幾何
三角形、圓、解析幾何與證明題。
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angle d and angle v are supplementary angles. write an equation that re…
\(d + v = 180\)
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angle a and angle b are complementary angles. angle a and angle f are s…
\(150\)
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angle a and angle f are supplementary angles. write an equation that re…
\(a + f = 180\)
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angle a and angle b are complementary angles. write an equation to repr…
\(a + b = 90\)
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use your equation to solve for the value of b, or the measure of angle …
$b = 90$
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angle a, angle e, and angle b form a straight angle. what is the measur…
The equation is \(a + e+ b = 180\) and the measure of angle \(b\) is \(110^{\circ}\).
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use your equation to solve for the value of a, or the measure of angle …
\(a = 55\)
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1 organize the figures in the tree diagram. write one category name in …
| Polygons | |--| | rectangles (quadrilaterals) | | triangles | | hexagons | | squares (quadrilaterals) | | equilateral triangles (triangles) |
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if (\triangle jklcong\triangle bca), which statement must be true? (ove…
\(\overline{JL}\cong\overline{BA}\) (the third option)
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angle a and angle e are complementary angles. write an equation to repr…
\(a + e = 90\)
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angle e and angle c are vertical angles. $c = e$ $e=square^{circ}$
\(35\)
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which statement is true? a scalene triangle and a right triangle are al…
An equilateral triangle and a right triangle are never congruent.
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find m∠abc and m∠cbd if m∠abd = 120° m∠abc = m∠cbd = need help?
\(m\angle ABC = 36^{\circ}\), \(m\angle CBD = 84^{\circ}\)
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kris claims that the two figures must be congruent. which statement bes…
He is incorrect because the lengths of the corresponding sides of the figures are unknown.
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m∠cbd if m∠abd = 120°.
\(84^{\circ}\)
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a line segment has endpoints at (-1,4) and (4,1). which reflection will…
a reflection of the line segment across the \(x\) - axis and then across the \(y\) - axis. But if we consider the composition of reflections, first reflecting across the \(y\) - a…
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proof complete the two - column proof. the statements are provided on t…
1. Given 2. Vertical angles are congruent 3. Transitive property of congruence
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the function rule ( t_{-4,6}(x,y) ) could be used to describe which tra…
a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
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deepak found that \\( \\angle g \\) has a measure of \\( 50 ^ { \\circ …
No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle \(MNP\).
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supplement theorem given: \\( \\angle pqt \\) and \\( \\angle tqr \\) f…
1. Given 2. \(\angle PQR\) is a straight angle 3. \(m\angle PQR = 180^{\circ}\) 4. Angle - Addition Postulate 5. \(m\angle PQT + m\angle TQR=180^{\circ}\) 6. Definition of supplem…
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rotate the figure 270° clockwise about the origin. then decide if each …
| Statement about rotated figures | True | False | |--|--|--| | The final angle measures are the same as the original angle measures. | ○ | | | The final side lengths are longer t…
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$\\overline{hi}$ is a translation of $\\overline{hi}$. write the transl…
\((x,y)\to(x + 9,y+9)\)
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triangle abc is shown on the graph. what are the coordinates of the ima…
\((4,2)\)
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if $\triangle mnocong\triangle nmo$, what statement best describes tria…
The triangle is isosceles and possibly equilateral.
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a parallelogram is transformed according to the rule $(x,y)\to(x,y)$. w…
\(R_{0,360^{\circ}}\)
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right triangle lmn has vertices l(7,-3), m(7,-8), and n(10,-8). the tri…
\((x,y)\to(x - 8,y + 11)\)
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jk is a translation of jk. write the translation rule. (x,y)→(x+□,y+□)
\((x,y)\to(x + 6,y+6)\)
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solve for x. round to the nearest tenth of a degree, if necessary.
$x\approx32.4^{\circ}$
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the angle of elevation to a nearby tree from a point on the ground is m…
$53.3$ feet
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the right triangle below has legs of length $a = 11$ and $b = 8$. the h…
Part 1: \(176\) Part 2: \(361\)
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which rule describes the composition of transformations that maps figur…
\(r_m\circ R_{C',180^{\circ}}\) (the fourth option)
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christian is trying to find the height of a radio antenna on the roof o…
\(8.8\) meters
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triangle pqr has vertices p(-2,6), q(-8,4), and r(1, -2). it is transla…
- 10
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triangle pqr has vertices p(-2,6), q(-8,4), and r(1,-2). it is translat…
- 10
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express cos m as a fraction in simplest terms.
$\frac{3}{5}$
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solve for x. round to the nearest tenth, if necessary.
\(x\approx2.9\)
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which figure represents the image of parallelogram lmnp after a reflect…
figure C
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a transformation of δklm results in δklm. which transformation maps the…
dilation
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which of the following congruency statements is correct? △yzx ≅ △bcd △y…
\(\triangle YZX\cong\triangle DCB\)
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graph the image of square j k l m after a translation 5 units up.
Plot the points \(J'(-5,-4)\), \(K'(-4,-4)\), \(L'(-4,-3)\), \(M'(-5,-3)\) and connect them.
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which transformation maps the large triangle onto the small triangle? d…
dilation
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a transformation of \\( \\triangle klm \\) results in \\( \\triangle kl…
dilation
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22. connor visits the following locations: museum at m (4, 0), sports c…
Plot the point \(M\) at \((4,0)\) (on the \(y -\)axis, 4 units from the origin), point \(S\) at \((5,2)\) (5 units right on \(y -\)axis and 2 units up on \(x -\)axis) and point \(…
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a rectangle is transformed according to the rule ( r_{0,90^{circ}} ). t…
\((4,3)\)
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graph the image of \\( \\triangle k l m \\) after a translation 10 unit…
Plot the points \(M'(-2,-8)\), \(K'(4,-7)\) and \(L'(3,-2)\) and connect them.
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the figure is an isosceles trapezoid. how many lines of reflectional sy…
1
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which statement about the transformation is true? it is rigid because a…
It is rigid because all side lengths and angles are congruent.
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20. higher order thinking one side of a rectangle is parallel to the x …
The other two vertices are \((1,2)\) and \((5,4)\)
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the image of trapezoid pqrs after a reflection across wy is trapezoid p…
\(90^{\circ}\)
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which of the following statements are correct based on the diagram? sel…
\(\overline{US}\cong\overline{XV}\)
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draw a model of each ratio. 1. the ratio of striped socks to solid - co…
Draw \(2\) shapes (e.g., circles) for striped socks and \(6\) shapes (e.g., circles) for solid - colored socks.
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triangle abc is rotated to create the image abc. which rule describes t…
\((x,y)\to(-x,-y)\)
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a composition of transformations maps pre - image efgh to final image e…
a translation down and to the left
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what are the coordinates of the image of vertex f after a reflection ac…
\((3,-1)\)
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complete the diagram using the given information. l and m are parallel …
1. (Diagrammatic step, not shown in text here but conceptually: \(\angle B\) and its corresponding angle (say \(\angle E\)) are in the same relative position with respect to the p…
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triangle abc has side lengths: ab = 3.5 cm, bc = 2.4 cm, and ac = 4.2 c…
\(3.5\)
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which diagram has all the correct lines of reflectional symmetry for th…
The diagram with the horizontal and vertical dashed lines (the second diagram in the problem description) is the correct one as it shows the two lines of reflectional symmetry (ho…
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which figure represents the image of trapezoid l m n p after a reflecti…
figure A
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cedric applied the rule ( r_{m} circ r_{p, 90^{circ}}(x, y) ) to figure…
He applied the reflection to the pre - image first. ; He used point \(P\) as the center of rotation.
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7. copy each square on grid paper. find its area. then write the side l…
a) Area \(A = 8\) square units, side - length \(s=2\sqrt{2}\) units b) Area \(A = 18\) square units, side - length \(s = 3\sqrt{2}\) units
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a transformation of △def results in △def. which transformation maps the…
The transformation is a translation.
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triangle def was tranformed to create triangle def. complete the statem…
point \(F\)
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16. fernanda wants to draw line segments to connect the points to form …
16. Ruler 17. Parallelogram
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rectangle ( abcd ) is the image of rectangle ( a b c d ) after it has b…
\((-1,-2)\), \((7,1)\), \((-1,1)\), \((7,-2)\)
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triangle abc was transformed to create triangle def. which statement is…
\(\overline{ED}\) corresponds to \(\overline{BA}\) because they are in the same position.
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a square on a coordinate plane is translated 9 units down and 1 unit to…
\(T_{1,-9}(x,y)\)
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find the value of x and the angle measures using the exterior angle the…
\(x = 20\), \(\angle R=50^{\circ}\), \(\angle S = 90^{\circ}\)
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square pqrs is transformed as shown on the graph. which rule describes …
\(R_{0,180^{\circ}}\)
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circle the unit rate in the table. use the unit rate to complete the ta…
| Seconds | Yards | |---------|-------| | 1 | 2 | | 5 | 10 | | 3 | 6 | | 2 | 4 | | 4 | 8 | For the graph: Plot the points \((1,2)\), \((5,10)\), \((3,6)\), \((2,4)\), \((4,8)\). T…
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which rule describes the composition of transformations that maps \\( \…
\(r_{x - axis}\circ T_{-6,-2}(x,y)\)
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graph the image of rectangle cdef after a translation 2 units right and…
Plot the points \(C'(-6,-6)\), \(D'(0,-6)\), \(E'(0,-1)\), \(F'(-6,-1)\) and connect them.
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triangle efg has vertices e(-3,4), f(-5,-1), and g(1,1). the triangle i…
\(T_{2,-4}(x,y)\)
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polygon lm nop was transformed to create polygon which angle correspond…
\(\angle N'\)
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a composition of transformations maps \\( \\triangle k l m \\) to \\( \…
a \(90^{\circ}\) rotation about point \(L\)
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graph the image of $\\triangle klm$ after a translation 15 units down.
Plot the points \( (2,-7) \), \( (6,-7) \), \( (8,-8) \) and connect them to get the image of \(\triangle KLM\) after the translation.
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graph the image of \\( \\triangle klm \\) after a translation 15 units …
Plot the points obtained by subtracting \( 15\) from the \( y\) - coordinates of the original triangle's vertices and connect them.
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in the figure below, ( bc = 9 ) and ( ab = 5 ). find ( ac ). ( ac=squar…
\(14\)
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graph the image of square bcde after a translation 4 units right.
Plot the points \((1,-4)\), \((9,-4)\), \((9,4)\), \((1,4)\) and connect them.
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1. using diagonals from a common vertex, how many triangles could be fo…
\(6\)
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graph the image of \\( \\triangle t u v \\) after a translation 9 units…
Plot the points \(T'(-8,-10)\), \(U'(0,-10)\), \(V'(-8,-8)\) and connect them.
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what is the order of rotational symmetry for a rhombus? 1 2 3 4
2
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graph the image of rectangle tuvw after a translation 6 units right.
Plot the points \((5,3)\), \((7,3)\), \((7,7)\), \((5,7)\) and connect them.
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which triangle has 0 reflectional symmetries?
The first - like triangle (scalene right - triangle) has 0 reflectional symmetries.
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which statements are true about the lines of symmetry of a regular pent…
C. Every line bisects a vertex angle. D. Every line bisects a side. E. Every line is perpendicular to a side.
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graph the image of rectangle cdef after a translation 4 units left and …
Plot the points \(C'(-10,3)\), \(D'(-6,3)\), \(E'(-6,9)\), \(F'(-10,9)\) and connect them.
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which figure has an order 3 rotational symmetry? right triangle equilat…
equilateral triangle
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if the smallest angle of rotation for a regular polygon is 18°, how man…
20
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which letter in the word happy has an order 2 rotational symmetry? h a …
H.
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how can a regular hexagon be folded to show that it has reflectional sy…
Fold the hexagon along a line that bisects two vertex angles.
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how many lines of reflectional symmetry does an equilateral triangle ha…
3
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example 2: the committee leave their homes at different times. here the…
1. agree 2. is 3. were 4. is 5. were 6. uses 7. lives 8. surround 9. go 10. depends 11. scatter 12. flies 13. plays 14. sell 15. gives 16. are 17. are 18. is 19. were 20. is
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determining angles of rotational symmetry of a regular polygon the regu…
\(40^{\circ}\), \(120^{\circ}\), \(240^{\circ}\)
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1. explain to a friend how to graph the point (1,5).
To graph the point \((1,5)\), start at the origin. Move 1 unit to the right along the x - axis and then 5 units up along the vertical line passing through \(x = 1\).
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rotational symmetry of parallelograms what is the order of rotational s…
2
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find the perimeter and area of each rectangle or square. find the unkno…
1. \(P = 16\)cm, \(A = 15\)cm² 2. \(P = 12\)cm, \(A = 9\)cm² 3. \(P = 26\)cm, \(A = 40\)cm² 4. \(b = 3\)cm 5. \(h = 2\)cm 6. \(s = 7\)cm 7. \(80\)ft² 8. \(44\)ft 9. \(12\)ft 10. \…
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which diagram has all of the correct lines of reflectional symmetry for…
The second diagram (the one with 5 lines of symmetry) is the correct one.
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6. hikmat says that dilating a figure by a scale factor of \\( \\frac {…
Hikmat's claim is incorrect. When the scale factor of a dilation is \(\frac{3}{2}\) (or \(1.5\)), since \(1.5 > 1\), the image produced by the dilation will be larger than the pre…
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calculating the smallest angle of rotational symmetry what is the small…
\(45\)
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analyzing the symmetry of trapezoids which statements are true regardin…
The trapezoid has 1 line of reflectional symmetry. The line of symmetry is a vertical line. The trapezoid has rotational symmetry of order 1.
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which diagram represents a line of symmetry of the regular octagon?
The last diagram (the one with the dashed line passing through two opposite vertices) represents a line of symmetry of the regular octagon.