Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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6. in the picture shown below, the measure of angle wzy is 82° and the …
$35^{\circ}$
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5. in the accompanying diagram, $overline{ab}$ and $overline{cd}$ inter…
$37^{\circ}$
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4. in the diagram below, transversal $overline{tu}$ intersects $overlin…
$x = 16$
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3. lines p and q are intersected by line r, as shown below. if m∠1 = 7x…
$x = 24$
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2. lines l and m are parallel and intersect transversal p, as shown in …
\(n = 6\)
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1. two parallel lines, $overline{rq}$ and $overline{xy}$ are intersecte…
$x = 15$
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in the triangle below, $angle i$ is a right - angle. suppose that $mang…
(a) Equation: $7x + 138=180$ (b) $m\angle H = 37^{\circ}$ $m\angle I = 90^{\circ}$ $m\angle J = 53^{\circ}$
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determine the point (x, y) on the unit circle associated with the follo…
$(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$
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rewrite the expression in terms of the given angles reference angle; th…
\(1\)
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determine in which of the four quadrants angle $\theta$ is located give…
Quadrant I
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determine the point (x, y) on the unit circle associated with the follo…
$(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$
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24. xy = 11a, yz = 9a - 2, xz = 5a + 28. textbook pg. 19 #24 - find the…
$a = 2$, $YZ = 16$
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6. in the diagram shown, $overline{qw}$ and $overline{sv}$ intersect at…
(a) $\angle SRT$ and $\angle SRQ$ (b) $\angle SRT$ and $\angle WRV$ (or $\angle SRQ$ and $\angle VRW$) (c) $\angle QRV = 110^{\circ}$, $\angle QRS = 110^{\circ}$
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22. xy = 6b, yz = 8b, xz = 175. find the value of the variable and yz i…
$b = 12.5$, $YZ=100$
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6. in the diagram shown, $overline{qw}$ and $overline{sv}$ intersect at…
$m\angle QRV = 70^{\circ}$, $m\angle QRS=110^{\circ}$
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6. in the diagram shown, $overline{qw}$ and $overline{sv}$ intersect at…
(a) $\angle SRQ$ and $\angle SRT$ (b) $\angle SRQ$ and $\angle WRV$ (c) $m\angle QRV = 70^{\circ}$, $m\angle QRS=110^{\circ}$
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determine the reference angle, in radians, associated with the given an…
$\frac{\pi}{14}$
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2. determine the length of $overline{uv}$. assume that the figure is no…
12
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given that $cos\theta=\frac{sqrt{50}}{10}$ and $\tan\theta$ is negative…
$\theta = 315^{\circ}$, $\tan\theta=-1$
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1. determine the length of $overline{wx}$. assume that the figure is no…
107
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rewrite the expression in terms of the given angles reference angle; th…
$-\frac{1}{2}$
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rewrite the expression in terms of the given angles reference angle; th…
$-\frac{\sqrt{3}}{2}$
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in a linear - angle pair, the measure of the larger angle is 15 degrees…
The smaller angle is 65 degrees and the larger angle is 115 degrees.
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the length of a rectangle is 11 yd less than three times the width, and…
Length: 7 yd Width: 6 yd
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the area of a rectangle is 63 yd², and the length of the rectangle is 5…
Length: 14 yd Width: 4.5 yd
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6. in the diagram shown, qw and sy intersect at point r and kj by dotte…
\(x = 14\)
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the circle below has center v, and its radius is 6 ft. given that m∠wvx…
$7\pi$ ft
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in the circle below, $overline{qs}$ is a diameter. suppose $moverparen{…
(a) \(m\angle QRT = 4^{\circ}\) (b) \(m\angle QSR=57^{\circ}\)
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find a vector equation and parametric equations for the line. (use the …
$\vec{r}(t)=\langle8 - 2t,3t,-4 + 8t angle$ $(x(t),y(t),z(t))=(8 - 2t,3t,-4 + 8t)$
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in the figure below, $overline{jm}$ and $overline{jk}$ are tangent to t…
\(7.5\)
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error analysis. your friend incorrectly says that line m is parallel to…
The measure of angle \(X\) for which line \(m\) is parallel to line \(n\) is \(72^{\circ}\). Your friend's likely mistake was confusing the relationship between the angles and thi…
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suppose s is between r and t. draw and label the diagram then use the s…
a. $y = 3.375$ b. $x = 4$ c. $z = 9$
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find the distance of the two given points: (-1, -3), (8, 6) (-1, 3), (7…
The distances are: $9\sqrt{2},8\sqrt{2},\sqrt{130},\sqrt{58},2\sqrt{53},5\sqrt{10}$ for the respective pairs of points.
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find the distance of the two given points: 1. (-1, -3), (8, 6) 2. (-1, …
1. $9\sqrt{2}$ 2. $8\sqrt{2}$ 3. $\sqrt{130}$ 4. $\sqrt{58}$ 5. $2\sqrt{53}$ 6. $5\sqrt{10}$
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find the measure of ∠1 and ∠2. justify the answer
\(\angle1 = 121^{\circ}\), \(\angle2 = 59^{\circ}\)
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find the values of x and y x = (do not include the degree symbol in you…
139
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1. appearance - the project must be done on a4 paper. it must be drawn …
No specific question is asked in the provided text.
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identify all the numbered angles that are congruent to the given angle.…
1, 3, 5
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2.3 determine the value of m. (give a reason for your answer) statement…
$m = 20^{\circ}$
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question 2 2.1 for each of the following questions, give only the corre…
2.1.1: Supplementary angles on a straight - line. 2.1.2: The sum of angles around a point is 360°. 2.1.3: Co - interior angles between parallel lines are supplementary. 2.1.4: Cor…
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mathematics - project term 3 9. angles opposite each other are the same…
10. Transversal 11. Straight - line 12. Acute angle 13. Intersecting lines 14. Co - interior angles 15. Lines; angles 16. Geometry 17. Parallel lines
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answer the following questions and complete the word search by searchin…
1. Protractor 2. Obtuse angle 3. Alternate - interior angles 4. Supplementary angles 5. Perpendicular 6. Reflex angle 7. Right - angle 8. Corresponding angles
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ellis is painting wooden fenceposts before putting them in his yard. th…
259.05 square feet
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kertas model pra - spm 1 (bab 1 - bab 5) 1 nombor manakah yang dibundar…
D. 1477, 1500
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pyramid a is a square pyramid with a base side length of 12 inches and …
900%
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jude says that the volume of a square pyramid with base edges of 7 in a…
No, he made a mistake in solving for the volume of the square pyramid.
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which of the following could be used to calculate the total volume of g…
$\pi(2\text{ft})^{2}(8\text{ft})+\frac{1}{3}\pi(2\text{ft})^{2}(9.5\text{ft}-8\text{ft})$
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one link in a chain was made from a cylinder that has a radius of 2.5 c…
$345.4$ $cm^2$
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if a rectangle was rotated about the y - axis, like the one shown below…
Cylinder
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a square prism and a cylinder have the same height. the area of the cro…
The volume of the square prism is equal to the volume of the cylinder.
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a triangle has sides that measure 4 units, 6 units, and 7.25 units. wha…
24 units²
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the length of the base edge of a square pyramid is 6 ft, and the height…
C. 240 ft³
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a cylindrical piece of iron pipe is shown below. the wall of the pipe i…
332 cubic inches
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question 15 (multiple choice worth 4 points) (06.04r mc) what is the su…
D. 384 units²
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question 42, 2.1.35 part 4 of 5 plot each point and form the right tria…
The sum of the squares of the lengths of the legs of the triangle is $90$. The square of the length of the hypotenuse of the triangle is $90$. The area of the right - triangle is …
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plot each point and form the right triangle abc. verify that the triang…
\([d(A,B)]^{2}=90\), \([d(A,C)]^{2}=45\), \([d(B,C)]^{2}=45\), and the area of the right - triangle is \(\frac{45}{2}\)
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find all points having an x - coordinate of 4 whose distance from the p…
$(4,7),(4,-9)$
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pablo folds a straw into a triangle with side lengths of $4x^{2}-3$ inc…
A. $12x^{2}-6$; 21 inches
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pablo folds a straw into a triangle with side lengths of 4x² - 3 inches…
A. $12x^{2}-6$; 21 inches
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kat is painting the edge of a triangular stage prop with reflective ora…
C. 76 feet
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are the triangles congruent? if so, write a congruence statement and re…
No, the triangles are not necessarily congruent.
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if you wanted to explain why △abd≅cbd by the sas congruence theorem, wh…
\(\overline{BD}\) is the angle bisector of \(\angle ABC\).
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which of the following pairs of triangles could you use to justify that…
The first pair of triangles (the upper - most pair of triangles in the image) can be used to justify the SAS Congruence Theorem.
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the sas congruence theorem quick check what does the sas congruence the…
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
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which of the following pairs of triangles illustrate the sas criterion …
The first pair of triangles.
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rotate triangle def 90° counterclockwise around the center f. plot poin…
(Please note that without specific grid coordinates for $E$ and $F$, we can't give exact numerical coordinates for $E'$. But the general method to plot it is as described above. I…
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area of triangle = $\frac{1}{2}bh$ what are the actual base and height …
$40$
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a = \\frac{1}{2}bh what are the actual base and height of the trampolin…
$60$
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what number can you multiply each length in the scale drawing by to fin…
160 \(ft^{2}\)
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jazlyn owns an indoor trampoline park. the scale drawing shows a new tr…
3
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chaya has a map that shows the lengths of some hiking trails. the scale…
$0.5$
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graph the inequality below on the number line. x>3
On the number - line, place an open - circle at 3 and draw an arrow to the right of 3.
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a sailboat is 12 km north of a lighthouse. a motor cruiser is 12 km eas…
$12\sqrt{2}$ km
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oscar has a map of the campground where he is staying. the scale shows …
1. $\frac{1}{2}$ 2. 1.5
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the scale drawing shows the dimensions of a motel. the scale is shown i…
10 yards
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a pine tree that is 10 m tall is damaged in a windstorm such that it le…
$5$ m
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a pine tree that is 10 m tall is damaged in a windstorm such that it le…
$\frac{10\sqrt{3}}{3}$ m
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a pine tree that is 10 m tall is damaged in a wind - storm such that it…
$\frac{10\sqrt{3}}{3}$ m
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a pine tree that is 10 m tall is damaged in a wind - storm such that it…
$\frac{10\sqrt{3}}{3}$ m
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a sailboat is 12 km north of a lighthouse. a motor cruiser is 12 km eas…
$12\sqrt{2}$ km
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a pine tree that is 10 m tall is damaged in a windstorm such that it le…
5
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a pine tree that is 10 m tall is damaged in a windstorm such that it le…
5
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question 1 (8 points) saved match the following angles with their exact…
1. $\frac{1}{\sqrt{2}}$ 2. $\frac{1}{2}$ 3. $\frac{\sqrt{3}}{3}$ (not in the given list, but if we consider standard values) 4. $1$ 5. $\frac{\sqrt{3}}{2}$ 6. $\sqrt{3}$ (not in t…
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the angle of elevation from point a on the ground to the top of a water…
$h = 5(1+\sqrt{3})\text{ m}\approx13.66\text{ m}$
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the angle of elevation from point a on the ground to the top of a water…
$5(1+\sqrt{3})\text{ m}\approx13.66\text{ m}$
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2. a sports car is 14 km south of an intersection. a van is 14 km west …
The distance between the two vehicles is $14\sqrt{2}$ km.
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using the paths shown, how long is the shortest route from westford to …
$13.9$
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using the paths shown, how long is the shortest route from brookfield t…
$27.2$
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using the paths shown, how long is the shortest route from lowell to as…
$17.3$
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using the paths shown, how long is the shortest route from danville to …
$20.7$
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using the paths shown, how long is the shortest route from newton to lo…
$19.5$
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using the paths shown, the distance from riverside to oakland is 14.7 k…
7
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using the paths shown, how long is the shortest route from seaside to b…
$23.7$
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using the paths shown, the distance from newton to bluepoint is 24. how…
$5.5$
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using the paths shown, how far is it from lexington to westford? lexing…
23.2
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using the paths shown, how far is it from rockport to dayton? rockport …
24.2
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using the paths shown, how long is the shortest route from livingston t…
$14$
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using the paths shown, how far is it from livingston to centerville? gr…
21.8
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using the paths shown, how far is it from vindale to summerfield? green…
16.5
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using the paths shown, the distance from somerville to lakewood is 15.7…
8.6