Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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the graph shows quadrilaterals abcd and abcd. which sequences of transf…
A reflection across the y - axis followed by a rotation 180° around the origin.
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write the term that best completes each statement. 1. the interior angl…
1. Triangle angle - sum property 2. Exterior angle theorem 3. Exterior angle
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unit 1 lesson 1 cumulative practice problems 1. here is a diagram of a …
1. The length of segment \(BD\) is the same as the length of segment \(AB\) because \(AB\) and \(BD\) are radii of the same circle (the circle centered at \(B\)), and all radii of…
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find the distance between the points (10, 0) and (2, 6). write your ans…
10
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3. list the side lengths from shortest to longest for each diagram. a. …
a. $k,m,l$ b. $w,y,x$
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this triangle is a scaled copy. it was scaled by a factor of 1/2. suppo…
Base: 40 cm Height: 20 cm
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find the distance between the points (8, 9) and (5, 5). write your answ…
5
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2. describe a sequence of transformations that takes trapezoid a to tra…
First, rotate Trapezoid A counter - clockwise about a center (e.g., centroid) by an appropriate angle. Then, translate the rotated trapezoid horizontally and vertically to match T…
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find the distance between the points (6, 6) and (2, 9). write your answ…
5
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select the correct image. a bowl is used to serve punch for a party. wh…
The hemisphere (the fourth figure)
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7 calculate the altitude ah in the triangle below. given the endpoints …
$\frac{9\sqrt{26}}{13}$
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the mid - point of $overline{ab}$ is $m=(-2,-1)$. one endpoint is $a = …
$(3,-3)$
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2. determine the measure of the unknown angle in each triangle. a) b.
a. The measure of $\angle B$ is $65^{\circ}$. b. The measure of $\angle R$ is $34^{\circ}$.
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this parallelogram is a scaled copy. it was scaled by a factor of 1/2. …
Base: 20 cm Height: 12 cm
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vw has endpoints at v(15, 11) and w(8, 19). find the midpoint m of vw. …
$(11.5,15)$
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v(4, 6) and w(0, 10) are the endpoints of a line segment. what is the m…
$(2,8)$
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an architect designed an attic space in the shape of a square - pyramid…
A. $V=\frac{1}{3}s^{2}a$
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a line segment has the endpoints t(6, -8) and u(-6, 0). find the coordi…
$(0,-4)$
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4. determine the value of x in each diagram. a. b. c. d.
a. $x = 24$ b. $x = 146$ c. $x = 30$ d. $x = 14$
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2. clare used a compass to make a circle with radius the same length as…
B. \(AB = CD\)
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select all the correct names there are six counties listed in the table…
Greene, Clark, Wade
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r(5, 6) and c(1, 10) are the endpoints of a line - segment. what is the…
$(3,8)$
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q(3, 9) and r(5, 9) are the endpoints of a line segment. what is the mi…
$(4,9)$
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f is the image of the point f after a reflection. f(5, -10)→f(-5, -10) …
y - axis
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what are the coordinates of g, h, and i after a rotation about (0,0) by…
The coordinates of $G'$ are $(1, - 3)$, the coordinates of $H'$ are $(4,0)$ and the coordinates of $I'$ are $(3,2)$.
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find the scale factor that takes the original triangle to the scaled co…
$\frac{1}{2}$
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cd has endpoints at c(-4, 0) and d(0, 4). find the midpoint m of cd. wr…
$(-2,2)$
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directions: find the missing endpoint if s is the midpoint $overline{rt…
$T(13,-6)$ ### 11.
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biconditional statements rewrite the biconditional statement as a condi…
Conditional statement: If a point is a mid - point of a segment, then it divides the segment into two congruent segments. Converse statement: If a point divides a segment into two…
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r(-4, 6) and s(-8, -6) are the endpoints of a line segment. what is the…
$(-6,0)$
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r(-4, 6) and s(-8, -6) are the endpoints of a line segment. what is the…
$(-6,0)$
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b is the image of the point b after a reflection. b(-7, -1) → b(7, -1) …
y - axis
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the graph shows parallelogram lm nop and lmnop. which sequences of tran…
D. a rotation 90° clockwise around the origin followed by a translation right 1 unit and down 7 units
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side length in original rectangle,corresponding side length in scaled c…
$2$
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maps leila is walking from the park at point p to a restaurant at point…
The point at which Leila should stop for her break is $(6.25,3.375)$
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find the perimeter of the rectangle. the perimeter is (simplify your an…
$4x^{2}+6x + 18$
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1. a. here are some points: what are the coordinates of a, b, and c aft…
The coordinates of \(A'\) are \((9,-5)\), the coordinates of \(B'\) are \((7,-1)\) and the coordinates of \(C'\) are \((4,0)\)
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in the triangles, tr = ge and sr = fe. if (overline{gf}=3.2) ft, which …
D. 4.0 ft
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task #1 - primary trigonometric ratios 1. determine the sin θ, cos θ an…
$\sin\theta=\frac{4\sqrt{65}}{65}$, $\cos\theta=\frac{7\sqrt{65}}{65}$, $\tan\theta = \frac{4}{7}$, $\theta\approx29.74^{\circ}$
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triangle abc has the angle measures shown. m∠a=(2x)°, m∠b=(3x)°, m∠c=(4…
\(m\angle B = 60^{\circ}\)
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7. if the rectangle has an area equal to the number of the week, what c…
2 feet
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9. figure abcd has vertices a(-2, -2), b(1, 1), c(0, 4), and d(-3, 5). …
$A''(1,-6)$ $B''(4,-3)$ $C''(3,0)$ $D''(0,1)$
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14. which figures represent a pair of similar figures? a. a and b b. a …
B. A and C
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draw the following triangle after a translation 4 units to the left and…
Plot the triangle with vertices obtained by applying the translation $(x,y)\to(x - 4,y - 4)$ to the original triangle's vertices.
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solve for m∠nlm if m∠klm = 118° and m∠kln = 55°. answer attempt 1 out o…
$63$
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solve for m∠cde if m∠cdf = 52° and m∠fde = 44°. answer attempt 1 out of…
$96$
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which represents the value of c? law of sines: $\frac{sin(a)}{a}=\frac{…
First, find angle \(A\): \(A=180^{\circ}-95^{\circ}-45^{\circ}=40^{\circ}\). By the Law of Sines \(\frac{\sin(A)}{a}=\frac{\sin(C)}{c}\), where \(a = 3.0\) cm, \(A = 40^{\circ}\),…
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does the sentence state a fact or an opinion? north of the arctic circl…
fact
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unit 1 lesson 1 cumulative practice problems 1. here is a diagram of a …
1. The length of segment \(BD\) is the same as the length of segment \(AB\) because \(B\) is the center of the circle and \(AB\) and \(BD\) are both radii of the circle centered a…
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solve for m∠rst if m∠rsu = 46° and m∠ust = 41°. answer attempt 1 out of…
$87$
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solve each problem. show your work. 10. angel needs a floor mat for his…
264 in²
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question point g is on line segment $overline{fh}$. given $fh = 4x$, $g…
30
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which distance measures 5 units? the distance between points w and x th…
the distance between points W and X, the distance between points Y and Z
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the graph shows triangles wxy and wxy. which sequence of transformation…
a rotation 180° around the origin followed by a translation left 4 units and down 3 units
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triangle efg has vertices e(-3, 4), f(-5, -1), and g(1, 1). the triangl…
C. $T_{2,-4}(x,y)$
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this triangle is a scaled copy. it was scaled by a scale factor of 5. s…
Base: 6 cm Height: 15 cm
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which best describes the dimensions of a plane? a plane has zero dimens…
A plane has two dimensions because it is a flat surface that has length and width but no depth.
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which statement describes the order of rotational symmetry for an isosc…
B. An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
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use the formulas for surface area & volume to find these values. rememb…
Using a mathematical formula can both increase and decrease precision depending on the formula and input values. It can introduce systematic and propagated errors based on assumpt…
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consider the triangle. the measures of the angles of the triangle are 3…
In a triangle, the longest side is opposite the largest - angle and the shortest side is opposite the smallest - angle. Given side lengths 8, 12, and 15. The smallest side is 8, t…
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which construction uses the compass for only one step in addition to dr…
C. a regular hexagon inscribed in a circle
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this triangle is a scaled copy. it was scaled by a scale factor of 5. s…
$\frac{1}{5}$
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a regular decagon has 10 sides. how many reflectional symmetries does a…
B. 10
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the diagram shows several points and lines. which statements are true b…
Points J, K, and Q are collinear. There is only one line that can be drawn through points L and P.
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which statements are true about trapezoid abcd and its translated image…
The rule for the translation can be written as \(T_{-3,1}(x,y)\); The rule for the translation can be written as \((x,y)\to(x - 3,y + 1)\)
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what is the minimum angle of rotational symmetry for the quadrilateral …
360°
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this rectangle is a scaled copy. it was scaled by a scale factor of $\f…
18
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which of the following is a step used to inscribe a square in a circle?…
Draw line segments to connect the points where the arc intersects the circle to both endpoints of the original diameter.
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this rectangle is a scaled copy. it was scaled by a scale factor of $\f…
60
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triangle abc has the angle measures shown. m∠a=(2x)°, m∠b=(5x)°, m∠c=(1…
\(m\angle A = 20^{\circ}\)
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use the figure below. o is between m and p, and n is the mid - point of…
8
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if the scale factor between two circles is $\frac{7a}{9b}$ what is the …
$\frac{49a^{2}}{81b^{2}}$
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using the graph, determine the coordinates of the x - intercepts of the…
$(1,0),(5,0)$
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the ratio of the radii of two circles is 4:5. what is the ratio of the …
D. 4:5
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what is the length and width of the original rectangle? 3in 10in scaled…
Length: $\frac{5}{3}$ in, Width: $\frac{1}{2}$ in
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write the coordinates of the vertices after a reflection over the x - a…
$A(3,-5), B(7,-6), C(4,-8), D(2,-7)$ (assuming original coordinates as in Step 2. If you provide actual original coordinates from the grid, we can give more accurate final answer …
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which step do the constructions of a regular hexagon, a square, and an …
Construct an arc using an endpoint of the diameter and the center of the circle.
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the ratio of the diameters of two circles is y:z. what is the scale fac…
B. \(\frac{y}{z}\)
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which of the following is true of the constructions of an equilateral t…
The diameter in the first step of the constructions divides each shape in half.
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this rectangle is a scaled copy. it was scaled by a scale factor of 1/2…
Length: 20 in Width: 6 in
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4. what is the midpoint of ab? (-5,-4)(-3,2) ((-5 + -3)/2, (-4 + 2)/2) …
$6.32$
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soni inscribed a hexagon in a circle. at exactly how many points do the…
D. 6
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biconditional statements rewrite the biconditional statement as a condi…
Conditional statement: If two lines intersect to form right angles, then they are perpendicular. Converse statement: If two lines are perpendicular, then they intersect to form ri…
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this rectangle is a scaled copy. it was scaled by a scale factor of 1/6…
6
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step m - place the compass point at the endpoint of the diameter and th…
M, P, O, N, Q
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8. triangle jkl has vertices j(3, -7), k(7, -3) and l(3, 7). what are t…
$(7,3)$
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in the figure below, b is between a and c, and c is between b and d. if…
18
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the circumferences of two circles are in the ratio of 2:5. the radius o…
B. 40 in.
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1. which of the following statements are true? select all that apply. a…
1. B. \(BC=\vert6 - 1\vert\), D. \(AB + BC=AC\) 2. \(30\) 3. \(5\)
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christopher kicks a football. the graph below shows the height of the f…
\(0\leq t<1\)
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example 5 determine whether each figure has rotational symmetry. if so,…
Figure 13: Has rotational symmetry. Center of symmetry: Intersection of relevant lines. Order: 3. Magnitude: $120^{\circ}$. Figure 14: Does not have rotational symmetry.
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which diagram shows possible angle measures of a triangle?
The first diagram (with angles \(118^{\circ},36^{\circ},26^{\circ}\)) shows possible angle measures of a triangle.
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this rectangle is a scaled copy. it was scaled by a scale factor of 1/2…
$2$
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5. the trapezoid qrst represents a game piece. sage rotates the trapezo…
D. 90° clockwise about the origin
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find the measure of each segment. 28. $overline{mo}$ 29. $overline{wy}$…
28. MO = 13.8 cm 29. WY = 8.8 mm 32. DE = 26 33. UX = 9x + 3
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this rectangle is a scaled copy. it was scaled by a scale factor of 8. …
Length: 8 in Width: 4 in
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write the coordinates of the vertices after a reflection over the x - a…
The new coordinates of $U$ is $(0,3)$, of $T$ is $(6,3)$, of $S$ is $(6,9)$, of $R$ is $(3,9)$
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using the graph, determine the coordinates of the x - intercepts of the…
(-6,0), (-4,0)
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rectangle is a scaled copy. it was scaled by a scale factor of 8. suppo…
$\frac{1}{8}$
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10. a guitar string is about 50 cm long, measured to the point of strum…
$2.615$ cm