幾何
三角形、円、座標幾何、証明問題。
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identify the rotation of the red figure to the blue figure. 180° 90° cl…
90° counterclockwise
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identify the rotation of the red figure to the blue figure. 180° 90° cl…
90° counterclockwise
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what is the measure of each interior angle of a regular 5-sided figure?…
108 (Option: ○ 108)
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which of the following characteristics do the square and rhombus not ha…
1. B. Diagonals are congruent. 2. D. 18
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question 12 1 pts which of the following statements is true? a rectangl…
A square is always a rectangle
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for a quadrilateral to be a square, the diagonals must be _____________…
1. For the square diagonal question: D. Congruent and Perpendicular 2. For $\angle KJL$: $25^\circ$
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what is the measure of the angle of rotation of an octagon?○ 30○ 45○ 90…
1. B. 45 2. B. 0
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the quadrilateral is a trapezoid. what is the value of $x$?○ 4○ 5○ 48○ …
5 (corresponding to the second option)
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what is the sum of the measures of the interior angles of a 20-sided fi…
1. 3240 2. 24
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a cylinder is sliced such that the cross section is perpendicular to it…
1. Rectangle 2. Triangle
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c. if cement costs $0.02/$\text{cm}^3$, what is the cost to fill the pr…
Surface Area: $576$ square inches Volume: $512$ cubic inches
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graph the set ${x mid x > 1}$ on the number line. then, write the set u…
Graph: Open circle at 1, ray extending right to positive infinity. Interval notation: $(1, \infty)$
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9. $x = \\underline{\\quad\\quad}$ 10. $x = \\underline{\\quad\\quad}$ …
9. $x = 75$ 10. $x = 226$ 11. $x = 50$ 12. $x = 77$
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5. which square has a longer side length: a square with an area of 121 …
The square with sides that are 12 units long has a longer side length.
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independent practice 1. q(2, 5), r(-1, 1). which point p makes pqr a ri…
1. A. P(6, 2) 2. B. A(1, 3) 3. A. X(0, 9), D. X(0, 2)
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5. which square has a longer side length: a square with an area of 121 …
The square with sides that are 12 units long has a longer side length.
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a rectangle has an area of $k^2 + 19k + 60$ square inches. if the value…
B. The width of the rectangle is $k + 4$ inches.
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let a equal the measure of angle a. the equation $360^{\\circ}=a + 90^{…
$60^\circ$
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which line has the greatest initial value?a) line ab) line bc) line cd)…
A. line a
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which equation has $h=5$ as the solution? $\boldsymbol{\textcircled{a}}…
A. $51 - h = 46$
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the diagonals of a rhombus are 6 units and 8 units long. what is the ar…
24 square units
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you do: check for understanding what are the coordinates of p if pqr is…
A. P(8, -5)
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geometric mean - leg theorem complete problems 1 - 6. show your work: 1…
4) $x = 50$ 5) $x \approx 48.02$ (or $x = \frac{3025}{63}$) 6) $x = 3\sqrt{15} \approx 11.62$, $y = 3\sqrt{10} \approx 9.49$, $z = 3\sqrt{6} \approx 7.35$
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9. the area of a triangle must be greater than $24\\ in^{2}$ $\frac{1}{…
$h > 6$
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3. $y = -\frac{1}{4}x^2 - 1$$a=$______ $b=$______ $c=$______y-intercept…
$a = -\frac{1}{4}$, $b = 0$, $c = -1$ Y-intercept: $-1$ Vertex: $(0, -1)$ Equation for Axis of Symmetry: $x = 0$ Opens Down Maximum Max Value: $-1$ *(To graph: Plot the vertex $(0…
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examine the triangle. solve $x$ and name which tool you use.
$x \approx 7.9$ miles (rounded to one decimal place). The tool used is the **Law of Sines**.
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5. is △tuv ~ △wxv? explain. 6. higher order thinking are the triangles …
No, $\triangle TUV$ is not similar to $\triangle WXV$, because their corresponding angles are not all congruent. --- ### Problem 6
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3) graph by finding the x-and y-intercepts. $2x - 3y = 6$ x-int: ( , 0 …
Completed table: | x | y | |---|---| | 3 | 0 | | 0 | -2 | x-int: $(3, 0)$ y-int: $(0, -2)$ *(To graph, plot the points (3,0) and (0,-2) and draw a straight line through them.)*
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the figure is rotated counterclockwise. which rotation could have taken…
a 45° rotation
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the figure is rotated $360^{\\circ}$ counterclockwise using the origin …
○ (-2, 2)
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which rotation may have occurred? ○ a 45° rotation clockwise ○ a 45° ro…
a 90° rotation clockwise
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triangle abc is rotated clockwise to create triangle abc. what is the a…
$90^\circ$ (90 degrees clockwise)
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which other rotation can be used to create triangle xyz from triangle x…
B. 270° clockwise C. 270° counterclockwise Wait, correction: The correct equivalent rotation: A 90° clockwise rotation is equivalent to a 270° counterclockwise rotation. Looking a…
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triangle gfh has vertices $g(2, -3)$, $f(4, -1)$, and $h(1, 1)$. the tr…
The correct graph is the lower one, with vertices $G'(3,2)$, $F'(1,4)$, and $H'(-1,1)$.
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name ____________ date ____________1. magnus covers the same shape with…
a. 6 triangles b. 4 rhombuses c. 2 trapezoids; The full shape requires 6 triangles, and since 3 triangles make 1 trapezoid, dividing 6 by 3 gives 2 trapezoids needed.
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what is the measure of $angle x$, in degrees, in the figure shown? $man…
$23$
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5 given: $overline{bc}\\parallel\\overline{ef}$. $d$ is the midpoint of…
The completed two-column proof is: | Statements | Reasons | |------------|---------| | 1. $\overline{BC} \parallel \overline{EF}$ | 1. Given | | 2. $D$ is the midpoint of $\overli…
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8-2: practice & problem-solving day 1 part 1 of 6 write the ratios for …
Exact value: $\frac{\sqrt{3}}{2}$ Four-decimal approximation: $0.8660$
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8-2: practice & problem-solving day 1 part 1 of 6 write the ratios for …
Exact value: $\frac{\sqrt{3}}{2}$ Four-decimal approximation: $0.8661$
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part b if $angle r = 110^circ$, $angle z = 35^circ$ and $angle pst = 40…
No, $\triangle WSR$ is not similar to $\triangle ZSP$. The angles of $\triangle WSR$ are $110^\circ$, $40^\circ$, and $30^\circ$, while the angles of $\triangle ZSP$ are $35^\circ…
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which three-dimensional figure is formed by the rotation given?
A cone (a three-dimensional figure with a circular base and a single curved surface tapering to a point, the apex)
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emma designed two triangular sails for a boat. answer parts a-c belowa.…
a. $36$ $\text{m}^2$ b. $16.47$ $\text{m}^2$
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a cone is sliced such that the cross section is perpendicular to its ba…
Triangle
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emma designed two triangular sails for a boat. answer parts a-c below. …
36
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activity 2 synthesis: what do we know for sure about isosceles triangle…
1. Kiran and Mai used the angle bisector because it splits the isosceles triangle into two congruent triangles, enabling proof via triangle congruence criteria. 2. Yes, they could…
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find the value of variable x. if your answer is not an integer, write i…
$x=5$
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activity 2: what do we know for sure about isosceles triangles? draw __…
1. Draw: $\boldsymbol{\overline{PQ}}$ (where $Q$ is on $\overline{BA}$) 2. Angle $\boldsymbol{\angle PAQ}$ is congruent to angle $\boldsymbol{\angle PBQ}$ because **base angles of…
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find the values of each variable. $a=\\square, b=\\square, c=\\square, …
$a=24$, $b=48$, $c=24$, and $d=24\sqrt{3}$
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in the knitting pattern, $m\\angle1 = 42^\\circ$. find the measure of $…
$m\angle2 = 42^\circ$
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find the value of each variable. $x = \\square$ and $y = \\square$ (sim…
$x = 18$ and $y = 18\sqrt{3}$
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find the value of each variable. if your answer is not an integer, writ…
$y = 18$ and $z = 18$
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11 activity 1 synthesis: proving the side-angle-side triangle congruenc…
1. **Commonality**: All preserve side/angle measures. **Difference**: Order of steps or inclusion of reflection (which changes orientation, while translations/rotations do not). 2…
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which of the following are pythagorean triples? select all that apply. …
(12, 16, 20), (8, 15, 17), (3, 4, 5), (9, 12, 15)
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given $\triangle abc$ with $a^{2}+b^{2}=c^{2}$, write a paragraph proof…
## Paragraph Proof: Construct right triangle $XZY$ where lines $m$ and $n$ are perpendicular at $Z$, $XZ = b$, $YZ = a$, and hypotenuse $XY = z$. By the Pythagorean Theorem, $a^2 …
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find the area of the composite figure, which is a semicircle atop a rec…
Exact value: $224 + 24.5\pi$ square feet Rounded to nearest hundredth: $224 + 24.5\times3.1416 \approx 301.07$ square feet
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8-1: practice & problem-solving day 1 find the value of x. if necessary…
$\sqrt{85}$
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the volume of this cylinder is 14,736.02 cubic meters. what is the radi…
$r \approx 18.99$ meters
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which of the following are pythagorean triples? select all that apply. …
(3,4,5), (6,8,10), (9,12,15), (12,16,20)
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1. (a)-(d), consider the inequality $x + 6 < -19$ a. solve the related …
1. For inequality $x + 6 < -19$: a. Boundary number: $x=-25$ b. Shade region left of $-25$ (test confirms validity) c. Number line: Open circle at $-25$, arrow pointing left d. So…
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7. $delta cde sim delta fge$, find $ce$8. $delta kmz sim delta kdh$, fi…
8. $x=16$ 9. $x=9$ (already solved correctly) 10. $EY=-\frac{15}{4}$ (or $\frac{15}{4}$ for magnitude) 11. Perimeter of $\Delta PQR$ is 55 12. Perimeter of $\Delta TFE$ is 72.5
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because two congruent angles. 2. if $\\triangle abc$ and $\\triangle ed…
$x = 23$ --- ### For Question 3:
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question 40 of 40 which of the following are congruence theorems or pos…
B. SSS D. AAS E. ASA F. SAS
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question 38 of 40 which of the following is the measure of an acute ang…
B. \(78^\circ\)
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question 37 of 40 for every how many degrees will a regular pentagon ha…
A. 72 degrees
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given $m \\parallel n$, find the value of $x$ and $y$. answer $x = \\sq…
$x = 138$, $y = 138$
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find the values of $x$ and $y$. answer $x = \\square$ $y = \\square$
$x = 140$ $y = 40$
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question 35 of 40 rebecca is given two triangles, $\triangle abc$ and $…
C. She can rotate $\triangle DEF$ 180° and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.
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question 32 of 40 which of the following is the correct definition of a…
D. A shape formed by two intersecting rays
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directions: answer the following questions to the best of your ability.…
1. enlarge; shrink 2. smaller 3. larger 4. $J$: $(2, 4)$; $J'$: $(4, 8)$ $K$: $(1, 1)$; $K'$: $(2, 2)$ $L$: $(4, 1)$; $L'$: $(8, 2)$ (Graph: Plot points $(4,8)$, $(2,2)$, $(8,2)$ …
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solve for $x$. round to the nearest tenth, if necessary.
2.9
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question 28 of 40 how many lines of symmetry does a regular dodecagon h…
C. 12
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question 27 of 40 a tree casts a 20-foot shadow. brian is 6 feet tall a…
B. 30 ft
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question 26 of 40 which triangle results from a reflection across the l…
B. <The triangle with vertices at (1,2), (-2,2), (0,4)>
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#1.) what are the coordinates of h? what are the coordinates of h?
$(3, 1)$
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15. $\triangle abc sim \triangle xyz$ find side length x. a) 30 b) 25 c…
15. b) 25 16. d) 7.5 17. a) Yes 18. b) proportional, congruent 19. c) 18 20. d) 18
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question 25 of 40 what is the missing justification in the proof of the…
D. Reflexive Property
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question 24 of 40 a triangle has angles a, b, and c. which of the follo…
A. $m\angle A = 46^\circ, m\angle B=90^\circ, m\angle C = 46^\circ$
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question 23 of 40 what is the equation of a line that is perpendicular …
D. $y=-\frac{1}{4}x+5$
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question 22 of 40 which graph represents the reflection of △abc over th…
B. <Graph with triangle having vertices (1,-1), (4,-1), (3,-3)>
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question 21 of 40 a hexagon forms a semi-regular tessellation with whic…
A. Square and equilateral triangle
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what is the volume of this rectangular pyramid? 16 yd 15 yd 15 yd _____…
1200 cubic yards
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date practice 19 1. for parts (a)-(d), consider the inequality $x + 6 <…
1. a. $x=-25$ 1. b. Shade the region left of $-25$ (tested $x=-30$ works) 1. c. Open circle at $-25$, shade all values to the left on the given number line 1. d. All real numbers …
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quadrilateral efgh is a rhombus and $m\\angle deh = 14t - 79^\\circ$. w…
$t = \frac{68}{7}$ (or approximately $9.71$)
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quadrilateral abcd is a rhombus. what is $m\\angle abd$? $m\\angle abd …
$54$
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what is the volume? 7 m 5 m 10 m cubic meters save answer
175 cubic meters
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i) quadrilateral ghij is a rhombus. what is the value of $w$? $4w+11$ $…
$w = 3$
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quadrilateral vwxy is a square. what is vy? $9v-39$ $6v-18$ $vy = \\squ…
24
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directions: determine if the given equations are parallel, perpendicula…
7. Parallel 8. Perpendicular 9. Perpendicular 10. Neither 11. Parallel 12. Perpendicular
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quadrilateral vwxy is a square. what is $m\\angle uvw$? $m\\angle uvw =…
$45$
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quadrilateral abcd is a rhombus. what is ad? $14z+14$ $6z+30$ $ad = \\s…
$42$
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quadrilateral qrst is a rhombus and $m\\angle rqs = 3y + 32^\\circ$. wh…
$y = -\frac{4}{3}$
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directions: determine if segments $\\overline{ab}$ and $\\overline{cd}$…
1. Perpendicular 2. Parallel 3. Neither 4. Perpendicular 5. Parallel 6. Neither
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quadrilateral stuv is a square. what is $m\\angle rst$? $m\\angle rst =…
$45^\circ$
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quadrilateral qrst is a rhombus. what is $m\\angle rsu$? $m\\angle rsu …
$14.5^\circ$
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quadrilateral ghij is a square. what is the value of c? $c+1$ $2c-89$ $…
$90$
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quadrilateral rstu is a rectangle, $rt = 4w + 20$, and $su = 3w + 61$. …
184
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(i) quadrilateral fghi is a rectangle, $fh = c + 86$, and $gi = 2c$. wh…
$172$
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quadrilateral hijk is a square. what is $m\\angle gkj$? $m\\angle gkj =…
$45^\circ$
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quadrilateral defg is a square. what is the value of t? $t+42$ $3t$ $t …
$21$
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question 20 of 40 which sequence of transformations carries abcd onto e…
D. Reflection across the x-axis followed by reflection across the y-axis