Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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for what angles of rotation does the figure map onto itself? a. an equi…
The angles of rotation about the center that map an equilateral triangle onto itself are \(120^{\circ}\) and \(240^{\circ}\).
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2. in the accompanying figure, \\( \\overrightarrow{ad} \\) is tangent …
\(BE = 10\)
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create zh ii g. based on these transformations, which statement is true?
\(\overline{FH} = 2\overline{FE}\), \(\overline{FG} = 2\overline{FI}\), and \(\overline{HG} = 2\overline{EI}\); \(\triangle EFI\sim\triangle HFG\)
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the angle $\\frac{12\\pi}{7}$ is in standard position. what quadrant is…
d. Four
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are quadrilaterals abcd and efgh similar? yes, quadrilaterals abcd and …
Yes, quadrilaterals \(ABCD\) and \(EFGH\) are similar because a translation of \((x + 2,y + 4)\) and a dilation by the scale factor of \(2\) from point \(D'\) map quadrilateral \(…
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try it! 2.b. how many lines of symmetry does the figure have? how do yo…
The figure (an isosceles trapezoid) has \(1\) line of symmetry. We know we have found them all by checking all possible orientations (horizontal, vertical, diagonal) of lines that…
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which set of transformations would prove \\( \\triangle gfe \\sim \\tri…
Reflect $\triangle GHI$ over $x = - 2$, and dilate $\triangle G'H'I'$ by a scale factor of 2 from point $G$.
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given: abcd is a parallelogram. prove: ( mangle a + mangle b + mangle c…
addition
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try it! 2.a. how many lines of symmetry does the figure have? how do yo…
The figure (a rectangle) has 2 lines of symmetry. We know we have found them all by checking all possible directions (horizontal, vertical, and diagonal) and verifying that only t…
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∠b ≅ ∠x ∠a ≅ ∠z ∠c ≅ ∠x ∠y ≅ ∠b
$\angle Y \cong \angle B$
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convert the angle $\frac{pi}{4}$ from radians to degrees. enter your an…
45
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5. other than translation, what transformation is used to create this f…
glide reflection
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segments eg and ih intersect at point f
Segments $EG$ and $IH$ intersect at point $F$
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the angle 270° is in standard position. what axis is its terminal side …
d. negative y - axis
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4. other than translation, what transformation is used to create this f…
glide reflection
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clients reenacting earlier conflicted relationships in their lives in t…
transference relationship
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3. other than translation, what transformation is used to create this f…
glide reflection
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suppose the angle 175° is in standard position. what quadrant is its te…
B. Two
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δabc was dilated from the origin by a scale factor to create δabc. whic…
Side \(AB\) is proportional to side \(A'B'\)
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2. other than translation, what transformation is used to create this f…
horizontal reflection
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given: abcd is a parallelogram. prove: ( mangle a + mangle b + mangle c…
The second blank (the side used as a transversal for \(\angle B\) and \(\angle C\)) should be filled with \(BC\).
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1. what transformation is used to create this frieze pattern? vertical …
horizontal reflection
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δpqr is dilated from the origin at a scale factor of \\( \\frac { 1 } {…
similar; proportional; congruent
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given rectangles lmno and pqrs, which statement explains a way to deter…
Verify corresponding pairs of sides are proportional by dilation.
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try it! 1. b. what transformations map the figure onto itself?
A \(180^{\circ}\) rotation about its center, a \(360^{\circ}\) rotation about its center, and a reflection across its horizontal line of symmetry.
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given: abcd is a parallelogram. prove: ( mangle a + mangle b + mangle c…
First blank: \(D\) (because when \(AD\) is a transversal for \(AB\parallel DC\), the angle that forms same - side interior angles with \(\angle A\) is \(\angle D\)). Second blank:…
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1. a. what transformations map the figure onto itself? 180 degrees
A \(180^{\circ}\) rotation about the center of the figure, and reflections across the vertical and horizontal lines passing through the center of the figure.
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if ∠1≅∠2, and ∠3≅∠2, then _____________. your answer if ∠j≅∠m, and ∠p≅∠…
\(\angle1\cong\angle3\); \(\angle J\cong\angle P\); \(\angle A\cong\angle B\); \(\angle6\cong\angle3\)
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the origin. which equation explains the relationship between \\( \\over…
\( \overline{A''B''}=\frac{\overline{AB}}{2} \)
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given: circle x with radius r and circle y with radius s prove: circle …
| Statements | Reasons | |--|--| | circle with center \( X \) has radius \( r \); circle with center \( Y \) has radius \( s \) | Given | | translate \( X \) to \( Y \) | Translat…
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ing the sums of the angle measures in quadrilaterals rectangle abcd has…
\(360\)
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ring the sums of the angle measures in quadrilaterals rectangle abcd ha…
\(360^{\circ}\)
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the sums of the angle measures in quadrilaterals rectangle abcd has fou…
\(360\)
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which best explains whether or not (\triangle abccong\triangle lmn)? th…
The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map \(\triangle ABC\) onto \(\triangle LMN\)
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g the sums of the angle measures in quadrilaterals rectangle abcd has f…
\(C\)
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find the value of x. 3) 4) 5)
3) \(x = 60\) 4) \(x = 9\) 5) \(x = 14\)
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exploring the sums of the angle measures in quadrilaterals rectangle ab…
\(360^{\circ}\)
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triangle pqr was dilated according to the rule ( d_{o,2}(x,y)\to(2x,2y)…
\(\angle R\) corresponds to \(\angle P'QQ'\) and Side \(RQ\) corresponds to side \(QQ'\)
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triangle abc is similar to triangle jkl, which is formed using (overlin…
\(6\) units (assuming correct grid - based counting where \(BC = 2\) units (from \(y = 1\) to \(y = 3\)) and \(KL\) is \(6\) units (from \(y = 0\) to \(y=-6\)) considering the sim…
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understanding classifications of quadrilaterals complete the statements…
A square is always a parallelogram. A rectangle is never a trapezoid. A rhombus is sometimes a square. A quadrilateral is sometimes a kite.
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triangle abc is rotated 45° about point x, resulting in triangle efd. i…
\(3.6\mathrm{cm}\) (the second option)
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the vertices of triangle abc are a(5,2), b(-1,-6) and c(1,5). if \\( \\…
C. \(D(-5,3)\) and \(E(-5,1)\)
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consider the system of equations shown: $$left{\begin{array}{l}y = 6 - …
a. The system has one solution. We know this because when we solve the system algebraically (by substitution as shown above), we find a unique pair of values for \( x \) and \( y …
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triangles abc and ade are similar, as shown. which must be true? check …
\(\frac{AC}{AE}=\frac{BC}{DE}\), \(\frac{AC}{AD}=\frac{AB}{AE}\), \(DE = 2BC\), \(AE = 2AC\)
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solve for x. 1) 2)
1) \(x = 10.5\) 2) \(x = 8\)
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learning goals from lesson 3.3 ✓ i can graph quadratic functions of the…
A. The axis of symmetry is \(x = 1\). The vertex is \((1,-4)\)
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what is the scale factor of the dilation of triangle def? ○ \frac{3}{10…
\(\frac{3}{7}\)
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describing an object which describes the pedestrian crossing sign shown…
The sign is a parallelogram because both pairs of opposite sides are parallel.
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triangle abc is congruent to triangle fde, and both triangles have the …
\(2\)
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1. read the email by mathieu talking about his free - time activities.s…
2a. Mathieu is 13 years old. 2b. Mathieu likes playing football with his friends. 2c. When it's raining, Mathieu prefers reading magazines or playing video games. 2d. Mathieu find…
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a monument casts a 36 - foot shadow, while a 5 - foot person casts a 4 …
\( 45\)
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a mountain casts a shadow of 120 meters. a 2 - meter pole beside it cas…
\(80\) meters
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in addition to the information given in the drawing, which statement is…
C. \(\overline{QR}\cong\overline{SP}\)
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y(2,-4) is the image of y after a translation along the vector (-4,-3).…
C. \((6,-1)\)
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5. if w(-10,4), x(-3,-1), and y(-5,11). find the length of each side an…
The lengths of the sides are \(WX=\sqrt{74}\), \(XY = 2\sqrt{37}\), \(YW=\sqrt{74}\). \(\triangle WXY\) is an isosceles triangle.
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here the breeze was fitful and allowed the strings of the parachute to …
The dead parachuter is described as having its helmeted head between its knees, held by tangled parachute strings. When the breeze blows, the strings strain taut and the head and …
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given triangles abc and def, which statement explains a way to determin…
Verify corresponding pairs of angles are congruent by translation.
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triangle hij is similar to triangle gfe. find the sine of ∠h. write an …
\(\sin(H)=\frac{20}{29}\)
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5. a quilt is being designed to have a tessellation of parallelograms a…
rotation and translation
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4. which transformation must be applied to object a to place it in the …
translation
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an open box here is a 36 - by - 24 - inch piece of cardboard. a. drag t…
Cut out equal - sized squares from each corner of the cardboard. Then fold up the sides that were adjacent to the cut - out squares.
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12. in \\( \\triangle b c d \\), if \\( \\overline{b c} \\cong \\overli…
\(x = 11\), \(m\angle B=108^{\circ}\), \(m\angle C = 36^{\circ}\), \(m\angle D=36^{\circ}\)
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graph this function. f(x)=\begin{cases}-\frac{1}{2}x - 3 & \text{if }x …
Plot the points \((-4,-1)\), \((-2,-2)\) (for \(x < 0\) part, with an open - circle at \(x = 0\) for this sub - function), and \((0,-3)\), \((1,4)\), \((2,11)\) (for \(x\geq0\) pa…
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8. if △abc is equilateral, find x. 10. if △rst is isosceles, find m∠s
\(x = 13\) ---
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① select the correct verb tense. then identify if the correct verb tens…
will have set (future perfect) # 2.
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1. the pavement at the new shopping mall is being laid. which transform…
translation
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two linear equations are graphed below. which point represents a soluti…
The point where the two lines cross each other (the intersection point) is the solution. From the graph, that is the middle - circle (the one that lies on both lines).
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11. find all missing angles. 11. m∠1=________ m∠2=________ m∠3=________…
\(m\angle1 = 51^{\circ}\) \(m\angle2 = 34^{\circ}\) \(m\angle3 = 85^{\circ}\) \(m\angle4 = 48^{\circ}\) \(m\angle5 = 47^{\circ}\) \(m\angle6 = 74^{\circ}\) \(m\angle7 = 59^{\circ}…
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4. which choice shows only a reflection of object a?
The second option.
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melissa wants to prove that if a transversal crosses parallel lines, th…
2. Corresponding Angles Postulate; 4. \(m\angle CGH\); 5. \(m\angle AFG\)
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dilate (\triangle abc) with a scale factor of 8. enter the new coordina…
\(A'=(-24,16)\), \(B'=(16,8)\), \(C'=(-8,-24)\)
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3. the pavement at the new shopping mall is being laid. which transform…
translation
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2. which transformation must be applied to object a to place it in the …
rotation
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circle c has a radius of 1 inch. arc ab has length \\frac{\\pi}{3} inch…
\(\frac{\pi}{3}\)
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40. aki needs 2 pounds of berries for a recipe. gia weighs the berries …
40. C 41. B 42. D 43. B 44. D 45. A 46. C 47. A, B, D
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warm-up write a number or expression for the volume of each box.
| Box | Volume (cubic units)| |---|---| |A|320| |B|160| |C|\(x^{3}+16x^{2}+64x\)|
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dilate \\( \\triangle abc \\) with a scale factor of 7. enter the new c…
\(A'=(-21,14)\), \(B'=(28,14)\), \(C'=(-7,-7)\)
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which angle forms an alternate exterior pair with angle 8? 1 2 7 4
A. 1
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which angle forms an alternate interior pair with angle 8? 5 6 7 4
5
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which angle forms an alternate interior pair with angle 8? 5 6 7 4
6
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which angle forms a corresponding pair with angle 4? 4 6 8 7
C. 8
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which angle forms an alternate interior pair with angle 2? 3 1 4 2
3
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△abc ~ △def find the value of x. x = ?
\(4\)
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1. a quilt is being designed to have a tessellation of parallelograms a…
rotation and translation
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find the measure of the indicated angle to the nearest degree. ?
$62^{\circ}$
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5. which of the following is not one of the ways that a tessellation ca…
Expansion
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4. what is the area of the tessellation? 16 in 8 in 1920 in² 320 in² 20…
\(1920\) in² (the first option)
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question 8 1 pts directions: classify each triangle by its angles and s…
By Angles: Obtuse triangle; By Sides: Isosceles triangle
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directions: classify each triangle by its angles and sides. 7. 60° 60° …
By Angles: Acute (or Equiangular); By Sides: Equilateral
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the graph of a linear equation is shown below. which point represents t…
The point with \(x = 0\) (the y - intercept) is the middle - left circle (the one on the y - axis).
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directions: classify each triangle by its angles and sides. 6. 20 ft 72…
By Angles: Acute Triangle; By Sides: Scalene Triangle
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directions: classify each triangle by its angles and sides. 5. 34 m 34 …
By Angles: Right - angled triangle; By Sides: Isosceles triangle
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3. what are the dimensions (length x height) of this tessellation? 80 i…
\(80\) in \(\times24\) in
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2. what is a tessellation? a tessellation is a collection of geometric …
A tessellation is a plane that is covered by a pattern of geometric shapes with no gaps and no overlaps.
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quadrilateral fghj is dilated according to the rule ( d_{o,\frac{2}{3}}…
\((-2,-4)\)
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directions: classify each triangle by its angles and sides. 4. 3 mm 3 m…
By Angles: Acute - angled triangle; By Sides: Equilateral triangle
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triangle abc will be dilated according to the rule $d_{f,0.25}(x,y)$, w…
\((1,0)\)
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directions: classify each triangle by its angles and sides. 3. 7 in 123…
By Angles: Obtuse triangle; By Sides: Scalene triangle
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1. what are the dimensions (length x height) of this tessellation? 12 i…
\(144\) in\(\times104\) in
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13 this is a scale drawing of a deck. the actual deck has a perimeter o…
The new scale drawing will have a perimeter of \(8\) units. For example, if the original deck (in the first scale drawing) had side - length relationships, we can divide each actu…