幾何
三角形、圓、解析幾何與證明題。
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15. find $m\\angle rtv$. consecutive=180 $(6x + 1)^\\circ$ $(x + 4)^\\c…
$29^\circ$
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$a=\\frac{1}{2} \\times b \\times h$ a triangle has a base of 18 in and…
63 in² (matches the red option: 63 in²)
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11. use figure 5 to find $m\\angle lmn$ and $m\\angle lkn$ 12. the side…
1. $\triangle ABC$ is a right triangle. Justification: $9^2 + 12^2 = 15^2$, satisfying the Pythagorean theorem, so $\angle B = 90^\circ$. 2. Quadrilateral $DPEB$ is a square. Just…
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the masters i: leonardo da vinci quiz complete 1 2 what symbolism does …
d. all of the above
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14. find $m\\angle cbf$. corresponding $\\cong$ $\\angle cbf=(9x + 2)^\…
$83^\circ$
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10. use figure 4 to prove that $\triangle wxy cong \triangle wzy$. (seg…
$\triangle WXY \cong \triangle WZY$ is proven by the HL congruence theorem for right triangles.
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a triangle is placed in a semicircle with a radius of 4 ft, as shown be…
$9.12$ square feet
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a rectangle is removed from a right triangle to create the shaded regio…
$16.5\,\text{square meters}$
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which formula finds the area of a trapezoid? $a=\\frac{a+b}{2}+h$ $a=\\…
D. $A=\frac{a+b}{2} \times h$
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$a=\\frac{1}{2}×b×h$ a triangle has base 10 cm and height 6 cm. what is…
30 cm² (corresponding to the green option with value 30)
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a figure is made of two rectangles. what should you do? find the area o…
A. Find the area of each rectangle and then add them together
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what is the area of the basement floor? round to the nearest hundredth …
Area of basement floor: $122.38$ square yards Total cost of carpet: $\$3365.45$
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$a = \\frac{a+b}{2} \\times h$ a trapezoid has bases 8 and 14 and heigh…
66
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find the missing side of the triangle. write your answer in simplified …
11. $\boldsymbol{\sqrt{14}}$ ft 12. $\boldsymbol{\sqrt{19}}$ m 13. $\boldsymbol{\sqrt{2}}$ m 14. $\boldsymbol{\sqrt{3}}$ mi 15. $\boldsymbol{\sqrt{61}}$ units 16. $\boldsymbol{10}…
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formula for circumference: $c=\\pi r$ $c=\\pi d^{2}$ $c=\\pi r^{2}$ $c=…
$C=2\pi r$ (the formula in the red box)
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a parallelogram has base 15 cm and slanted side 13 cm. the height is 8 …
120 cm²
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which formula finds area of a circle? $a=2\\pi r$ $a=\\pi d$ $a=\\pi r$…
Red box: $A=\pi r^2$
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for each figure below, determine if it has rotational symmetry. if it d…
1. Sun-like figure: Rotational symmetry? Yes, Angle? $36^\circ$ 2. Right triangle: Rotational symmetry? No, Angle: (N/A)
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a circle has diameter 10. radius is: 5 1 2 10
5 (the orange box option)
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the length of a rectangle is 5 in longer than its width. if the perimet…
length: 17 in width: 12 in
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the length of a rectangle is three times its width. if the perimeter of…
length: 21 in width: 7 in
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the length of a rectangle is 4 in longer than its width. if the perimet…
length: 15 in width: 11 in
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what two measurements are required to find triangle area? perimeter and…
Base and height
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review & refresh write a linear function that relates y to x. 1. 2. | x…
1. $\boldsymbol{y=\frac{1}{2}x - 1}$ 2. $\boldsymbol{y=-\frac{2}{3}x + 5}$ 3. Dilation image vertices: $A'(-9,3)$, $B'(-3,9)$, $C'(-3,3)$; Type: Enlargement 4. Dilation image vert…
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what is the area of this figure? if necessary, round your answer to the…
236.54 square kilometers
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distance the player traveled? module 13 • lesson 13.1 23. use repeated …
A. $\tan P = 2.4$, $\tan Q = \frac{5}{12} \approx 0.42$ B. One possible set: 20 m, 48 m, 52 m (any scaled version of 10 m, 24 m, 26 m is valid) --- ### Problem 24
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find the perimeter of the polygon if $m\\angle a = m\\angle c$. $p = ?$…
43 ft
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try it! what is the circumference of the rim of a basketball hoop with …
First blank: 2, second blank: 18, third blank: 56.52 When the diameter is doubled, the circumference also doubles, because circumference is directly proportional to diameter ($C=\…
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distance the player traveled? module 13 • lesson 13.1 23. use repeated …
A. $\tan P = 2.4$, $\tan Q = \frac{5}{12} \approx 0.42$ B. One possible set: 20 m, 48 m, 52 m (any positive scale factor works) --- ### Problem 24
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3 select the correct answer from the drop-down menu. compare the steps …
segment BC
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3. what is the area of the tessellation? $96\\ \\text{in}^2$ $14,976\\ …
1,152 in² (assuming 12 small rectangles as a corrected count matching options)
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2. which of the following is not one of the ways that a tessellation ca…
C. Dilation
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3 select the correct answer from the drop-down menu. compare the steps …
1. When using paper to construct the perpendicular line, the paper is folded so that **point C lies on the fold** and the two sides of line AB will lie exactly on top of each othe…
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1. what is a tessellation?○ a tessellation is a collection of geometric…
C. A tessellation is a plane that is covered by a pattern of geometric shapes with no gaps and no overlaps.
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3 select the correct answer from the drop-down menu. compare the steps …
First dropdown (paper folding): point C lies on the fold Second dropdown (reflective device): point A coincides with point B
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4. which is not a tessellation?
B. The image with blue/light blue connected oval shapes and white gaps between them
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3. which regular polygon can completely tessellate a plane?○ a regular …
a regular hexagon
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2. in the tessellation below, what transformation(s) maps brick a onto …
a glide reflection
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1. which is not a necessary characteristic of a tessellation?○ using sh…
A. using shapes with straight sides
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(i) fill in the missing side lengths in the special triangles in the bl…
- (■): No valid solution (invalid triangle) - (I): $4\sqrt{2}$ (not in given options) - (F): $\sqrt{6}$ - (D): No valid solution (invalid triangle) - (E): $3$ - (W): $2$ - (N): $7…
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3. what transformations are shown from the smaller image to the larger …
dilation by a scale factor of 2 and rotation of 90° counterclockwise
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2. the ferris wheel in the image below has 10 compartments. a couple is…
rotation
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1. which transformations would map the triangle below into quadrant 4?○…
Rotate about the origin 180° clockwise and then reflect across the y-axis.
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write an equation of the parabola in vertex form that passes through (1…
$\frac{3}{50}(x-3)^2 + 2$
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applying the sine ratio what is the length of the side opposite ∠d? uni…
Length of side opposite ∠D: 5 units $\sin(D) = \frac{5}{13}$
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write an equation of the parabola in vertex form. an equation of the pa…
$\frac{1}{4}(x-4)^2-1$
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2. a point a (x, y) is translated 7 units to the left and 2 units up. w…
A. $(x-7, y+2)$
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6. the figure below has reflectional symmetry, double-click on the figu…
1. A vertical line through the center of the figure, splitting it into left and right mirror-image parts. 2. A horizontal line through the center of the figure, splitting it into …
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5. the figure below has rotational symmetry, what is the angle of rotat…
$72^\circ$
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what is the measure of $angle p$ to the nearest whole degree?$\bigcirc$…
57° (Option C)
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3. what type of symmetry does the figure below have?4. what type of sym…
3. ONLY Rotational 4. Neither Rotational nor Reflectional
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3. in $\\triangle bdc, a^{2}=(b - x)^{2}+h^{2}$ 3. pythagorean thm. 4. …
substitution
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find the measure of $angle j$, the smallest angle in a triangle with si…
34°
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rotational and reflectional symmetry assignment resources: help video o…
1. ONLY Reflectional 2. Both Rotational and Reflectional
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organize the following terms into those that do and do not relate to th…
## Relates to the Pythagorean Theorem - leg - hypotenuse - right triangle ## Does NOT directly relate to the Pythagorean Theorem - scientific notation - radius - volume
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what is the value of n to the nearest whole number?○ 10○ 13○ 18○ 21law …
13
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homework 12. solve for t $8t + 7$ $2s + 25$ $9t - 2$ $8t + 7=9t - 2$ $-…
$t=9$
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use the image to answer the question.(2 points)first, we will use side …
First blank: 3 cm and 4 cm Second blank: 13 cm
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on which triangle can the law of cosines be applied once to find an unk…
# Explanation: ## Step1: Recall Law of Cosines use case The Law of Cosines can be used to find an unknown angle when **all three side lengths of the triangle are known**, or when …
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4. what is the angle of rotation for the following figure?$90^{\\circ}$…
$\boldsymbol{60^\circ}$ (Option: $\boldsymbol{60^\circ}$)
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which equation correctly uses the law of cosines to solve for the missi…
$p^2 = 6^2 + 8^2 - 2(6)(8)\cos(39^\circ)$ (the second option)
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3. how many lines of symmetry does the following figure have?options:16…
4 (Option: ○ 4)
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the law of cosines is used to find the measure of $angle z$. to the nea…
$51^\circ$ (Option C)
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what is the slant height of this square pyramid?hint: dont forget to us…
17 (Option: ○ 17)
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8.6 special right triangles 30-60-90 3) $x$ $y$ $\\frac{7\\sqrt{3}}{2}$…
$x=7$ $y=\frac{7}{2}$
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2. how many lines of symmetry does the following figure have? options: …
2
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apply the pythagorean theorem to find the length between the two points…
7.21 (Option A)
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on which triangle can the law of cosines be used to find the length of …
The second triangle (with sides 12, 7, included angle $57^\circ$ at vertex S)
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8.6 special right triangles 30-60-90 7) find the values of x and y for …
$x=4\sqrt{3}$ $y=2\sqrt{3}$
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solving a navigation problem a ferry transports passengers to three dif…
7.7 miles
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applying the law of cosines to navigation a pilot flies 720 miles from …
918 miles
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$30 + 40$ + $8 + 7$ $70 + 15$ calculate the result of the above arithme…
85
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applying the law of cosines to surveying a surveyor measures the length…
$\cos^{-1}(0.125) = 83^\circ$
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2. which set of binomials were multiplied together to produce the produ…
$\boldsymbol{(2x + 1)(x + 1)}$
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determining when to use the law of cosines which of these triangles can…
The second triangle (with sides 12, 8, included angle $138^\circ$ and missing side $x$)
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in $delta def$, $de = 11$, $ef = 9$, and angle $e = 140^{circ}$. which …
$e^2 = 11^2 + 9^2 - 2(11)(9)\cos(140^\circ)$
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g.3 6. parallelogram wtpy is shown below. it goes through a translation…
A. Line segment TP is congruent to line segment SZ. B. The measure of angle T equals the measure of angle R.
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if a triangle has sides measuring 50 in., 65 in., and 45 in. in length,…
No, because 4,525 does not equal 4,225.
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$\\overline{qr}$ is tangent to circle p at point q. what is the measure…
37°
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4. what is the formula for the area of a segment? $a_{segment}=a_{secto…
A. $A_{\text{segment}} = A_{\text{sector}} - A_{\text{lower triangle}}$
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tangents to the circle are congruent and form a square. the perimeter o…
B. 3 cm
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the chords intersect at point u. what is the value of y? ○ 2 ○ 4 ○ 6 ○ …
6
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g.2 5. point t is located at (-8, 5). point t is rotated $90^\\circ$ co…
The coordinates of $T''$ are $\boldsymbol{(5, -8)}$
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in circle y, what is $mwidehat{tu}$? ○ $82^circ$ ○ $100^circ$ ○ $106^ci…
$66^\circ$ *Note: This result does not match the provided options, indicating a potential error in the problem's given values or options. The calculation follows the tangent-chord…
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3. what is the area of major sector dfe? 8.7 cm 260° 158.49 square cm 2…
171.69 square cm
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what is the center of a circle represented by the equation $(x-5)^2+(y+…
(5, -6)
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quiz 11.7.3: spheresquestion 1what is the surface area of the sphere be…
1. A. $324\pi$ units$^2$ 2. C. $144\pi$ units$^2$ 3. C. $576\pi$ units$^2$ 4. D. $484\pi$ units$^2$
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triangle bcd is isosceles and $overline{bc} cong overline{bd}$. what is…
D. $160^\circ$
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2. how would you classify the shaded region of the circle? a segment an…
D. A sector
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the face of a clock is divided into 12 equal parts. the radius of the c…
- The circumference of the clock is approximately 62.8 inches. - The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°. - The length of the minor…
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the measure of central angle xyz is $1.25\\pi$ radians. what is the are…
$40\pi$ units$^2$
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consider circle n with radius 30 cm and $\theta = \frac{pi}{6}$ radians…
15.7 centimeters
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1. consider a segment of a circle. which of the following statements ab…
A. A segment is bound by a major arc.
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consider circle c with angle acb measuring $\frac{3pi}{4}$ radians. if …
12 inches
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$overline{uv}$ and $overline{rv}$ are secant segments that intersect at…
$2\frac{1}{2}$ units
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circle o has a circumference of approximately 28.3 cm. what is the appr…
A. 4.5 cm
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line segment bd passes through the center of circle c, bh = a, and hd =…
12.5 units
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line segment wx is the radius of circle x, and line segment zy is the r…
$324\pi$ units²
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use the image to answer the question.can we use the pythagorean theorem…
Yes
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fiona draws a circle with a diameter of 14 meters. what is the area of …
49π m² (Option D: $49\pi \, m^2$)