question 5 of 10 according to this diagram, what is sin 23°? a. $\frac{…
B. $\frac{5}{13}$
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writing converses write the converse of the statement. 18. if ∠1 measur…
If ∠1 is obtuse, then ∠1 measures 123°.
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refer to the number line. find the coordinate of point x such that the …
10
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question 4 of 10 the ____ of an angle is the ratio of the opposite leg …
B. tangent
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question 3 of 10 what is sin 45°? a. $\frac{1}{2}$ b. $\frac{1}{sqrt{2}…
B. $\frac{1}{\sqrt{2}}$
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according to this diagram, what is tan 62°? a. $\frac{17}{15}$ b. $\fra…
D. $\frac{15}{8}$
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refer to the number line. find the coordinate of point x such that the …
14
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question 1 of 10 what is tan 30°? 1 60° 2 90° 30° √3 a. 1/√3 b. √3/2 c.…
A. $\frac{1}{\sqrt{3}}$
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refer to the number line. find the coordinate of point d that is 7/16 o…
9
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which is not a correct description of the graph below? y = sin(θ + π), …
The graph of $y = \sin\theta$ shifted to the left by $\pi$ units.
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9. plot the following points on the coordinate plane below. 1) p(5,5) 2…
Points in part 9 are plotted on the first coordinate - plane. 11) $A(3,-2)$ 12) $B(0,-1)$ 13) $C(4,3)$ 14) $D(-2,2)$ 15) $E(3,-1)$ 16) $F(3,0)$ 17) $G(-3,2)$ 18) $H(-1,-2)$ 19) $J…
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question 25 of 25 in the diagram below, $overline{bc}$ is an altitude o…
B. 23
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determine if the graph is symmetric with respect to the x - axis, y - a…
A. No symmetry
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question 24 of 28 based on the information marked in the diagram, △fgh …
A. True
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question 23 of 25 according to the diagram below, which similarity stat…
A. $\triangle PQR\sim\triangle PSQ$ C. $\triangle PQR\sim\triangle QSR$ D. $\triangle PQS\sim\triangle QRS$