Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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homework assignment #7.4 score: 4.92/20 5/20 answered question 16 csc 1…
$\frac{2\sqrt{3}}{3}$
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angle of elevation & depression worksheet (cont.) find all values to th…
\(78.8\) feet
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the endpoints of \\(\\overline{wx}\\) are \\(w(-5,-1)\\) and \\(x(2,6)\…
D. \( 7\sqrt{2} \)
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the endpoints of \\(\\overline{gh}\\) are \\(g(-7,3)\\) and \\(h(1,-2)\…
A. \((-3,\frac{1}{2})\)
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what is the midpoint between points a and b? a is at -4 (with a red dot…
A. \(-0.875\)
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select the correct answer. brian sets up the distance formula to find t…
C. The point he chose to draw the legs of the triangle does not form a right angle.
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statements reasons 1. r ∥ s given 2. $m_r = \\frac{d - b}{c - 0} = \\fr…
A. \(d - 0=b - a\)
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1. brian’s kite is flying above a field at the end of 65 m of string. i…
The kite is flying approximately \(62.3\) m above the ground.
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question 6 fill in the following with the exact value of the trig. rati…
$\sin\theta = -1$, $\cos\theta = 0$, $\tan\theta$ undefined, $\sec\theta$ undefined, $\csc\theta = -1$, $\cot\theta = 0$
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my angle looks like a c b d b and c) list one positive and one negative…
B. The angle graph in option B 510° and -170° 30°
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given the angle 210° in standard position: sketch the angle on your wor…
C
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my angle looks like a c b d b and c) list one positive and one negative…
B and C) 510°, -210° (wait no, correct options from list: 510° and -210° not listed—wait the correct pair is 510° and -110°? No, wait the reference angle is 30°. So final answers:…
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2. given the angle 210° in standard position: a) sketch the angle on yo…
C. The graph with terminal side in the third quadrant
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homework assignment #7.4 score: 3/20 3/20 answered question 4 for each …
$\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$
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homework assignment #7.4 score: 2/20 2/20 answered question 3 find the …
(i) $\frac{\pi}{3}$ (ii) $\frac{\pi}{6}$ (iii) $\frac{\pi}{4}$
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homework assignment #7.4 score: 1/20 1/20 answered question 2 the refer…
61 20 14
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for each angle below, determine the quadrant in which the terminal side…
a. Quadrant III, $\frac{\pi}{3}$ b. Quadrant II, $\frac{\pi}{4}$ c. Quadrant III, $\frac{\pi}{6}$
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solve the triangle. a = 13.0 ft, b = 14.0 ft, c = 26.0 ft what is the m…
\( A\approx15.07^{\circ} \) \( B\approx15.83^{\circ} \) \( C\approx149.10^{\circ} \)
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determine the remaining sides and angles of the triangle abc. a=111.93°…
\(226.0\)
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determine the remaining sides and angles of the triangle abc. a = 115.9…
\(38.15\)
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determine the remaining sides and angles of the triangle abc. the measu…
\(43.1\)
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determine the remaining sides and angles of the triangle abc. a = 58° (…
$c\approx\boxed{11.87}$
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determine the remaining sides and angles of the triangle abc. a = 58° (…
\(b\approx12.82\)
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determine the remaining sides and angles of the triangle abc. a = □° (r…
\(A = 61^\circ\) \(b\approx13.72\) m \(c\approx13.86\) m
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solve the equation in degrees for all exact solutions where appropriate…
D. The solution set is \(\{240^{\circ}+ 720^{\circ}n, 480^{\circ}+ 720^{\circ}n\}\), where \(n\) is any integer\}
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determine the solution set of the following equation, where θ is an ang…
C. \(\{6.4^{\circ}+ 360^{\circ}n,173.6^{\circ}+360^{\circ}n,187.2^{\circ}+360^{\circ}n,352.8^{\circ}+360^{\circ}n,\text{ where }n\text{ is any integer}\}\)
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20 true or false 1 point all pairs of lines are either parallel or perp…
False
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18 true or false 1 point the graph of every ordered pair that has a pos…
True
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lines that do not intersect and have the same slope are answer lines.
parallel
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plot, order, and compare decimals 3. four students volunteered at the a…
- **Part B**: Erin (\(3.05\)), Matt (\(3.249\)), Kayla (\(3.45\)), Thomas (\(3.6\)) - **Part C**: Example: \(3.05<3.249\) (Erin < Matt) - **Part D**: When comparing decimals, we l…
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6) there is a triangle uvw, with a line extending from u to c. the angl…
\(x = 4\)
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in the given geometric figure, triangle edc with angle at e being 70°, …
\(x = 7\)
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solve for x. 5) triangle with vertices e, d, c; angle at e is 70°, segm…
\(x = \frac{7}{3}\)
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write the coordinates of the vertices after a reflection over the line …
\(K'(-1,-1)\), \(N'(-1,6)\), \(L'(-6,-1)\), \(M'(-6,6)\)
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geometry cii triangle sums skills practice solve for x. 1) right triang…
\(x = 6\) ### 2)
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a dilation of \\( \\overline{ab} \\) occurs using a scale factor of \\(…
A' is at (1, 2) and B' is at (3, 3) (the third option, with the blue dot)
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problem solving • make reasonab circle the most reasonable estimate. 1.…
For Lily's cats: 3 (circle 3) For Ann's stickers (assuming typical large collection estimates, e.g., if options were like 10, 50, 100, 100 is more "large" than 10/50, but since th…
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a side of the triangle below has been extended to form an exterior angl…
\(112\)
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a side of the triangle below has been extended to form an exterior angl…
\(x = 36\)
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question in $\\triangle nop$, $\\overline{np}$ is extended through poin…
\(x = 5\)
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in $\\triangle jkl$, $\\overline{jl}$ is extended through point $l$ to …
\(58^{\circ}\)
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question in $\\triangle lmn$, $m\\angle l = (4x - 4)\\degree$, $m\\angl…
\(102^{\circ}\)
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question in $\\triangle bcd$, $\\overline{bd}$ is extended through poin…
\(71^{\circ}\)
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question in $\\triangle jkl$, $m\\angle j = (4x - 1)\\degree$, $m\\angl…
\(x = 17\)
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the measures of the angles of a triangle are shown in the figure below.…
\(70\)
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multiple similarity transformations are performed on a triangle. which …
angle measure
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two similar triangles are shown. δmno was dilated, then _________, to c…
B. reflected
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right triangle abc is reflected over \\(\\overline{ac}\\), then dilated…
△ABC ~ △DEC, ∠B ≅ ∠E, 3DE = 2AB
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read the proof. given: \\(\\overline{ae} \\perp \\overline{ec}; \\overl…
∠ACE ≅ ∠BCD
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δxyz was reflected over a vertical line, then dilated by a scale factor…
△XYZ ~ △X'Y'Z', ∠XZY ≅ ∠Y'Z'X', XZ = 2X'Z'
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which composition of transformations will create a pair of similar, not…
D. a rotation, then a dilation
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two similar triangles are shown. δrst was ____________, then dilated, t…
rotated
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which piece of additional information can be used to prove △cea ~ △cdb?…
A. ∠BDC and ∠AED are right angles
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which transformations could be performed to show that △abc is similar t…
B. a reflection over the x-axis, then a dilation by a scale factor of $\frac{1}{3}$
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in the diagram below, $m\\angle a = 55^{\\circ}$ and $m\\angle e = 35^{…
D. The triangles are similar because all pairs of corresponding angles are congruent.
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given: m∠b = 46°; m∠c = 45°; m∠r = 46°; m∠t = 89° prove: △abc ~ △trs me…
The sum of the measures of the interior angles of a triangle is 180°.
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recognizing necessary information for similarity what additional inform…
∠B ≅ ∠M, △ABC was rotated and dilated by a scale factor between 0 and 1, ∠C ≅ ∠L
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triangle xyz was reflected across m and then dilated to form a similar …
The Right Graph
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given: $overline{fh} perp overline{gh}$; $overline{kj} perp overline{gj…
Step4 reason: All right angles are congruent Step6 statement: $\angle FGH \cong \angle KGJ$ Step7 reason: AA Similarity Postulate
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the composition $d_{o,0.75}(x,y) \\cdot d_{o,2}(x,y)$ is applied to $\\…
∠M ≅ ∠M'', △LMN ~ △L''M''N'', The coordinates of vertex N'' are (3, -1.5)
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triangle abc is similar to triangle abc. which sequence of similar tran…
A. dilation and reflection, B. dilation and translation, C. translation and rotation, D. translation and reflection B. dilation and translation
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parallelogram mnpq was dilated to create parallelogram mnpq. which stat…
A. The length of side MN is 2 units, B. The length of side M'N' is 5 units, D. Sides MQ and M'Q' both have the same slope, 1
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is trapezoid abdc the result of a dilation of trapezoid mnpq by a scale…
No, because AB is $\frac{2}{5}$ the length MN but CD is $\frac{1}{3}$ the length QP.
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triangle mnp is dilated according to the rule $d_{o,1.5} (x,y) \\to (1.…
B. M'(-6, 9) and N'(3, 9)
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triangle mnp will be dilated according to the rule ( d_{p,2}(x,y) ), wh…
B. (-2, 6)
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which graph shows a dilation? three graphs with coordinate grids and re…
The bottom graph (third graph)
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trapezoid abcd was dilated to create trapezoid abcd. which statements a…
A. The length of side AD is 8 units, B. The length of side A'D' is 4 units, E. The scale factor is $\frac{1}{2}$
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triangle stv was dilated with the origin as the center of dilation to f…
B. \( \frac{2}{3} \)
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which composition of similarity transformations maps polygon abcd to po…
a dilation with a scale factor less than 1 and then a reflection
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triangle def was dilated according to the rule $d_{o, \\frac{1}{3}}$ $(…
∠F corresponds to ∠F', The distance from point D' to the origin is $\frac{1}{3}$ the distance of point D to the origin, △DEF ~ △D'E'F'
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triangle qrs is dilated according to the rule $d_{o,2} (x,y)$. what is …
A. $D_{O,2}(x,y)=(2x,2y)$, B. Side $Q'S'$ lies on a line with a slope of -1, E. The distance from $Q'$ to the origin is twice the distance from $Q$ to the origin.
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△rst is dilated with the rule $d_{t,1/3} (x, y)$, where the center of d…
3 6 1/3 the distance (2, 0)
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which composition of similarity transformations would map polygon abdc …
a dilation with a scale factor greater than 1 and then a translation
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quadrilateral qrst is dilated and translated to form similar figure qrs…
$\frac{1}{3}$
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using dilations to make similar figures given △abc, use a dilation with…
D. (6, -3)
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derek tried to dilate the isosceles trapezoid abdc with the center of d…
The slope of AC is undefined. The slope of EG is undefined. The polygons are not dilations of each other because corresponding side lengths are not scaled by the same factor.
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triangle qrs was dilated using the dilation rule ( d_{p,4} ). what is (…
C. 12 units
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line segment xy is dilated to create line segment xy using point t as t…
C. 12 units
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jeremy wants to verify that the transformation shown is a dilation. he …
A. QB = 1/2 QE, C. DE = 2AB, D. AC = 1/2 EF
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triangle tuv was dilated to create triangle tuv using point a as the ce…
B. $\frac{2}{3}$
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line segment ab was dilated to create line segment ab using the dilatio…
C. 13.6 units
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sylvia enlarged a photo to make a 24 x 32 inch poster using the dilatio…
B. 6 × 8
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line segment qr is dilated to create line segment qr using the dilation…
A. 3 units
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the perimeter of δabc is 13 cm. it was dilated to create δabc. what is …
D. 52 cm
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dilation $d_{q,\frac{2}{5}}$ was performed on a rectangle. how does the…
A. The image is a reduction because \(0 < n < 1\), B. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image, D. The center of di…
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triangle abc was dilated using the rule d_{o,a}. triangle abc is the re…
B. 3 units
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identifying the type of rigid transformation pre - image image which ty…
rotation
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properties of dilations a dilation is a nonrigid transformation that ca…
A dilation produces similar figures because it scales all sides by a constant factor (proportional sides) and preserves corresponding angles (congruent angles), which meets the de…
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sissy wants to enlarge a picture of a constellation so that she can put…
D. 486 in.²
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finding the missing distance line segment su is dilated to create su us…
C. 6 units
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triangle abc is dilated to create triangle abc using point o as the cen…
3
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calculating a scale factor triangle abc is dilated to create triangle a…
B. 3
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calculating measures of a dilation triangle bcd was dilated using the r…
95, 6, 11
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rectangle lmnp was dilated using the rule ( d_{p,3} ). which statements…
The length of line segment M'N' is 18 units, The dilation is an enlargement, The scale factor is 3.
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analyzing a scale factor a rectangle is dilated by a scale factor of n …
B. The image will be congruent to the pre-image because n = 1.
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using scale factors to find missing lengths line segment lm is dilated …
6
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a triangle is dilated by a scale factor of $n = \\frac{1}{3}$. which st…
B. It is a reduction because \(0 < n < 1\).
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Question was provided via image upload.
2
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drag the vertices of the triangle below to draw a right triangle with s…
A right triangle with legs of length 8 and 15, and hypotenuse of length 17 (drawn by positioning vertices 8 and 15 units apart perpendicularly and connecting to the third vertex).
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2. sketch the following quadric surface. \\(\\frac{x^2}{4} + \\frac{y^2…
The given quadric surface \(\frac{x^2}{4}+\frac{y^2}{9}+\frac{z^2}{6}=1\) is an ellipsoid with semi - axes \(a = 2\) (along \(x\) - axis), \(b = 3\) (along \(y\) - axis) and \(c=\…