幾何
三角形、圓、解析幾何與證明題。
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find the value of the variable and the measure of each labeled angle. p…
\(x = 37\)
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find the values of the variables. $x = $y = (simplify your answer.)
$x = 49$ $y = 56$
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if ef = 8x + 6, fg = 9x - 17, and eg = 18x - 19, what is fg? simplify y…
55
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name line m in a different way use proper notation when entering your a…
\(\overleftrightarrow{AE}\)
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17. dig deeper! the houses are identical. a. what is the length of side…
a. 32 ft b. $\angle N$ c. $AB = 12$ ft, perimeter of $ABCDE = 80$ ft
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figure wxyz is rotated 90° counterclockwise around the origin to form f…
9. $5$ 10. $-1$ 11. (No answer as original coordinates of $Y$ not given) 12. (No answer as original coordinates of $Z$ not given)
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figure wxyz is rotated 90° clockwise around the origin to form figure w…
Since the original coordinates of points $W$, $X$, $Y$ and $Z$ are not given, we cannot provide specific numerical answers for the coordinates of $W'$, $X'$, $Y'$ and $Z'$ after r…
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performing a rotation in the coordinate plane > fill in the missing num…
1. $2$ 2. $4$ 3. $1$ 4. $3,8$ 5. $- 5$ 6. $-4$ 7. $6$ 8. $8,-3$
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find the measures of the labeled angles. (x + 100)° 6x° (x + 100)° = 12…
$x = 20$, $6x=120$
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find the measures of the labeled angles. (x + 100)° 6x° (x + 100)° = □°…
$120$
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find m∠1, m∠2, and m∠3. explain your reasoning. m∠2 = by the m∠1 = by t…
\(m\angle1 = 133^{\circ}\) by the corresponding - angles postulate \(m\angle2 = 133^{\circ}\) by the vertical - angles theorem \(m\angle3 = 47^{\circ}\) by the linear - pair postu…
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find the measures of the labeled angles. 3x° = 63° (type a whole number…
\(3x = 63\), \((84 - x)=63\)
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find the measures of the labeled angles. 3x° = □° (type a whole number.)
63
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in the figure below, the measure of ∠1 = 4x°, the measure of ∠2 = y°, a…
$x = 18$ $y = 108$
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2. the slope of a graph may also be considered a ratio of “changes”. wh…
The ratio of the change in the $y$ - values (vertical change) to the change in the $x$ - values (horizontal change) makes up the slope ratio.
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figure wxyz is rotated 90° clockwise around the origin to form figure w…
1. $W'(5,6)$ 2. $X'(4,1)$ 3. $Y'(-6,6)$ 4. $Z'(3,7)$
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in the figure below, the measure of ∠1 = 4x°, the measure of ∠2 = y°, a…
$x = 18$
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problems 1 - 2: here is a polygon. 1. draw a scaled copy of the polygon…
1. Follow the side - length or coordinate - multiplication method to draw the scaled polygon with a scale - factor of 2. 2. The perimeter of the scaled copy is 2 times the perimet…
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area of composite figures - set 3 find the area of the composite figure…
Area of figure A: 219 Area of figure B: 125 Area of figure C: 408 Area of figure D: 78
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in the figure below, the measure of ∠4 = 90°, the measure of ∠5 = 65°, …
$m\angle2 = 25^{\circ}$, $m\angle3=65^{\circ}$
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find m∠1, m∠2 and m∠3. explain your reasoning. m∠1 = m∠3 = m∠2 = 80° 10…
\(m\angle1 = 80^{\circ}\) by the Corresponding Angles Theorem \(m\angle3 = 80^{\circ}\) by the Alternate Exterior Angles Theorem \(m\angle2 = 100^{\circ}\) by the Linear - Pair Po…
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find the value of x . show your steps. step 1: (8x + 9)°+99°= step 2: 8…
Step 1: \((8x + 9)^{\circ}+99^{\circ}=180^{\circ}\) Step 2: \(8x + 108 = 180\) Step 3: \(8x = 72\) Step 4: \(x = 9\)
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area of composite figures - set 3 find the area of the composite figure…
- E: 132 - G: 522 - F: 330 - H: 267
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2. a scale drawing of a lake has a scale of 1 cm to 80 m. if the actual…
20 cm
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if angle w measures 45°, what are the measures of the other angles in t…
∠U = 45°, ∠V = 45°, ∠X = 135°, ∠Y = 135°, ∠Z = 135°
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area of composite figures - set 3 find the area of the composite figure…
First figure: 282 Second figure: 403
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activity the image shows a transversal passing through two parallel lin…
1. $\angle S$ and $\angle T$ 2. $\angle T$ and $\angle U$ 3. $\angle U$ and $\angle V$ 4. $\angle V$ and $\angle S$ 5. $\angle W$ and $\angle X$ 6. $\angle X$ and $\angle Y$ 7. $\…
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activity in this activity, you will explore the relationships between t…
| Angle in Upper Intersection | Corresponding Angle in Lower Intersection | | ---- | ---- | | A | E | | B | F | | C | G | | D | H |
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area of composite figures - set 2 find the area of the composite figure…
C: 370 E: 342 D: 370 F: 225
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complete the steps to find the value of x. 72° (7x + 24)° □+(7x + 24)=1…
The first blank is 72, the second blank is 96, the third blank is 84, the fourth blank is 12.
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lesson practice 2.1.03 problems 1 - 2: here is a polygon. 1. draw a sca…
1. Follow the rule of multiplying vertex coordinates by 2 to draw the scaled polygon. 2. Use \(P_{scaled}=2P\) and \(A_{scaled}=4A\) after finding \(P\) and \(A\) of the original …
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complete the steps to find the value of x. 128° 2x = x =
$2x = 128$ $x = 64$
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area of composite figures - set 2 find the area of the composite figure…
G. 522 H. 267 I. 238 J. 240
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area of composite figures - set 1 find the area of the composite figure…
I: 763 A: 346 J: 343 B: 458
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what is the total area of her room? kaceys room is 9 feet long by 7 fee…
63 square feet
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the area of a square is 49 square feet. what is the measure of one of t…
7 feet
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area of composite figures - set 1 find the area of the composite figure…
E: 396 G: 348 F: 363 H: 726
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10 what is true for an image and a preimage in a reflection? a the imag…
C. The image and the preimage have different orientations.
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the area of a square is 49 square feet. what is the measurement of one …
C. 7 feet
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in the graph below, what is the line of reflection for △xyz and △xyz? a…
C. \(x = 2\)
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refer to the coordinate grid. find point y on cd such that the ratio of…
A. \((1,\frac{1}{3})\)
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the figure on the right is a scaled copy of the figure on the left. wha…
Corresponding side: $XV$ Scale factor: $\frac{1}{2}$
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the figure on the right is a scaled copy of the figure on the left. ans…
Corresponding side: $PS$ Scale factor: $\frac{1}{2}$
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a picture on a wall is 4 feet wide and 4 feet long. the figure shows th…
16
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a (1,7) b (8,7) d (1,2) c (8,2) what is the coordinate for b after a re…
$(-6,3)$
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word problem involving the pythagorean theorem in three - dimensions. a…
(a) \(a\approx15.2\) ft (b) \(b\approx17.2\) ft
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undefined term in geometry. use the number line for items 6 - 9. 6. wha…
6. \(AB = 20\) 7. The coordinate of the mid - point of \(AB\) is \(-2\). We used the mid - point formula \(M=\frac{x_1 + x_2}{2}\) with \(x_1=-12\) and \(x_2 = 8\). 8. The coordin…
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the figure on the right is a scaled copy of the figure on the left. ans…
Which side in the figure on the right corresponds to segment $FG$: ML What is the scale factor: $\frac{1}{2}$
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a tent has the shape of an isosceles triangular prism. the campers add …
(a) \(a\approx15.2\) ft (b) \(b\approx17.2\) ft
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graph the inequality below on the number line. x<5
Use an open circle at 5 and shade the number line to the left of 5.
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6 what is the line of reflection for the two polygons? a y = x b x = 1 …
B. \(x = 1\)
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exponents, polynomials, and radicals word problem involving the pythago…
(a) $a = 15$ in (b) $b\approx15.8$ in
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chantel graphs △s and △t. the corresponding angles are congruent. the s…
A dilation with a scale factor of 5 centered at a chosen point (e.g., the origin) will map $\triangle S$ onto $\triangle T$.
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the area of a square is 9 square feet. what is the side length?
3 feet
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5 what is the image of a(3, -1) after a reflection across the y - axis …
A. (-3, -1)
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refer to the coordinate grid. find point x on ab such that the ratio of…
A. \((4,\frac{5}{4})\)
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3. draw a scaled copy of figure abcd using a scale factor of 1.3.
Plot the scaled - copy of figure ABCD with vertices obtained by multiplying the coordinates of the original vertices by 1.3.
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a rectangle has two sides that are 6 inches in length and two sides and…
42 square inches
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the figures below are similar. use proportions to find the length of m.…
$m = 5$
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janice plots △abc in the coordinate plane. her teacher asks her to rota…
Use the rule $(x,y)\to(y, - x)$ to find the correct coordinates of $A'$, $B'$, $C'$ after a 270 - degree counter - clockwise rotation about the origin.
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solve the inequality and graph the solution. 7x - 2>6x - 4. choose the …
D
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the figures below are similar. use proportions to find the length of s.…
$12$
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frank is drawing a treasure map using a scale of 1 cm to 10 m. he wants…
2
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9. a sector of a circle has central angle 36° and arc length 7.8 cm. fi…
$48$ $cm^{2}$
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question the figure on the right is a scaled copy of the figure on the …
The scale factor is the ratio of the length of the corresponding side in the right - hand figure to the length of the side $KH$ in the left - hand figure. Without specific length …
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select the coordinates of point x on rs that is ⅙ of the distance from …
B. \((-3,1\frac{1}{3})\)
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select the coordinates of point x on ab that is ⅕ of the distance from …
C. \((-3.6,-2.2)\)
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describe a real - world object that can be modeled by a rectangular pri…
A real - world object like a shoe - box can be modeled as a rectangular prism. The volume formula is \(V=l\times w\times h\), where \(l\) is length, \(w\) is width and \(h\) is he…
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given the quadrilateral, find the perimeter. let the units be in feet.
500 feet
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the midpoint of jk is m(5.5, 8). one endpoint is k(9, 12). find the coo…
$(2,4)$
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which angle number represents the linear pair of ∠txs? answer attempt 1…
3
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given the quadrilateral, find the perimeter. let the units be in feet.
400 feet
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what is the smallest angle of rotational symmetry for a square? 45° 90°…
90°
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if m∠lrk = 84°, then what is m∠jrm? answer attempt 1 out of 2 m∠jrm =
$84$
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uv has a midpoint at m(-2, 1.5). point u is at (14, 3). find the coordi…
$(-18,0)$
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a regular polygon has 15 sides. which is a possible angle of rotational…
$72^{\circ}$
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for each set of figures, figure a is rotated around the origin to form …
First pair: 90° counterclockwise Second pair: 180° clockwise (or 180° counterclockwise) Third pair: 270° counterclockwise
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which type of triangle will always have at least 1 - fold reflectional …
D. isosceles triangle
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which angle number represents an angle vertical to ∠fhc? answer attempt…
$5$
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which angle of rotation is an angle of rotational symmetry for all figu…
D. 360°
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notah draws figure x in the coordinate plane. then he performs a sequen…
a. A reflection across the y - axis followed by a translation 1 unit up. b. Another possible sequence could be a translation 1 unit up first followed by a reflection across the y …
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how many lines of reflectional symmetry does an equilateral triangle ha…
C. 3
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which transformation is not isometric?
Dilation
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suppose m is the mid - point of $overline{jk}$, $mk = 5x + 5$, and $jk …
$x = 3.8$
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if m∠wyt = 108°, then what is m∠uyv?
$108^{\circ}$
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the midpoint of (overline{tu}) is (m(-11.5, -4.5)). one endpoint is (t(…
$(-7,-17)$
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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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which angle number represents ∠uxr? answer attempt 1 out of 2 submit an…
3
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the midpoint of $overline{cd}$ is $m=(1, 3)$. one endpoint is $c=(-1, 7…
$(3,-1)$
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how can a regular hexagon be folded to show that it has reflectional sy…
Fold the hexagon along a line from a vertex to the midpoint of an opposite side. Fold the hexagon along a line that bisects two vertex angles.
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what is the translation rule for sliding triangle abc? (use parenthesis)
(x,y)→(x - 6,y + 2)
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what is the order of rotational symmetry for a rhombus? 1 2 3 4
2
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question 8 lesson 1 - 4 practice: midpoints and bisectors the point q i…
$7$
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which angle number represents ∠sxu? answer attempt 2 out of 2
3
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find the location of b, the midpoint of ac. location of b:
-3
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which angle number represents ∠sxu? answer attempt 1 out of 2
3
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find the location of b, the mid - point of $overline{ac}$. location of …
5
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if m∠uxr = 80°, then what is m∠sxt? answer attempt 1 out of 2 m∠sxt =
$80$
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find the location of b, the mid - point of ac. question 6 lesson 1 - 4 …
\(5.5\)
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which angle number represents the linear pair of ∠tyw?
5