幾何
三角形、円、座標幾何、証明問題。
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what is the final transformation in the composition of transformations …
a 180° rotation about point B'
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determine the volume of each box. each block is 1 cubic unit (u³).
60
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reflect what are some similarities and differences between translations…
Similarities: Both preserve shape and size (congruence). Differences: Translations are sliding motions along a path, while reflections are flips over a line.
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what is the final transformation in the composition of transformations …
a reflection across line m
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jason has 144 feet of material to build a fence around a rectangular ga…
21 yards
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the area of a square can be found using the equation a = s², where a is…
$s = \sqrt{227}\ in$
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makayla is taking a math course and is working with the perimeter of re…
$W=\frac{P - 2L}{2}$
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which composition of transformations maps figure efgh to figure efgh? a…
A. a reflection across line k followed by a translation down
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for exercises 10 and 11, use the graph and description to answer the qu…
10. The coordinates of $L'$, $M'$, $N'$ are $(x_{L},4 - y_{L})$, $(x_{M},4 - y_{M})$, $(x_{N},4 - y_{N})$ respectively (where $(x_{L},y_{L})$, $(x_{M},y_{M})$, $(x_{N},y_{N})$ are…
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a triangle is rotated 90° about the origin. which rule describes the tr…
B. $(x,y)\to(-y,x)$
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triangle xyz has vertices x(1, 3), y(0, 0), and z(-1, 2). the image of …
A. $R_{0,90^{\circ}}$
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a model of a sports arena is being created using a scale factor of 0.04…
A. 32 meters
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a pentagon is transformed according to the rule (r_{0,180^{circ}}). whi…
$(x,y)\to(-x,-y)$
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translations of shapes graph the image of the figure using the transfor…
Graph the new figures on the given coordinate grids according to the above - described translation rules for each vertex of the original figures.
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one vertex of a triangle is located at (0, 5) on a coordinate grid. aft…
C. $R_{0,270^{\circ}}$, D. $R_{0, - 90^{\circ}}$
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a model of a sports arena is being created using a scale factor of 0.04…
d. 20 meters
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figure 2 was constructed using figure 1. for the transformation to be d…
- A. The segment connecting the center of rotation, C, to a point on the pre - image (figure 1) is equal in length to the segment that connects the center of rotation to its corre…
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triangle rst was transformed using the rule (x,y)→(−x,−y). the vertices…
B. The transformation was a 180° rotation about the origin.
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which shows the image of quadrilateral abcd after the transformation r0…
To find the image of a point $(x,y)$ after a $90^{\circ}$ counter - clockwise rotation about the origin $R_{0,90^{\circ}}$, we use the transformation rule $(x,y)\to(-y,x)$. Let's …
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parallelogram abcd is rotated to create image abcd. which rule describe…
C. $(x,y)\to(-x, -y)$
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5 multiple choice 10 points find the area of the rectangle shown. 6√10 …
5. D. $36\sqrt{5}$ 6. A. $\sqrt{2}$ 7. A. irrational
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triangle xyz is rotated to create the image triangle xyz. which rules c…
B. $R_{0,180^{\circ}}$, E. $(x,y)\to(-x,-y)$
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notes kuta software - infinite pre - algebra translations of shapes gra…
# Explanation: ## Step1: Recall translation rule For a translation \(a\) units left or right and \(b\) units up or down, if a point \((x,y)\) is translated \(a\) units right (\(a>…
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what is the result of a dilation with a scale factor between 0 and 1? a…
C. The figure is reduced in size
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the rule as a mapping for the translation of a rectangle is (x, y) → (x…
D. a translation of 2 units to the left and 7 units up
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a rectangular garden measures 25 ft × 40 ft. if the scale on a blueprin…
A. 5 in × 8 in
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trapezoid lmnp was constructed using trapezoid lmnp. for the transforma…
1. $LL' = PP'$ 2. $LL' = MM'$ 3. Trapezoid $LMNP$ is congruent to trapezoid $L'M'N'P'$ 4. All line segments that connect a point on the pre - image to its corresponding point on t…
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1. here is a map that shows parts of texas and oklahoma. a. about how f…
a. Suponiendo una escala de 1 pulgada = 100 millas y una distancia de 3 pulgadas en la carta, la distancia es de 300 millas. b. No es posible, ya que en 3 horas a 70 millas por ho…
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if a translation of $t_{2, - 7}(x,y)$ is applied to $\triangle abc$, wh…
$(3, - 12)$
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question 12 (01.03 mc) the perimeter of a rectangle can be found using …
Question 12: No. If the length is 20 and the width is 11, the perimeter is $P = 40+22 = 62$, not 64. Question 13: No, because $2(4)+4 eq15$
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if a translation of (t_{2,-7}(x,y)) is applied to (\triangle abc), what…
$(1,-12)$ (Note: There seems to be an error in the provided options as the correct answer based on the steps above is not among them. But following the steps, the correct coordina…
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rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3, -6), and d(-6, …
A. \(T_{-4,3}(x,y)\)
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hexagon defghi is translated 8 units down and 3 units to the right. if …
B. (-6, -6)
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triangle abc is translated according to the rule (x, y) → (x + 2, y - 8…
D. \((6, - 13)\)
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rectangle efgh is translated according to the rule (t_{-5,9}(x,y)). if …
B. (-7,6)
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how was figure a transformed to become figure a? 1. ? 2.
1. Reflect 2. No second - step transformation indicated in the problem setup (or could be left blank as per the given problem structure)
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3. use the pythagorean theorem to solve for x
$x = 24$
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what is the perimeter of square cdef? perimeter = units
8
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3. use the pythagorean theorem to 4. what is the length of bd?
$x = 24$
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dion is laying brick down to make a patio. he plans for the patio to be…
Dion estimated correctly by rounding up. He ordered enough brick. The exact area is 129.5 square feet.
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which statements are true about triangle abc and its translated image, …
The rule for the translation can be written as \(T_{3,-5}(x,y)\); Triangle ABC has been translated 3 units to the right and 5 units down.
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square abcd was translated using the rule (x,y)→(x - 4,y + 15) to form …
$(13,-23)$
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identify the similar triangles. a) △bca ~△bde b) △abc ~△dbe c) △cba ~△b…
B. $\triangle ABC\sim\triangle DBE$
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the proof that δrst ≅ δvst is shown. given: st is the perpendicular bis…
perpendicular bisector theorem
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equilateral triangle abc has a perimeter of 96 millimeters. a perpendic…
16 mm
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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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a. what is the distance from the lighthouse to the end of the lighthous…
a. 64 ft b. 56 ft
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cell towers a cell phone tower casts a shadow that is 100 feet long. at…
135
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nessa proved that these triangles are congruent using asa. roberto prov…
$\angle A\cong\angle Q$ because of the third angle theorem.
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determine whether the pair of triangles is similar. explain your reason…
No
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which rigid transformation would map △abc to △edc? a rotation about poi…
a rotation about point C
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use the figure below, give the following. (a) one pair of angles that f…
(a) $\angle1$ and $\angle2$ (b) $\angle3$ and $\angle4$ (c) $\angle5$ and $\angle7$
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practice plotting points on a coordinate plane graph these points in or…
By following the above steps and plotting all the given points in order for each shape on the coordinate - plane, the picture of the fictional character will be created.
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in triangle abc, bg = 24 mm. what is the length of segment ge? 12 mm 24…
12 mm
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select the statement that is the contrapositive of the following statem…
If all a polygon's interior angles don't have the same measure, then it isn't equiangular.
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triangle def is congruent to △def by the sss theorem. which single rigi…
reflection
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determine whether the pair of triangles is similar. explain your reason…
No
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in triangle abc, the segments drawn from the vertices intersect at poin…
Point G can be the centroid because 12:6 equals 2:1.
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select the statement that is the contrapositive of the following statem…
If the side lengths of a triangle don't satisfy the equation \(a^{2}+b^{2}=c^{2}\), then it isn't a right triangle.
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a triangle is drawn on the coordinate plane. it is translated 4 units r…
(x,y)→(x + 4,y - 3) (corresponds to the third option)
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triangle def is isosceles, where df ≅ fe. angle fde is bisected by segm…
64°
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in the figure below, m∠1 = 6x° and m∠2=(x + 6)°. find the angle measure…
$m\angle1 = 72^{\circ}$, $m\angle2 = 18^{\circ}$
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given: ab = bc prove: b is the midpoint of ac. ab = bc given ab ≅ bc de…
C. two - column proof
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select the statement that is the converse of the following statement: i…
If a quadrilateral is a parallelogram, then it has two pairs of parallel sides.
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determine whether the pair of triangles is similar. explain your reason…
Yes, $\triangle SKM\sim\triangle RTQ$ by AA Similarity
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select the statement that is the inverse of the following statement: if…
If a quadrilateral doesn't have four right angles, then it's not a rectangle.
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in the figure below, m∠1=(x + 38)° and m∠2 = 3x°. find the angle measur…
$m\angle1 = 51^{\circ}$, $m\angle2 = 39^{\circ}$
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select the statement that is the converse of the following statement: i…
If two segments are congruent, then they have the same measure.
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determine whether the pair of triangles is similar. explain your reason…
Yes
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which is another way to name ∠ust? ∠tsr ∠uts ∠tsu ∠usr
∠TSU
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in the figure below, m∠1=(x + 30)° and m∠2 = 3x°. find the angle measur…
$m\angle1 = 45^{\circ}$, $m\angle2 = 45^{\circ}$
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could △abc be congruent to △adc by sss? explain. yes, but only if (over…
Yes, but only if \(\overline{BC}\cong\overline{DC}\)
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foundations of euclidean geometry. which statement must be true about t…
Ray KM is an angle bisector of $\angle NKL$
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graph the rectangle with vertices (-1, 2), (5, -8), (10, -5), and (4, 5…
Graph with rectangle formed by given vertices.
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angle mon is a straight angle and op bisects ∠moq. what is the measure …
61°
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in the figure below, m∠1=(x - 6)° and m∠2 = 5x°. find the angle measure…
$m\angle1 = 25^{\circ}$, $m\angle2 = 155^{\circ}$
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determine whether the pair of triangles is similar. explain your reason…
The triangles would be similar by AA Similarity if segment AB $\parallel$ segment DF
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select the statement that is the contrapositive of the following statem…
If a triangle doesn't have congruent base angles, then it isn't isosceles.
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which diagram shows possible angle measures of a triangle?
The diagram with angle measures $32^{\circ}$, $33^{\circ}$, and $115^{\circ}$ shows possible angle measures of a triangle.
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determine whether the pair of triangles is similar. explain your reason…
No
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foundations of euclidean geometry which line segment is drawn in the fi…
C. $\overline{WZ}$
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how can △abc be mapped to △xyz? first, translate. next, rotate △abc abo…
vertex A to vertex Y
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determine whether the pair of triangles is similar. explain your reason…
Yes, $\triangle RST\sim\triangle UWV$ by AA Similarity
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in geometry, a transformation that does not change the size or shape of…
1. Rigid - motion 2. Bilateral 3. Translation 4. Center of rotation 5. Dilation 6. Line of reflection 7. Rotational 8. Translational
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a triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft. wh…
A. \(x - 1 < n < 3x+5\)
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determine whether the pair of triangles is similar. explain your reason…
Yes
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in the figure below, m∠1 = 3x° and m∠2=(x + 84)°. find the angle measur…
m∠1 = 72°, m∠2 = 108°
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given: hf || jk; hg ≅ jg prove: △fhg ≅ △kjg to prove that the triangles…
$\angle HFG\cong\angle KJG$ because alternate interior angles are congruent.
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a triangle △jkl with side lengths 4, 6, and 8 is dilated by k = 3. what…
D. \(12,18,24\)
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determine whether the pair of triangles is similar. explain your reason…
Yes, $\triangle FGH\sim\triangle KJH$ by AA Similarity
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is δwxz ≅ δyzx? why or why not? yes, they are congruent by sas. yes, th…
D. No, there is only one set of congruent sides.
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△abc ~ △def find the value of x. a 7 ft b 6 ft c d x ft e 12 ft f x = ?
Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. If we assume the ratio of the sides of \(\triangle ABC\) to \(\triangle DEF\) gives \(\frac{…
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in the figure below, m∠1=(x + 42)° and m∠2 = 2x°. find the angle measur…
m∠1 = 58°, m∠2 = 32°
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a square has vertices at a(-2,-2), b(-2,2), c(2,2), and d(2,-2). if it …
C. $(8,8)$
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determine whether the pair of triangles is similar. explain your reason…
Yes; by the AA similarity criterion since $\angle F = \angle K$ and $\angle FHG=\angle KHJ$ (vertical angles are equal).
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a triangle has vertices a(1,2),b(3,4),c(5,1). after a dilation with a s…
B. \((6,8)\)
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determine whether the pair of triangles is similar. explain your reason…
The triangles are similar by the AA similarity criterion if $\angle F = \angle K$.
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a square has vertices at a(-2,-2), b(-2,2), c(2,2), and d(2,-2). if it …
C. $(8,8)$
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use the figure to complete each part. (a) name the vertex of ∠dba. (b) …
(a) B (b) ∠2, ∠DBC (c) Ray BA, Ray BC
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a triangle has vertices x(1,1),y(5,1),z(3,4). after a dilation, its ima…
C. 3