几何
三角形、圆、解析几何与证明题。
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Question was provided via image upload.
\( m\angle 1 = 25^\circ \), \( m\angle 2 = 115^\circ \), \( m\angle 3 = 65^\circ \)
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extra practice level up your skills! find the measure of ∠fgh. m∠fgh = …
\(141\)
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is this a polygon? yes no
no
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extra practice level up your skills! find the measure of ∠acb. a (2x + …
\(120\)
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consider $\\triangle xyz$ in the figure below. the perpendicular bisect…
\( XS = 80 \) \( YZ = 132 \) \( VY = 64 \)
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find the volume of this rectangular pyramid. be sure to include the cor…
\( 72 \) cubic inches (or \( 72\ \text{in}^3 \))
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using the graph, determine the coordinates of the x-intercepts of the p…
$(-7, 0)$ and $(-2, 0)$
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question determine the relationship between the two triangles and wheth…
The two triangles are related by a correspondence of all three pairs of congruent sides (SSS congruence criterion), so the triangles can be proven congruent.
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select the two correct answers. a right rectangular prism has a volume …
B. Base area of 10 square feet and height of 4 feet D. Length of 2 feet, width of 4 feet, and height of 5 feet
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find the midpoint m of the line segment joining the points a = (8, -8) …
$M=(3, -2)$
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what is the length of \\(\\overline{bc}\\)? round to the nearest tenth.
\(14.5\) cm
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question figure 1 and figure 2 below are congruent. which side correspo…
$\overline{JL}$
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what is the length of \\(\\overline{ab}\\)? round to the nearest tenth.…
38.6 m
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which relationship in the triangle must be true? options: $sin(b) = cos…
\( \sin(\text{B})=\cos(90 - \text{B}) \) (the first option among the given options)
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question figure 1 and figure 2 below are congruent. which side correspo…
$\overline{US}$
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question figure 1 and figure 2 below are congruent. which side correspo…
$\overline{WT}$
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which equation can be used to solve for b? there is a right triangle ab…
The equation $\boldsymbol{\tan(30^\circ) = \frac{5}{b}}$ (assuming the left - most option is $\tan(30^\circ)=\frac{5}{b}$) can be used to solve for $b$.
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which equation can be used to solve for b? triangle with right angle at…
\(b=(8)\sin(30^{\circ})\) (the option with \(b=(8)\sin(30^{\circ})\))
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which equation can be solved to find one of the missing side lengths in…
\( \cos(60^\circ)=\frac{a}{12} \) (the first option among the given options with this formula)
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what is the length of \\(\\overline{ac}\\)? round to the nearest tenth.…
\( 10.5 \) m
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what is the approximate value of x? round to the nearest tenth. triangl…
\(4.6\) cm
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question determine the relationship between the two triangles and wheth…
The two triangles are related by having corresponding congruent right angles, one pair of congruent legs, and one pair of congruent hypotenuses, so the triangles can be proven con…
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question figure 1 and figure 2 below are congruent. which side correspo…
$\overline{BC}$
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5) in the parallelogram (labeled with vertices a, b, c, d), angle at a …
$x = 29$ $y = 28$ $\angle A = 116^\circ$ $\angle B = 64^\circ$ $\angle C = 116^\circ$ $\angle D = 64^\circ$
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given $m \\parallel n$, find the value of $x$. (there is a diagram show…
67
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the sum of the measures of the interior angles of a polygon is given. d…
s: - Problem 32: \(12\) sides - Problem 33: \(5\) sides - Problem 34: \(9\) sides - Problem 35: \(23\) sides - Problem 36: \(40\) sides
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in the parallelogram abcd, diagonals ac and bd intersect at point e. th…
$x = 4$ $AE = 16$ $EC = 16$ $AC = 32$ $y = 4$ $BE = 22$ $DE = 22$ $BD = 44$
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6. if abcd ≅ efgh, find the values of x and y. a. x = 7, y = 8 b. x = 8…
c. x = 9.8, y = 41.75 --- ### Problem 7
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4th. find the measure of the unlabeled angles in each item a 30. find t…
$\angle 1 = 34^\circ$, $\angle 2 = 45^\circ$, $\angle 3 = 45^\circ$, $\angle 4 = 135^\circ$ --- #### Part b
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calculate the sum of the interior angle measures of each polygon. 25 a …
\(1260^\circ\) ### Problem 27: A polygon has 13 sides.
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practice problems 1) what is an equation for the line that passes throu…
\(y = 3x+1\) ### Problem 2
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there is a parallelogram (judging from the marks of equal sides and par…
$d = 100$ $\angle D = 100^\circ$ $\angle B = 100^\circ$ $c = 6$ $\angle I = 80^\circ$ $\angle A = 80^\circ$
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1. find the area of a circle with the radius of 7 inches?
The area is $49\pi$ square inches (or approximately 153.86 square inches)
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5. if the circumference of a circle is 25.12 in, then what is the diame…
Diameter: 8 inches Area: 50.24 square inches
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∠vpz and ∠zpy are congruent. find the measure of major arc \\(\\overarc…
\(263^\circ\)
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4) what is the slope of the line? slope = \\frac{vertical change}{horiz…
12
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determining the exact trig function value of an angle what is the exact…
\(-2-\sqrt{3}\)
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trigonometric ratios given right triangle xyz, which correctly describe…
The correct description is "a is adjacent, b is opposite, c is the hypotenuse" (assuming this is one of the options, for example, if the first option is "a is adjacent, b is oppos…
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$\\angle ape$ and $\\angle epd$ are congruent. find the measure of majo…
\(243^\circ\)
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find the area of the parallelogram. 7 in. 14 in. the area of the parall…
98
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1. find the area. use 3.14 for pi and round your answer. (a circle with…
153.86 square meters
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find the area of the parallelogram. image of parallelogram with base 6 …
48
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trigonometric ratios given right triangle mnl, what is the value of cos…
\(\frac{4}{5}\) (assuming the option with \(\frac{4}{5}\) is one of the choices, e.g., if the options are as per the image, the correct option with \(\frac{4}{5}\))
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4. gears on a bicycle are just circles in shape. one gear has a diamete…
The circumference of the larger gear is 2 times bigger than the smaller one, or $4\pi - 2\pi = 2\pi$ inches longer.
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which of the following are pythagorean triples? select all that apply. …
\((9, 12, 15)\), \((8, 15, 17)\), \((5, 12, 13)\), \((6, 8, 10)\)
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trigonometric ratios given right triangle jkm, which correctly describe…
The correct option is the one with "a is the hypotenuse, b is adjacent, c is opposite" (the right - most boxed option).
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gillian is a farmer who is building a pen for some animals. the first s…
\(22.45\) feet
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trigonometric ratios which trigonometric ratios are correct for triangl…
The correct trigonometric ratios are: - \(\sin(C)=\frac{\sqrt{3}}{2}\) - \(\sin(B)=\frac{1}{2}\) - \(\tan(C)=\sqrt{3}\)
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4. find the arc length of each quarter circle, round to one decimal pla…
### Problem 3: a) $18.8$ cm b) $204.2$ mm c) $28.3$ m d) $8.0$ m ### Problem 4: a) $17.3$ m b) $12.9$ cm c) $241.9$ mm
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hannah is a farmer who is building a pen for some animals. the first si…
The length of the third side of the pen is approximately \(17.89\) feet.
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given the following side lengths of a triangle, use the pythagorean the…
The triangle with side lengths \(a = 39\) in, \(b = 89\) in, and \(c = 99\) in is not a right triangle.
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4. a parallelogram has one angle that measures 155°. what are the measu…
The other angles are $25^\circ$, $155^\circ$, and $25^\circ$.
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given the following side lengths of a triangle, use the pythagorean the…
The triangle with side lengths \(a = 55\) in, \(b = 77\) in, and \(c = 78\) in is not a right triangle.
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3. find the area 10 units
$25\pi$ square units (or approximately 78.54 square units)
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based on the diagram, pick the two choices below that represent the exp…
The two choices are $\sin(23^\circ)$ and $\frac{5}{13}$
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julian describes an angle in the triangle using these statements. (over…
\(\angle G\) (assuming the option with \(\angle G\) is the correct one. If the options are labeled, for example, if \(\angle G\) is option A, then the answer would be A. \(\angle …
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4. a parallelogram has one angle that measures 60°. what are the measur…
The other angles are $60^\circ$, $120^\circ$, and $120^\circ$.
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which trigonometric ratios are correct for triangle def? choose three c…
- \( \sin(D)=\frac{24}{25} \) - \( \sin(E)=\frac{7}{25} \) - \( \tan(D)=\frac{24}{7} \)
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topic 2 justifying line and angle relationships skills practice continu…
\( m\angle FJK = 61^\circ \), \( m\angle FKJ = 18^\circ \) ### Problem 8
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4. a parallelogram has one angle that measures 155°. what are the measu…
The other angles are $25^\circ$, $155^\circ$, and $25^\circ$.
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exploring properties of parallelograms name 1) (figure of a parallelogr…
### For Figure 1: $x = 6$ $AB = 19$ $DC = 19$ $y = 2$ $AD = 8$ $BC = 8$ ### For Figure 2: $d = 100$ $\angle D = 100^\circ$ $\angle B = 100^\circ$ $c = 6$ $\angle I = 80^\circ$ $\a…
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graph the line whose y-intercept is -2 and whose x-intercept is -8.
To graph the line, plot the points \((0, - 2)\) (y - intercept) and \((-8, 0)\) (x - intercept) on the coordinate grid and draw a straight line through them, extending the line in…
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find the measure of each interior angle. m∠u = 59 m∠v = 163 m∠w = 75 m∠…
\( m\angle U = 64^\circ \), \( m\angle V = 178^\circ \), \( m\angle W = 80^\circ \), \( m\angle Y = 68^\circ \), \( m\angle Z = 150^\circ \)
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trifles, continued part b directions circle the word that correctly com…
16. cold 17. Sheriff 18. potatoes 19. rocking back and forth 20. laughed 21. cherries 22. apron 23. motive 24. damaged 25. Mr.
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multi-step find the side lengths of each triangle. 18. 19.
(Problem 18): The side lengths of the triangle are 8, 8, 8.
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you make a scale drawing of a banner for a school dance. you use a scal…
14
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you make a scale drawing of a banner for a school dance. you use a scal…
6 (assuming drawing width is 3 inches; if drawing width is different, adjust. But likely, the drawing width is, say, 3 inches, so answer is 6. But wait, maybe the drawing width is…
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the scale of a map is 1 cm = 80 km. what is the actual distance between…
240
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do these measurements form a right triangle? side 1: $3\\sqrt{91}$ side…
No, these measurements do not form a right triangle.
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special right triangles consider triangle pqr. what is the length of si…
16 units (corresponding to the option with "16 units" text)
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the length of segment ef is 12 cm. which statements regarding triangle …
The correct statements are: - \( DF = 6\space cm \) - \( EF \) is the longest side of \( \triangle DEF \) - \( DE = 6\sqrt{3}\space cm \)
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do these measurements form a right triangle? side 1: $8\\sqrt{17}$ side…
These measurements do not form a right triangle.
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consider triangle ghj. what is the length of line segment hj? (options:…
\( 5\sqrt{3} \) units
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do these measurements form a right triangle? the figure may not be draw…
Yes
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the hypotenuse of a 45°-45°-90° triangle measures 128 cm. what is the l…
\(64\sqrt{2}\) cm (corresponding to the option with text "64√2 cm")
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consider triangle def. the legs have a length of 36 units each. what is…
\(36\sqrt{2}\) units (corresponding to the option "36√2 units")
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question determine a series of transformations that would map polygon a…
First: Dilation by a scale factor of 3 with the origin as the center of dilation followed by a: Translation 1 unit left and 3 units up
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3. image of 5 shaded rectangles, 7 unshaded small squares on the left; …
18
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what is the area of this figure? 5 mi 6 mi 2 mi 4 mi 18 mi 3 mi 8 mi 6 …
100 square miles
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what is the area of this figure? 3 in 3 in 2 in 15 in 8 in 3 in 4 in 8 …
81 square inches
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what is the area of this figure? 9 in 2 in 4 in 4 in 3 in 11 in 5 in 2 …
48 square inches
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1. image content: two vertical rectangles, an equal sign, two black squ…
28 (assuming the left side represents the number 28 and we are to find its value from the visual representation)
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x - y = -1 y = -4x - 4 click to select points on the graph.
The solution to the system of equations is \( x=-1,y = 0 \), so the intersection point (the solution of the system) is \((-1,0)\)
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what is the area of this figure? 2 mm 4 mm 6 mm 13 mm 9 mm 7 mm 5 mm 6 …
76 square millimeters
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triangle mrn is created when an equilateral triangle is folded in half.…
4√3 units (the option with 4√3 units)
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the area of a rectangle is $54x^{9}y^{8}$ square yards. if the length o…
H. $9x^6y^4$
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what is the area of this figure? 6 yd 9 yd 11 yd 17 yd 6 yd 8 yd 2 yd 9…
183 square yards
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what is the value of c? (options: 5 units, 4 units, 6 units, 7 units) (…
5 units
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find the distance between the two points in simplest radical form.
$5$
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what is the value of x? 12 units 15 units 20 units 24 units
15 units
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cx is an altitude in triangle abc. which statements are true? choose tw…
\(\triangle ACB \sim \triangle AXC\), \(\triangle AXC\sim\triangle CXB\)
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graph the image of $\\triangle klm$ after a rotation $180^{\\circ}$ clo…
The image of $\Delta KLM$ is $\Delta K'L'M'$ with vertices at $(-1, 9)$, $(-7, 9)$, and $(-4, 7)$ (plotted and connected on the coordinate grid).
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what is the length of line segment kj? options: 3√3 units 3√2 units 2√3…
\( 3\sqrt{5} \) units (corresponding to the option with \( 3\sqrt{5} \) units)
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what is the area of this figure? (the figure has dimensions: 5 m, 3 m, …
$112$ square meters
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△qrs is a right triangle. select the correct similarity statement. △str…
A. \(\triangle STR \sim \triangle SQR\)
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triangle fgh is an isosceles right triangle with a hypotenuse that meas…
8 units (corresponding to the option with 8 units)
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what is the area of this figure? figure with dimensions: left square 6m…
66 square meters
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one leg of an isosceles right triangle measures 5 inches. rounded to th…
7.1 inches
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what is the value of x? triangle diagram with points a, b, c, d; ad = x…
5
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what is the area of this figure? 3 ft 4 ft 7 ft 7 ft 7 ft 9 ft 2 ft 3 f…
73 square feet