Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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reflect the vector $\\langle -3,5 \ angle$ across the y - axis. $\\lang…
\(\langle3,5 angle\)
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the point given below is on the terminal side of an angle θ in standard…
\(-\frac{3}{4}\)
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rotate the vector $\\langle - 5,3\ angle$ $180^{circ}$ degrees clockwis…
\(\langle5,-3 angle\)
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rotate the given triangle 90° counterclockwise about the origin. 0 - 3 …
\(\begin{bmatrix}-1\\-3\end{bmatrix}\)
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the point given below is on the terminal side of an angle \\( \\theta \…
\(-\frac{3}{5}\)
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dilate the given triangle by a magnitude of 3. \\( \\left \\begin{array…
The matrix after dilation is \(\begin{bmatrix}9&18&9\\- 9&9&9\end{bmatrix}\), so the green box (first - row second - column) is \(18\) and the box below it (second - row second - …
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rotate the vector (0,2) 270° degrees clockwise about the origin.
\(\langle - 2,0 angle\)
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reflect the vector $\\langle 4,13\ angle$ across the line $y = x$.
\(\langle13,4 angle\)
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rotate the vector $\\langle -3,5\ angle$ $270^{circ}$ degrees clockwise…
\(\langle5,3 angle\)
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reflect the vector \\( \\langle 3, - 7 \ angle \\) across the x - axis.…
\(\langle3,7 angle\)
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consider the sets below. a {x|x is a polygon} b {x|x is a triangle} whi…
\(B\subset A\)
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reflect the vector $\\langle -3,5 \ angle$ across the x - axis.
\(\langle-3,-5 angle\)
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write the percent from the circle graph as a decimal and a fraction. re…
\(\frac{71}{500}\)
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the formula for the volume, v, of a pyramid is $v=\frac{1}{3}bh$, where…
C. \(288m^{3}\)
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reflect the given triangle over the line ( y = -x ). \begin{bmatrix} 0 …
\(\begin{bmatrix}0&3&\\0&-7&\end{bmatrix}\)
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reflect the given triangle over the x - axis. \\( \\left \\begin{array}…
The value in the green - box (second column of the new matrix) is \(6\).
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rotate the given triangle 90° counterclockwise about the origin. \\( \\…
\(\begin{bmatrix}0&-1&-2\\0&-3&5\end{bmatrix}\)
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rotate the given triangle 90° counterclockwise about the origin. $\\beg…
\(\begin{bmatrix}-1\\-3\end{bmatrix}\)
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rotate the given triangle 90° counterclockwise about the origin. \\( \\…
The value in the green box (corresponding to the \(x\) - coordinate of the rotated point of \((-3,1)\)) is \(-1\).
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reflect the given triangle over the line y = x. \\( \\left \\begin{arra…
\(\begin{bmatrix}-3&3&3\\3&6&3\end{bmatrix}\)
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reflect the given triangle over the line y = x. \\( \\left \\begin{arra…
The value in the green box is \(3\) and the value in the box below the green box is \(6\). The completed matrix for the reflected triangle (assuming the order of points is maintai…
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rotate the given triangle 90° clockwise about the origin. \\( \\left \\…
\(\begin{bmatrix}0&-3&-4\\0&-7&1\end{bmatrix}\)
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rotate the given triangle 90° clockwise about the origin. \\( \\left \\…
The value in the green - box (corresponding to the \(y\) - coordinate of the rotated point from \((7,-3)\)) is \(-7\) and the value below it (corresponding to the \(x\) - coordina…
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5. what is the side length, s, of the square? a = 81 m²
\(9\space m\)
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find the exact values of the six trigonometric functions of the given a…
\(\tan225^{\circ}=1\)
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21) calcule laire totale de ce solide ? 8 cm épaisseur = 1,5 cm 30 cm
\( 3461,85\ cm^{2} \)
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u is the midpoint of \\( \\overline{tv} \\), \\( \\overline{vx} \\cong …
4. Reason: Definition of mid - point; 5. Reason: SSS (Side - Side - Side) congruence criterion.
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which sets can be represented using the venn diagram below? a = {states…
A = {animals}; B = {mammals}
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consider the following sets. u = {all triangles} e = {x|x ∈ u and x is …
E. Option Text
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△pqs is equilateral, \\( \\overline { p t } \\cong \\overline { q r } \…
The reason for \(PS\cong QS\) is "Definition of equilateral triangle".
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three quadrilaterals exist such that ghijk = aedf and ghijk = vbnm. if …
KJ
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△pqs is equilateral, \\( \\overline { pt } \\cong \\overline { qr } \\)…
\(\triangle QRS\cong\triangle PTS\) by the SAS (Side - Angle - Side) congruence criterion.
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in \\( \\triangle xyz, m \\angle x = 90 ^ { \\circ } \\) and \\( m \\an…
No congruency statement can be made because the side lengths are unknown.
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two rigid transformations are used to map △abc to △qrs. the first is a …
a rotation about point \(C\)
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is there a series of rigid transformations that could map \\( \\triangl…
Yes, \(\triangle QRS\) can be translated so that \(Q\) is mapped to \(A\) and then reflected across the line containing \(\overline{QS}\).
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the triangles are congruent by the sss congruence theorem. which rigid …
translation, then reflection
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quadrilateral abcd is translated down and left to form quadrilateral ol…
Since \(AB = 6\) units and \(AB\) and \(LO\) are corresponding sides (because of translation, which is a rigid transformation), \(LO=6\) units. So the answer is \(6\) units.
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△stv is equilateral. complete the proof that △svw ≅ △tvu. statement 1 △…
By the SAS (Side - Angle - Side) congruence criterion.
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identify each pair of angles as corresponding, alternate interior, alte…
1. Corresponding angles 2. Alternate - exterior angles 3. Alternate - interior angles 4. Consecutive - interior angles 5. Corresponding angles 6. Alternate - interior angles 7. Al…
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in the diagram, \\( \\angle j=\\angle m \\) and \\( j l=m h \\). what a…
\(JK\cong MN\) (the fourth option)
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lesson 1: congruent parts, part 1 * lets figure out what the correspond…
1. All the shapes are rectangles. 2. Whether these rectangles are congruent.
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the proof that ( \triangle qptcong\triangle qrt ) is shown. given: ( sp…
definition of perpendicular bisector
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lesson 1: congruent parts, part 1 • lets figure out what the correspond…
1. All shapes are rectangles and appear to be the same size. 2. Whether these rectangles are congruent (i.e., if all corresponding sides and angles are equal).
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quadrilateral lmno is reflected over the line as shown, resulting in qu…
\(\overline{DC}\)
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5. 14x - 5 6. 8. 9. x =____ (14x - 5) =____x =____ (15x) =____ x = ∠(6x…
5. \(x = 3\), \((14x−5)=37\) 6. \(x = 5.75\), \((15x)=86.25\) 8. \(x = 8\), \((6x−12)=36^{\circ}\) 9. \(y = 23\), \(\angle(3y)=69^{\circ}\)
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monday 11.03.25 question #1 which expression is equivalent to ( 5(3 + 4…
For the first problem (assuming some mis - typing in the original problem, but if we go with the option \(27+23k\) (maybe through wrong expansion steps in a test - taker's mind, b…
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the triangles shown are congruent by the sss congruence theorem. the di…
rotation, then reflection, then translation
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a denotes the area of the sector of a circle of radius r formed by the …
\(12.566\)
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triangle abc is congruent to △abc by the hl theorem. what single rigid …
reflection
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the triangles are congruent by sss or hl. the diagram shows the sequenc…
rotation, then reflection, then translation
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find the volume of a cone with a height of 6 cm and a base diameter of …
\(56.52\space cm^{3}\)
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the triangles are congruent by the sss congruence theorem. which rigid …
rotation, then translation
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1. determine the length of a 65° arc on a circle with a 4.2 - inch radi…
The length of the arc is approximately \(4.8\) inches.
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which explains whether (\triangle fgh) is congruent to (\triangle fjh)?…
They are not congruent because only two pairs of corresponding sides are congruent.
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the triangles are congruent by sss or hl. which transformation(s) can m…
reflection, then translation
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the triangles are congruent by sss and hl. which transformation(s) can …
reflection, then translation
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examine this figure. which two pieces of information, if true, would he…
Line \(MK\) is the perpendicular bisector of \(\overline{LN}\), \(\overline{ML}\cong\overline{MN}\)
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the triangles are congruent by the sss congruence theorem. which rigid …
rotation, then translation
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graph line segment rs with endpoints r(2, -1) and s(6, -5) and its imag…
Plot the original line segment \(RS\) with \(R(2,-1)\) and \(S(6,-5)\), then plot the translated - reflected line segment \(R''(-1,3)\) and \(S''(-5,-1)\)
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use a half - angle identity to find the exact value. cos 105° cos 105° …
$-\frac{\sqrt{2-\sqrt{3}}}{2}$
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the triangles are congruent by sss. which transformation(s) can be used…
reflection only, rotation, then translation
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a regular pentagon is shown what is the length of the apothem, rounded …
\(6.5\mathrm{cm}\)
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the triangles are congruent by sss and hl. which transformation(s) can …
reflection, then translation
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a regular octagon has an apothem measuring 10 in and a perimeter of 68.…
\(332\) in\(^{2}\) (since \(331.5\approx332\) when rounded to the nearest square inch)
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the triangles shown are congruent by the sss congruence theorem. the di…
rotation, then translation, then reflection
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verify the identity $(5\\sin\\theta + 5\\cos\\theta)^2 = 25 + 25\\sin2\…
The first blank: \(25\sin^{2}\theta+50\sin\theta\cos\theta + 25\cos^{2}\theta\) The second blank: \(25 + 50\sin\theta\cos\theta\) For the multiple - choice question: D. Double - A…
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the base of the right triangle drawn in the regular octagon measures 0.…
\(11.2\space cm\) (the first option)
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manuel wants to buy a window shade to cover the window and frame shown.…
\(11.2\ ft^{2}\)
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the triangles are congruent by sss or hl. which transformation(s) can m…
reflection only
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a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.…
\(32.7\space cm^{2}\)
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the area of the regular octagon is approximately 54 cm². what is the le…
3.4 cm
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the triangles are congruent by the sss congruence theorem. which transf…
translation, then reflection
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which value of x would make △suv ≅ △tuw by hl? 2 3 4 5
\(5\)
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the triangles are congruent by the sss congruence theorem. which rigid …
rotation, then translation
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fiona must find the length indicated by the dotted line for the tiles s…
3.75 in.
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a square has an apothem measuring 2.5 cm and a perimeter of 20 cm. what…
\(25\) \(cm^{2}\) (the second option)
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given: ( \triangle bcdcong\triangle efd ), b is the midpoint of ( overl…
A quadrilateral \(ABEF\) has one pair of opposite sides (\(\overline{AB}\) and \(\overline{EF}\)) that are both parallel and congruent. By the definition of a parallelogram (a qua…
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a regular hexagon has a radius of 20 in. what is the approximate area o…
\(1,038\space in^{2}\) (the closest value to the calculated \(1039.2\) among the given options)
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what additional information is needed to prove that the triangles are c…
\(\angle L\cong\angle P\) (the fourth option)
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given: ∠abc and ∠fgh are right angles; (overline{ba}paralleloverline{gf…
AAS congruence theorem.
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use identities to find values of the sine and cosine functions of the f…
\(\frac{5}{9}\)
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problem 23 given: \\( \\triangle b c d \\cong \\triangle e f d \\), b i…
2. \(BC = EF\) 3. Definition of mid - point 4. \(AB = EF\) and \(AB\parallel EF\); If a quadrilateral has one pair of opposite sides that are both equal and parallel, then the qua…
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what additional information could be used to prove that the triangles a…
\(\overline{CB}\cong\overline{QM}\), \(AB = 2.5cm\) and \(MQ = 2.5cm\)
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problem 23 given: ( \triangle bcdcong\triangle efd ), b is the midpoint…
Since \(AB = EF\) and \(AB\parallel EF\), by the definition of a parallelogram (a quadrilateral with one pair of opposite sides both equal and parallel), \(ABEF\) is a parallelogr…
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(d) problem 22: (first taught in lesson 16) two angles are supplementar…
\( 125 \) and \( 55 \)
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1) graph the solution to each compound inequality $x < - 9$ or $x \\geq…
On the number - line, place an open circle at \(-9\) and shade to the left of \(-9\). Place a closed circle at \(-2\) and shade to the right of \(-2\).
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the exterior sides of two adjacent angles make a right angle. the first…
\(34\) and \(56\)
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1. determine the radius of a circle that has a circumference of 15.27 m…
The radius of the circle is approximately \(2.43\) meters.
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(c) problem 20: (first taught in lesson 53) in this parallelogram, find…
\(x = 5\), \(y=\frac{14}{3}\)
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in this parallelogram, find x, y, and z. after you enter your answer pr…
\(x = 82\), \(y = 98\), \(z = 98\)
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bianca calculated the height of the equilateral triangle with side leng…
The apothem, rounded to the nearest tenth, is \(2.9\) units. The perimeter of the equilateral triangle is \(30\) units. Therefore, the area of the equilateral triangle is \(\frac{…
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(b) problem 18: (first taught in lesson 51) find u, x, y, and z. after …
\(u = 70\), \(x = 70\), \(y = 110\), \(z = 70\)
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a hexagon has a radius measuring 23 cm. what is the approximate area of…
1374.4 square cm
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finding missing measures in regular polygons a regular pentagon has a p…
- The measure of angle \( CBD\) is \(36^{\circ}\) - The length of segment \( CD\) is \(6\mathrm{cm}\) - The trigonometric ratio is \(\sin\) - The approximate length of \( BC\) is …
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which postulate or theorem proves that \\( \\triangle cfe \\) and \\( \…
SSS Congruence Postulate
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which postulate or theorem proves that △cfe and △dfe are congruent? hl …
HL Congruence Theorem
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from this given statement, select the definition, property, postulate, …
The SSS (Side - Side - Side) congruence theorem justifies that \(\triangle RST\cong\triangle TUR\)
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which postulate or theorem proves that \\( \\triangle abc \\) and \\( \…
HL Congruence Theorem
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from this given statement, select the definition, property, postulate, …
The theorem that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram justifies that \(RSTU\) is a parallelogram.
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which postulate or theorem proves that these two triangles are congruen…
B. AAS Congruence Theorem