几何
三角形、圆、解析几何与证明题。
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estimates of π example estimate π. circular object d = diameter c = cir…
| Circular Object | Diameter, \(d=\frac{C}{\pi}\) | Circumference, \(C = \pi d\) | pi, \(\frac{C}{d}=\) estimate of \(\pi\) | |---|---|---|---| | tabletop | \(2\) ft | \(6.5\) ft …
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circles example a chord is a line segment connecting two points on the …
1. chord 2. radius 3. tangent 4. chord 5. diameter 6. chord 7. radius 8. chord 9. radius 10. tangent
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the reference angle of - 156° is the reference angle of 323° is the ref…
\(24\), \(37\), \(50\)
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name date period workbook activity chapter 10, lesson 6 area formulas e…
1. \(120\mathrm{cm}^2\) 2. \(42\mathrm{in}^2\) 3. \(294\mathrm{ft}^2\) 4. \(40\mathrm{in}^2\) 5. \(169\mathrm{m}^2\)
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congruence, similarity, and symmetry example the two triangles are simi…
1. \(20\) 2. \(16\) 3. \(12\) 4. \(18\) 5. \(52\) 6. \(64\) 7. \(18\) 8. \(9\) 9. \(8\) 10. \(20\)
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4.5. non - preserving distance transformations 1. select the transforma…
Horizontal translation, Reflections, Clockwise rotations, Dilations, Vertical Translations, Counterclockwise rotations.
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polygons example find the perimeter. find the perimeter of a regular po…
1. \(81\) in. 2. \(40\) ft. 3. \(35\) in. 4. \(68\) cm. 5. \(75\) in. 6. \(36\) ft. 7. \(66\) in. 8. \(73\) cm. 9. \(72\) in. 10. \(91\) ft.
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angle sums of triangles example two angles of a triangle measure 45° an…
1. \(70^{\circ}\) 2. \(85^{\circ}\) 3. \(65^{\circ}\) 4. \(30^{\circ}\) 5. \(20^{\circ}\) 6. \(23^{\circ}\) 7. \(41^{\circ}\) 8. \(63^{\circ}\) 9. \(29^{\circ}\) 10. \(52^{\circ}\)
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4. what is the length of segment df? (lesson 3 - 9) a. 3 units b. \\( \…
C. 36 units
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18. architecture find the amount of glass needed to build the greenhous…
The amount of glass needed is \(1680\) square - feet.
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problem solving the vertices of a trapezoid are ( a(-2,3) ), ( b(2,3) )…
The coordinates of the image are \(A'(-2,3)\), \(B'(6,3)\), \(C'(12,-7)\), and \(D'(-2,-7)\)
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b. what is the length of segment ( bb )? 2. explain how you know that s…
a. The area of triangle \(ABC\) is \(10\). b. The area of triangle \(DEC\) is \(2.5\). c. Yes, the scale factor for the side lengths (if \(k\) is the scale factor of side lengths)…
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critical thinking the blue figure is a transformation of the red figure…
\((x,y)\to(x + 1,y + 2)\)
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towers a lookout tower sits on a network of struts and posts. leslie me…
\(84^{\circ}\)
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splitting triangle sides with dilation (part 2) 1. segment ( ab ) is pa…
a. The length of segment \(AB\) is \(7.5\). b. The length of segment \(B'B\) is \(3.5\).
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find the area of this sector if ( r=\frac{8}{3} ) and ( \theta=\frac{pi…
\(\frac{16\pi}{9}\)
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consider the following inequality. -\\frac{8}{7}>y - \\frac{1}{7} solve…
\( y<-1 \) For graphing: - On a number line, place an open circle at \( y=-1 \) (because the inequality is \( < \), not \( \leq \)). - Shade the part of the number line to the lef…
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laura is sking on a circular ski trail that has a radius 1.4 km long. s…
a. \(1\) radian(s) b. \(\frac{15}{7}\approx2.14\) radian(s)
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inca architecture has many noteworthy features, one of which is the use…
\(11968.0\) square centimeters
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calculate the volume of the sphere. round to the nearest hundredth if n…
\(1439750.5\)
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find the volume. round to the nearest hundredth if necessary, do not in…
36
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find the surface area of the prism. round to the nearest hundredth if n…
78
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consider the following inequality. -3 - 5x > -2 - 6x solve the inequali…
The solution of the inequality is \(x>1\). On the number - line, we have an open circle at \(x = 1\) (because \(x = 1\) is not included in the solution) and the arrow points to th…
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find the lateral area of the cylinder. round to the nearest hundredth i…
1388.58
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polygon abcdefgh will be dilated by a scale factor of 3.4 with the orig…
D. 6.8 units
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write the equation of the line, in standard form, with the given inform…
\(x + y=-6\)
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given triangle a in the coordinate plane, which image shows a dilation …
Assuming we check the size (distance between vertices) and the position (centered at origin), the image that has vertices with coordinates twice of triangle \(A\)'s vertices (afte…
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polygon abcd, shown in the figure, is dilated by a scale factor of 8 wi…
\(\frac{1}{3}\)
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line segment lm is dilated by a scale factor of \\( \\frac { 1 } { 3 } …
D. Line segment \(L'M'\) has a slope of \(6\) and passes through point \(H\)
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consider the following inequality. 8 - 4x ≥ 20 solve the inequality for…
The solution of the inequality \(8 - 4x\geq20\) is \(x\leq - 3\). On the number - line, we have a solid circle at \(x = - 3\) (since the inequality includes equality, i.e., \(\geq…
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critical thinking the coordinate notation shows how the coordinates of …
A horizontal stretch by a factor of \(2\), a horizontal translation \(4\) units to the right, a vertical stretch by a factor of \(2\), and a vertical translation \(3\) units down.
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wnat statement best describes tne error in tne following solution? -13 …
The arrow is pointing in the wrong direction on the graph.
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find the arc length, s, if r = 8 and the measure of the angle, \\( \\th…
\(40\)
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5. respond to each question. (lesson 3 - 10) a. are triangles abc and d…
a. Yes, triangles \(ABC\) and \(DEF\) are similar. Because \(\angle A=\angle D = 60^{\circ}\), \(\angle B=\angle E = 100^{\circ}\), \(\angle C=\angle F=20^{\circ}\), so by AA simi…
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find the radius of this circle if the arc length is \\( \\frac { 10 \\p…
\(5\)
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find the arc length, s, if r = 6 and the measure of the angle, \\( \\th…
\(9\)
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write an inequality describing the range of x for each pair of triangle…
\(x < 20\)
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c) $x>2.5$
We need to change the arrow direction (from left - pointing to right - pointing) and move the open circle from \(0\) to \(2.5\) on the number - line.
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write an inequality describing the range of x for each pair of triangle…
\(x>27\)
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find the measure of θ, in radians, if r = 15 and the arc length is 23. …
\(\frac{23}{15}\)
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standard 14 homework score: 8/30 answered: 6/18 progress saved question…
\(b = 8.4\), \(c = 14.7\), \(B = 35.0\) degrees
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graph the following inequalities on the number lines below. a) ( x geq …
For part a), on the number - line, make the circle at \(0\) solid and change the arrow direction to the right. For part b), on the number - line, keep the circle at \(1\) open (as…
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standard 14 homework score: 6/30 answered: 5/18 question 6 suppose ( c …
\( a = 1.2 \), \( b = 6.9 \), \( B = 80.0 \) degrees
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standard 14 homework score: 5/30 answered: 4/18 question 5 find exact v…
\(x = 10\), \(y = 5\sqrt{3}\)
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standard 14 homework score: 4/30 answered: 3/18 progr question 4 < > su…
\(a = 5\) \(c = 5\sqrt{2}\)
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c) $x>0.5$ change endpoint solidity change arrow direction
The number - line is incorrect for the inequality \(x > 0.5\). The open circle should be at \(0.5\) and the arrow should point to the right.
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graph the following inequalities on the number lines below. a) ( x geq …
a) On the number line, place a solid circle at \(0\) and draw an arrow to the right. b) On the number line, place an open circle at \(1\) and draw an arrow to the left.
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prove that \\( \\triangle t u v \\cong \\triangle t w v \\).
$\triangle TUV\cong\triangle TWV$ by SSS (Side - Side - Side) congruence.
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standard 14 homework score: 2/30 answered: 2/18 progress question 3 sup…
\(\sin(A)=\frac{2\sqrt{29}}{29}\), \(\cos(A)=\frac{5\sqrt{29}}{29}\), \(\tan(A)=\frac{2}{5}\), \(\sec(A)=\frac{\sqrt{29}}{5}\), \(\csc(A)=\frac{\sqrt{29}}{2}\), \(\cot(A)=\frac{5}…
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what is the correct equation? sin 40 = 28/w cos 40 = w/28 sin 40 = w/28…
\(\sin40^{\circ}=\frac{w}{28}\) (the orange - colored option)
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6 \listen, guvnor. just a minute of your time.\ 7 mr. parsons said, \it…
The beggar views Mr. Parsons as someone who can afford to help him (a poor person) and as someone with social circles (to whom he can give the cigarette - lighter as a present).
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sina find sina 32/24 24/40 24/32 32/40
\(\frac{32}{40}\) (the option with \(32/40\))
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the side opposite the right angle in a right triangle. hippopotamus hyp…
Hypotenuse
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the side opposite the right angle in a right triangle. hypotenuse hip h…
Hypotenuse
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which trig function do you use? tangent sine cosine
Sine
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susan is flying a kite, which gets caught in the top of a tree. use the…
\(87\) ft
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a yacht is anchored 90 feet offshore from the base of a lighthouse. the…
45 feet
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4. which of these statements is true? (lesson 3 - 10) a. to know whethe…
C. To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
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find the radius of this circle if the arc length is $\\frac{5\\pi}{2}$ …
\(\frac{5}{3}\)
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from ∠c, what side is ab?
Opposite
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find the measure of the missing angle. 64° 61° 26° 008°
$26^{\circ}$
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which of the following is correct for finding the measure of angle z? ∠…
\(\angle Z=\cos^{-1}\frac{55}{73}\) (the orange - colored option)
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a 16 foot ladder leans against a building. if the angle the ladder make…
$14.8$
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in the figure, line a and line b are parallel. based on the figure, mat…
- angles congruent to \(\angle1\): \(\angle4,\angle8,\angle5\) - angles congruent to \(\angle2\): \(\angle3,\angle6,\angle2\) - angles congruent to \(\angle7\): \(\angle3,\angle7,…
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q. solve for the missing distance.
$18.9$ m
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select the correct answer from each drop - down menu. study this incomp…
The first blank: an angle congruent to \(\angle B\); The second blank: arc \(JK\) and draw an arc centered at \(L\) intersecting the existing arc through \(L\)
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1. r || s 2. ( m_{r}=\frac{d - b}{c - 0}=\frac{d - b}{c} ) ( m_{s}=? ) …
A. \(\frac{0 - a}{c-0}=-\frac{a}{c}\)
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than the length of segment ac. 2. draw an arc which intersects line ab …
A. only Elias
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post test. coordinate geomeiry a. ( b e = b g ) b. ( a e = 2 ( b g ) ) …
D. \(AG = BG\)
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post test. coordinate geometry a. ( a = \frac { 1 } { 2 } ( y _ { 3 } -…
D. \(A=\frac{1}{2}(y_2 - y_1)(x_3 - x_1)\)
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3. in right triangle abc, ac = 4 and bc = 5. a new triangle dec is form…
a. The area of triangle \(ABC\) is \(10\). b. The area of triangle \(DEC\) is \(2.5\). c. Yes, if the scale - factor of side - lengths is \(k\), the scale - factor of the areas is…
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linear pair vertical angles theorem corresponding angles theorem altern…
\(m\angle LFG + m\angle GFK = 180^{\circ}\) → linear pair; \(m\angle KFE = m\angle FEJ\) → Alternate interior angles theorem; \(m\angle HED = m\angle FEJ\) → Vertical angles theor…
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unit 2 day 12 proofs about parallelograms practice name: sean breyer pe…
For the parallelogram \(ABCD\), we have proved \(AO\cong CO\) and \(BO\cong DO\). For the isosceles trapezoid \(ABED\), we have proved \(AD\cong BE\).
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type the correct answer in each box. if necessary, round your answers t…
The perimeter is \(32.44\) units and the area is \(30\) square units.
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6. given: abcd is a rectangle prove: the diagonals are congruent (\\( \…
| Statement | Justification | |--|--| | \(AB = CD\) | Opposite sides of a rectangle are equal | | \(\angle ABC=\angle DCB = 90^{\circ}\) | Definition of a rectangle (all angles ar…
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post test: coordinate geometry what is the length of \\overline{wx}? a.…
E. \(6\sqrt{2}\)
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select the correct answer. based on the construction shown, what is the…
D. Keep the string length and draw an arc centered at point \(B\) that crosses the other arc in two places.
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select the correct answer from each drop - down menu. jamal is finding …
subtracting the \(x\) - coordinates and \(y\) - coordinates
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select the correct answer. the coordinates of point j are (-7,2), and t…
B. \((13,8)\)
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select the correct answer from each drop - down menu. the given diagram…
The diagram shows the construction **for copying angle \(ABC\)**. If \(m\angle ABC\) is \(24^{\circ}\), then \(m\angle FDE\) is \(24^{\circ}\).
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select the correct answer from each drop - down menu. the given diagram…
\(24\)
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type the correct answer in each box. use numerals instead of words. if …
\(y =-\frac{5}{2}x+\frac{31}{2}\)
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5: use a two - column or paragraph proof to prove that the diagonals of…
| Statement | Justification | |--|--| | \(ABCD\) is a rhombus | Given | | \(AB = BC\), \(AM = CM\), \(BM = BM\) | \(AB = BC\) (sides of a rhombus), \(AM = CM\) (diagonals of a par…
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2. explain how you know that segment de is not parallel to segment bc.
Since \(\frac{AD}{DB}=\frac{4}{2} = 2\) and \(\frac{AE}{EC}=\frac{9}{5}=1.8\), and \(2 eq1.8\), by the converse of the basic proportionality theorem (Thales' theorem), segment \(…
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peters proof: by the linear pair theorem, \\( \\angle 1 \\) is suppleme…
Peter used "direct proof" because "evidence is used to support the conclusion". Vivian used "indirect proof" because "the final statement is a contradiction".
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select the correct answer from each drop - down menu. complete the sent…
First blank: distance; Second blank: absolute value of the difference.
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1. segment ab is parallel to segment ab. a. what is the length of segme…
a. The length of segment \(AB\) is \(7.5\). b. The length of segment \(BB'\) is \(7\).
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determine whether a triangle with the given vertices is a scalene, isos…
(a) Scalene triangle (b) Scalene triangle (c) Isosceles triangle
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drag the tiles to the boxes to form correct pairs. not all tiles will b…
\(\overrightarrow{CD}\) matches the blue tile (second from the top in the left - hand column of blue tiles, with an arrow starting at \(C\) and going through \(D\) and extending).…
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select the correct answer from each drop - down menu. given: ( u x = w …
values were not added to each side
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select the correct answer from each drop - down menu. given: ( u x=w z …
The reason in line \(3\) does not justify the statement because \(UX\) and \(WZ\) are substituted. Instead, the reason should be the substitution property of equality.
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select the correct answer from each drop - down menu. given: ( u x=w z …
The reason in line \(3\) does not justify the statement because we are not using the addition property of equality. Instead, the reason should be the substitution property of equa…
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drag each label to the correct location on the flowchart. given: line (…
The first blank (linear pair theorem) is filled with \(\angle2\) is supplementary to \(\angle3\). The second blank (congruent supplements theorem) is filled with \(\angle1\cong\an…
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a clique is a group of __________. a. close friends that do not let oth…
A. close friends that do not let others into their circle easily
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type the correct answer in the box. use numerals instead of words. if n…
\(1:1\)
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determine whether the figures are similar. explain your reasoning.
no
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given: ( mangle mxy = mangle kxy ) what is the conclusion reached by th…
C. \(m\angle JXY = m\angle NXY\)
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select the correct answer from each drop - down menu. point a is the ce…
The ratio of the lengths of \(CI\) (assuming diameter from the circle structure, if we consider the general property) to \(AH\) (assuming radius) is \(2:1\). But if we consider th…
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select the correct answer from each drop - down menu. point a is the ce…
The ratio of the lengths of \(CI\) (diameter) to \(AF\) (radius) is \(2:1\)
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the vertices of a pair of figures are ( a(-8,-2) ), ( b(-4,2) ), ( c(-4…
no