幾何
三角形、圓、解析幾何與證明題。
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if ∠k and ∠b are supplementary and m∠b = 128°, solve for m∠k.
$52^{\circ}$
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22. geometry find the value of x so the rectangles have the same area.
$8$
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find the value of a. show your work here (-10a - 16)° (-3a + 15)°
$a = - 7$
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the vertices for quadrilateral abcd are (0, 9), (9, 0), (0, -9), and (-…
$\frac{1}{3}$
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solve for x. show your work here enter your answer
41
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a quadrilateral with sides measuring 12, 15, 9, 6 dilated to a quadrila…
$\frac{2}{3}$
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a triangle with sides measuring 6, 12, 4 dilated to a triangle with sid…
The scale - factor of dilation is $\frac{3}{2}$.
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every day a food truck sets up at a location that is conveniently half …
1. Food truck location: (2,0) 2. Mid - point between food truck and Milk Jug: $(4,-\frac{5}{2})$ 3. Bumper Cars are closer to the Entrance. 4. a. x - coordinate of Intimidator: $\…
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for exercise 5 - 7, find the scale factor used in each dilation. 5. a s…
8
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4. a triangle with sides measuring 9 centimeters, 21 centimeters, 15 ce…
The new side - lengths are 3 centimeters, 7 centimeters, and 5 centimeters.
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2. fill out the figurative language chart below. textual evidence, figu…
1. - Textual Evidence: "While I grew up with a grass - is - always - greener attitude deeming things outside of my household better" - Figurative Language Used: Idiom - Author's m…
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2) name the angle in four ways.
$\angle B$, $\angle ABC$, $\angle CBA$, $\angle 1$
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question 8 of 10 knowing that all three - sided figures are triangles i…
D. concept formation
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review (10 pts) 0 / 6 pts
x = 67, y = 50, z = 45
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which point would map onto itself after a reflection across the line y …
(4, -4)
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Question was provided via image upload.
$x = 11^{\circ}$, $y = 105^{\circ}$, $z = 75^{\circ}$
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a line segment has endpoints at (-4, -6) and (-6, 4). which reflection …
a reflection of the line segment across the y - axis
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figure abcdef was reflected across the line y = -x to create figure abc…
$(4,2)$
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what we have learned about triangle angle
$x = 11^{\circ}$, $y = 105^{\circ}$, $z = 75^{\circ}$
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the image of trapezoid pqrs after a reflection across wy is trapezoid p…
C. \(\overline{RR'}\parallel\overline{SS'}\)
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figure abcd was reflected across the x - axis to create figure abcd. wh…
C. $(-2,8)$
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the solid below is made from cubes. find its volume. 1 cm
64
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use the properties of rigid motions to complete the proof. given: $over…
The proof is completed by using the properties of rigid motions (reflection preserves distance and angle measure), the Side - Angle - Side (SAS) congruence criterion, and the prop…
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use the properties of rigid motions to complete the proof. given: pq¯≅q…
QR
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for exercises 5-6, answer the questions. 5. a photographer wants to fra…
She should check if the inner - dimensions of the frame are exactly 8 inches by 10 inches (or 10 inches by 8 inches).
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△abc was constructed using △abc and line segment eh. for eh to be the l…
BD = DB', $m\angle EFA = 90^{\circ}$, The line of reflection, $\overline{EH}$, is the perpendicular bisector of $\overline{BB'}$, $\overline{AA'}$, and $\overline{CC'}$
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what is the rule for the reflection? o (r_{y = x}(x,y)-( - y,-x)) o (r_…
$r_{y=-x}(x,y)=(-y,-x)$
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what are the coordinates of the image of vertex d after a reflection ac…
$(5,3)$ It seems there is a mistake in the provided options as the correct answer $(5,3)$ is not among them. If we assume there was a mis - typing in the problem setup and we work…
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the image of parallelogram pqrs after a reflection across wy is paralle…
6
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finding a pre - image using a rule the image of a point is given by the…
A. $(-9,4)$
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14. use coordinate notation to describe the rotation. then determine th…
The rotation in coordinate notation is $(x,y)\to(-y,x)$ and the angle of rotation is 90°.
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finding a pre - image figure abcde was reflected across the line y = x …
$(-4,8)$
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13. use coordinate notation to describe the rotation. then determine th…
The angle of rotation is \(90^{\circ}\) clockwise.
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what are the measures of ∠1 and ∠2? explain. the measure of ∠1 is □ bec…
The measure of ∠1 depends on the measure of the base angles of the isosceles triangle. If the base angles are \(x\) each, then \(m\angle1 = 2x\) (using the Triangle Exterior Angle…
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12. use coordinate notation to describe the rotation. then determine th…
The coordinate notation for the rotation is $(x,y)\to(y,-x)$ and the angle of rotation is 90 degrees.
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analyzing statements about a reflection which are true if figure defg i…
D(0,4)→D(0, - 4), E(-2,0)→E(-2,0), The perpendicular distance from G' to the x - axis will equal 2 units.
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write three things that you notice or wonder about the diagram: 1) 2) 3)
1. Multiple rays share endpoint V. 2. Angles are formed at V. 3. Is the sum of the angles a straight - angle?
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which reflection will produce an image of △rst with a vertex at (2, -3)…
a reflection of $\triangle RST$ across the line $y = -x$
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reflecting a triangle consider reflections of △jkl. what line of reflec…
The line of reflection that maps point K to point K' is $x = 0$. The line of reflection that maps point L to point L' is $y=-x$.
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for exercises 10 and 11, polygon qrst has vertices q(-5, -1), r(-3, 1),…
For 10: Coordinate notation: $(x,y)\to(y, - x)$. Vertices of $Q'R'S'T'$ are $Q'(-1,5)$, $R'(1,3)$, $S'(-2,2)$, $T'(-5,4)$. For 11: Coordinate notation: $(x,y)\to(-x,-y)$. Vertices…
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triangle abc is a scaled copy of triangle def. side ab measures 12 cm a…
a. The scale factor is $\frac{3}{2}$. b. The scale factor is $\frac{2}{3}$.
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consider the reflection of △abc across the line of reflection, (overlef…
C'Q = QC, PT⊥AA', m∠TRB = 90°
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trapezoid lmnp was reflected using the rule $r_{y - axis}(x,y)\to(-x,y)…
C
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4. nai puts 3 oranges on each tray. how many oranges does he put on 5 t…
4. 15 oranges 5. 16 toys 6. 5 pencils 7. 15 apples 8. 8 9. 16
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sumy is working in geometry class and is given figure abcd in the coord…
B. $(b,a)$
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state if the given point is interior, exterior, or on the angle. 21) 22…
21) Exterior 22) Interior 23) Exterior 24) On the angle
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is $-2$, where the rise is - 2 and the run is 1.
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for exercises 8 and 9, polygon efgh has vertices e(4, -3), f(2, -4), g(…
Coordinate notation: $(x,y)\to(y, - x)$ $E'( - 3,-4)$, $F'( - 4,-2)$, $G'( - 1,-1)$, $H'(0,-5)$
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problem 1 segment ab measures 3 cm. point o is the center of dilation. …
a. 15 cm b. 11.1 cm c. 0.6 cm d. $3s$ cm
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for exercises 8 and 9, polygon efgh has vertices e(4, - 3), f(2, - 4), …
The coordinate notation for a $270^{\circ}$ clock - wise (or $90^{\circ}$ counter - clockwise) rotation about the origin is $(x,y)\to(-y,x)$. $E'(3,4)$, $F'(4,2)$, $G'(1,1)$, $H'(…
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3. how has communication technology changed the way people connect? 4. …
3. Communication technology has made long - distance connection instant, increased interaction frequency, and broadened social circles. 4. Advantages: speed, convenience, wide acc…
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what quadrant is (5, -10) in? ○ quadrant i ○ quadrant ii ○ quadrant iii…
D. Quadrant IV
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what is the rule for the reflection? $r_{y - axis}(x,y)\to(-x,y)$ $r_{y…
D. \(r_{x - axis}(x,y)=(x, - y)\)
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a) name the angle relationship. b) congruent or supplementary c) angle …
A) Corresponding angles B) Congruent C) 97°
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for exercises 6 and 7, triangle jkl has vertices j(3, 1), k(2, -1), and…
6. $J'(1,-3)$, $K'(-1,-2)$, $L'(2,-1)$ 7. $J''(-3,-1)$, $K''(-2,1)$, $L''(-1,-2)$
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what is the rule for the reflection? m(-5,4) m(5,4) l(-6,2) n(-3,2) n(3…
$r_{y - axis}(x,y)\to(-x,y)$
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quadrangle abcd is dilated by a scale factor of 4 about the origin to t…
(12,4)
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5. polygon wxyz has vertices w(-2,1), x(1,3), y(2,2), and z(-1,0). grap…
$W'(1,2)$, $X'(3, - 1)$, $Y'(2, - 2)$, $Z'(0,1)$
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given: ∠1 and ∠2 a linear pair; ∠2, ∠3, and ∠4 supplementary; prove: m∠…
| Statements | Reasons | |--|--| | 1. ∠1 and ∠2 a linear pair; ∠2, ∠3, and ∠4 supplementary; | 1. Given | | 2. \(m\angle1 + m\angle2 = 180^{\circ}\) | 2. Supplement Theorem | | 3.…
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name all the angles that have v as a vertex. 13) 14) 15) 16)
13) $\angle HVJ$, $\angle HV I$, $\angle IVJ$; 14) $\angle DV E$, $\angle DV F$, $\angle EV F$; 15) $\angle RV T$, $\angle RV S$, $\angle SV T$; 16) $\angle DV E$, $\angle DV F$, …
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a) name the angle relationship. b) congruent or supplementary c) solve …
A. Same - side interior angles B. Supplementary C. \(x=-12\)
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draw and label an angle to fit each description. 9) an obtuse angle, ∠y…
The angles are drawn as described above.
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4. polygon pqrs has vertices p(-3,1), q(-4,3), r(0,3), and s(-1,1). gra…
$P'(3, - 1),Q'(4,-3),R'(0,-3),S'(1,-1)$
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jacob is playing miniature golf. he states that he cannot hit the ball …
A. Jacob is incorrect. To make the shot, he should first reflect the hole over the back wall. He should aim at the midpoint between the hole and the reflection of the hole.
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given: ∠1 and ∠2 form a linear pair; m∠1 = m∠3 prove: ∠2 and ∠3 are sup…
| Statements | Reasons | |--|--| | 1. $\angle1$ and $\angle2$ form a linear pair; $m\angle1 = m\angle3$ | 1. Given | | 2. $\angle1$ and $\angle2$ are supplementary | 2. If two ang…
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jacob is playing miniature golf. he states that he cannot hit the ball …
B. Jacob is incorrect. To make the shot, he should first reflect the hole over the back wall. He should aim at the midpoint between the starting position and the reflection of the…
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finding a pre - image vertex. what is the pre - image of vertex a if th…
A(2,4)
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3. polygon jklm has vertices j(1, 2), k(3, 3), l(4, -1), and m(2, -1). …
$J'(-2,1)$, $K'(-3,3)$, $L'(1,4)$, $M'(1,2)$
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jacob is playing miniature golf. he states that he cannot hit the ball …
C. Jacob is incorrect. To make the shot, he should first reflect the hole over the back wall. He should aim at the midpoint between the hole and the reflection of the hole.
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look at the colored part of each shape. which shape shows two - fourths?
The fourth shape.
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dilations (module 2) quadrangle abcd is dilated by a scale factor of 4 …
If the coordinates of $A$ are $(x,y)$, the coordinates of $A'$ are $(4x,4y)$. For example, if $A=(1,1)$, then $A'=(4,4)$.
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dilations (module 2) quadrangle abcd is dilated by a scale factor of 4 …
(The coordinates of $A'$ are obtained by multiplying the coordinates of A by 4. Without seeing the exact coordinates of A on the graph, we can't give a specific numerical answer. …
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2. triangle efg has vertices e(0, -1), f(4, 1), and g(4, -3). graph the…
$E'(-1,0)$, $F'(1,-4)$, $G'(-3,-4)$
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name the vertex and sides of each angle. 1) 2) 3) 4) name each angle in…
1) Vertex: \(M\), Sides: \(\overrightarrow{MN}\), \(\overrightarrow{ML}\) 2) Vertex: \(D\), Sides: \(\overrightarrow{DE}\), \(\overrightarrow{DC}\) 3) Vertex: \(R\), Sides: \(\ove…
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given: ∠2 and ∠3 form a right angle; m∠1 + m∠2 = 90° prove: ∠1 ≅ ∠3 sta…
| Statements | Reasons | |--|--| | 1. ∠2 and ∠3 form a right - angle; \(m\angle1 + m\angle2 = 90^{\circ}\) | 1. Given | | 2. ∠2 and ∠3 are complementary | 2. Definition of complem…
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question 15 of 25 oc is perpendicular to ab. what is the length of ab? …
C. 8.8 units
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name the vertex and sides of each angle. 1) 2) 3) 4) name each angle in…
1) Vertex: \(M\), Sides: \(\overrightarrow{MN}\), \(\overrightarrow{ML}\) 2) Vertex: \(D\), Sides: \(\overrightarrow{DE}\), \(\overrightarrow{DC}\) 3) Vertex: \(R\), Sides: \(\ove…
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question 14 of 25 if a circle is inscribed in a square, which of the fo…
B. Each vertex of the square lies outside the circle. C. The circle is tangent to each side of the square. D. The square is circumscribed about the circle.
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the expression $\frac{1}{2}(b_1 + b_2)$ gives the area of a trapezoid w…
$100$
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1. triangle abc has vertices a(-2, 1), b(-1, 4), and c(3, 4). graph the…
$A'(1,2),B'(4,1),C'(4,-3)$
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a science fair poster is a rectangle 48 in long and 36 in wide. some of…
12
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a rectangular floor is 21 ft long and 12 ft wide. carmen wants to carpe…
28
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you start at (-1, -4). you move down 1 unit and left 3 units. where do …
(-4, -5)
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15. the coordinates of △pqr and its image are shown. describe the trans…
Reflection over the $x$-axis.
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what is the volume of this object? cubic units
60
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the coordinates of △xyz and its image are shown. describe the transform…
The transformation is a reflection over the x - axis.
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four quadrant ordered pairs tell what point is located at each ordered …
1. F 2. M 3. E 4. S 5. P 6. X 7. V 8. D 9. \((-5,-4)\) 10. \((-1,1)\) 11. \((6,8)\) 12. \((-8,1)\) 13. \((-6,-6)\) 14. \((-4,5)\) 15. \((-1,7)\) 16. \((3,-3)\) 17. Plot 8 units ri…
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fill in the blank under each figure below. cube triangular prism tetrah…
Number of faces (cube) = 6 Number of edges (triangular prism) = 9 Number of vertices (tetrahedron) = 4
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complete the sentence below. a rhombus is ______ a trapezoid. always so…
C. never
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under a transformation, a preimage and its image are both squares with …
Yes, the transformation is a rigid motion because it preserves angle measures (90) and side lengths (3).
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fill in the blank under each figure below. rectangular prism square pyr…
Number of faces for rectangular prism = 6 Number of edges for square pyramid = 8 Number of vertices for octahedron = 6
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4. the coordinates of △xyz and its image are shown. describe the transf…
The transformation is a reflection over the x - axis.
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fill in the blank under each figure below. triangular prism octahedron …
Number of faces (triangular prism) = 5 Number of edges (octahedron) = 12 Number of vertices (tetrahedron) = 4
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complete the mapping of the vertices of △def. d(2, -4) → d e(1, -1) → e…
D'(-4,2) E'(-1,1) F'(1,5) $(y,x)$
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example 3 use the law of syllogism to draw a valid conclusion from each…
no valid conclusion 13.
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12. polygon defg has coordinates d(2, 4), e(-3, -2), f(-5, 1), and g(3,…
D'(-2, 4), E'(3,-2), F'(5,1), G'(-3,-1)
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graph the points (0.5, -3) and (-3, 4) on the coordinate plane. click t…
The points $(0.5,-3)$ and $(-3,4)$ are graphed on the coordinate - plane as described above. (Since this is a graphing task and can't be directly shown in text, the instructions o…
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determined that the casting director would notice her, the would - be a…
1. flamboyant 2. foible 3. innocuous 4. exhort 5. repugnant 6. magnanimous 7. masochist 8. rancor 9. meticulous 10. recriminations
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5 given: $overline{db}$ bisects $angle abc$, $angle1$ and $angle2$ are …
2. $\angle2 = \angle3$; 3. Definition of complementary angles; 4. Transitive property of equality; 5. Substitution property (since $\angle2=\angle3$); 6. $m\angle1=m\angle4$; 7. D…
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give a pair of alternate exterior angles, a pair of alternate interior …
(a) $\angle1$ and $\angle7$ (b) $\angle2$ and $\angle8$ (c) $\angle1$ and $\angle3$