幾何
三角形、圓、解析幾何與證明題。
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consider the diagram. name two similar triangles. explain how you know …
The two similar triangles are \(\triangle ABD\) and \(\triangle CDB\) (or other possible pairs like \(\triangle ABD\) and \(\triangle BCA\) if the angle interpretation is differen…
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in the diagram, \\( \\triangle a b c \\sim \\triangle d b e \\). what i…
\( 12.5 \) (or \( \frac{25}{2} \))
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dilate △abc by a scale factor of \\( \\frac { 1 } { 2 } \\) with the ce…
at point \(C\)
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figure a is dilated to form figure d. what is the scale factor of the d…
\(3\)
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a volleyball player hits the ball when it is h feet above the ground. t…
\(14.45\)
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which figure is a dilation of figure a with the center of dilation at p…
figure \(D\)
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in the diagram, the right triangles have horizontal and vertical legs, …
\(\frac{1}{6}\)
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figure abcd is dilated from point q, the center of dilation. write the …
\(\frac{2}{8}\)
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6. - 225° circle one: clockwise counterclockwise quadrant: _ reference …
- For \(-45^{\circ}\): Circle one: clockwise; Quadrant: IV; Reference Angle: \(45^{\circ}\); Coterminal Angles: \(315^{\circ}\), \(-405^{\circ}\) - For \(-225^{\circ}\): Circle on…
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figure abcd is dilated from point q, the center of dilation. which figu…
figure \(IJKL\)
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draw an angle with the given measure in standard position. determine if…
2. - Circle one: clockwise - Quadrant: II - Reference Angle: \(30^{\circ}\) - Coterminal Angles: \(150^{\circ}\), \(-570^{\circ}\) 3. - Circle one: counterclockwise - Quadrant: I …
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figure ( j k l m ) is dilated by a scale factor of ( \frac { 1 } { 2 } …
the original figure
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3) in the figure below, a||b. what is the value of x? 2) which lines ar…
$40^{\circ}$
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△rst is dilated by a scale factor of 2 to form its image, △rst. when th…
the dilated image
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in the figure below, ( mangle2 = 74^{circ} ). find ( mangle1 ), ( mangl…
\(m\angle1 = 106^{\circ}\), \(m\angle3 = 106^{\circ}\), \(m\angle4 = 74^{\circ}\)
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1) using a compass and a straightedge, a student constructed a triangle…
C. between \( \frac{1}{2}AB \) and \( AB \)
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in the figure below, ( mangle3 = 143^{circ} ). find ( mangle1 ), ( mang…
\(m\angle1 = 143^{\circ}\), \(m\angle2 = 37^{\circ}\), \(m\angle4 = 37^{\circ}\)
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given wxyz ≅ pqrs, find the measure of the angle or the length of the s…
11) \(145^{\circ}\) 12) \(8.6\) 13) \(5\) 14) \(100^{\circ}\) 15) SSS 16) HL 17) SAS
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which best describes the area of a polygon? a. the distance around the …
B. The number of square units contained in the interior
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what is the area of the triangle below? a. 50 sq. units b. 25 sq. units…
C. 68 sq. units
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question 8 of 10 what is the area of the acute triangle given below? a.…
C. 36 sq. units
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question 7 of 10 what is the area of the triangle given below? a. 11 sq…
A. 11 sq. units
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in the figure below, ( mangle4 = 98^{circ} ). find ( mangle1 ), ( mangl…
\( m\angle1 = 82^{\circ} \), \( m\angle2 = 98^{\circ} \), \( m\angle3 = 82^{\circ} \)
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what is the area of the obtuse triangle given below? a. 97.5 sq. units …
A. 97.5 sq. units
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the area of a triangle is 24 sq. inches. if the base of the triangle is…
D. 8 inches
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the area of the triangle below is ____ sq. units. a. 33 b. 66 c. 50 d. …
A. 33
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question 2 of 10 what is the area of the rectangle below? 8 17 a. 136 s…
A. 136 sq. units
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question 1 of 10 the area of the rectangle below is ____ sq. units. 5 1…
B. 80
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question 10 of 10 according to this diagram, what is tan 67°? 13 67° 5 …
D. $\frac{12}{5}$
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question 1 - 36 a glass is in the shape of a cylinder with a height of …
\( 157\ \text{in}^3 \) (corresponding to the option "157 in³")
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what is the approximate value of ( x ) in the diagram below? (hint: you…
D. 39.59
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according to this diagram, what is cos 16°? a. \\( \\frac { 24 } { 25 }…
A. $\frac{24}{25}$
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question 7 of 10 what is sin 60°? a. \\( \\frac { \\sqrt { 3 } } { 2 } …
A. $\frac{\sqrt{3}}{2}$
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the ____ of an angle is the ratio of the opposite leg length to the adj…
A. tangent
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question 5 of 10 the ____ of an angle is the ratio of the adjacent leg …
A. cosine
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ariana uses a flag in a shadow play. when the flag moves closer to the …
\(D'E'\) is \(2\) times as long as \(DE\). \(E'F'\) is \(2\) times as long as \(EF\).
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question 4 of 10 what is sin 45°? 1 90° 45° 45° √2 1 a. 1/2 b. 1 c. √2 …
D. $\frac{1}{\sqrt{2}}$
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question 3 of 10 what is tan 30°? a. $\\frac{1}{\\sqrt{3}}$ b. $\\frac{…
A. $\frac{1}{\sqrt{3}}$
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question 1 - 32 if in a triangle ( abc ), ( abcong ac ), and ( mangle b…
\( 80^\circ \) (corresponding to the option with \( 80^\circ \))
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question 2 of 10 according to this diagram, what is sin 28°? a. 15/8 b.…
B. $\frac{8}{17}$
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what is the length of ab? s (2, 3) a (1, 0) t (6, -1) b (3, -2) r (0, -…
2.8
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the ____ of an angle is the ratio of the opposite leg length to the hyp…
A. sine
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step reason 1. ( l parallel k ) 1. given 2. ( angle 2 cong angle 4 ) ( …
Step 2: If two lines are cut by a transversal, then corresponding angles are congruent Step 4: Substitution property
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which of the following transformations carry the isosceles trapezoid on…
reflection across \(l_2\)
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read the statement and the argument statement: if point p lies on the p…
The statement is true, but the argument is not a valid argument to justify the statement.
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question 10 of 10 in the diagram below, \\( \\triangle wxy \\) is an eq…
A. \(WX = 2\cdot WZ\)
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ty uses a sailboat in a shadow play. when the sailboat moves closer to …
It changes position, Its vertices move along the rays, It changes size.
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3.4.4 quiz: 30 - 60 - 90 right triangles in the diagram below, △wxy is …
A. \(WX = 2\cdot WZ\)
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3. point f is a centroid of the triangle bde. if ab = 24 cm, what is be…
48 cm (corresponding to the option with 48 cm)
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question 9 of 10 in the 30 - 60 - 90 triangle below, side s has a lengt…
A. \(\sqrt{3}\); 2
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question 1 - 27 a tent in the shape of a square pyramid has a volume of…
\( 2.5 \)
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the diagram shows a convex polygon. what is the sum of the interior ang…
\(180\)
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question 8 of 10 which of the following could be the ratio of the lengt…
C. \(\sqrt{3} : 2\), F. \(2\sqrt{3} : 4\)
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2. point l is a centroid of the triangle fwd. if rl = 54 cm, what is rd…
162 cm (corresponding to the option with 162 cm)
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1. point o is a centroid of the triangle lmn. if om = 38 cm, what is mp?
\(45\) cm
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quadrilateral tuvw is a rectangle, tv = 5s + 96, and uw = 19s + 40. wha…
\(116\)
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quadrilateral tuvw is a rectangle, vx = 10c + 19, and wx = 9c + 23. wha…
\(118\)
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question 7 of 10 which of the following are true statements about a 30 …
B. The hypotenuse is twice as long as the shorter leg, D. The longer leg is \(\sqrt{3}\) times as long as the shorter leg
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quadrilateral pqrs is a rectangle, pr = 7y + 80, and qs = 15y. what is …
\(y = 10\)
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question 6 of 10 what is the length of the altitude of the equilateral …
A. \(4\sqrt{3}\)
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what is the length of the altitude of the equilateral triangle below? a…
B. 6
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question 4 of 10 the diagonal of a tv is 28 inches long. assuming that …
B. 14 inches by \(14\sqrt{3}\) inches
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question 3 of 10 which of the following could be the ratio between the …
A. \(1:\sqrt{3}\), C. \(\sqrt{3}:3\)
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question 2 of 10 a certain triangle has a 30° angle and a 60° angle. wh…
A. The second - longest side is \(\sqrt{3}\) times as long as the shortest side.
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question 1 of 10 which set of values could be the side lengths of a 30 …
A. \(\{6, 6\sqrt{3}, 12\}\)
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△jkl is rotated 90° clockwise around the origin to form △jkl. 90° clock…
\((5, - 7)\)
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question 10 of 10 what is the length of leg s of the triangle below? a.…
B. 4
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question 9 of 10 a softball diamond is in the shape of a square. the di…
C. $60\sqrt{2}$ feet
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question 8 of 10 a right triangle with two congruent legs is always a 4…
A. True
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question 7 of 10 which is a true statement about a 45 - 45 - 90 triangl…
C. The hypotenuse is \(\sqrt{2}\) times as long as either leg.
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△lmn is rotated 90° clockwise around the origin to form △lmn. which coo…
Opposite of \(x -\)coordinate of point \(M\)
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quadrilateral rstu is a rectangle, rt = 2w - 30, and su = 3w - 75. what…
\(60\)
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what is the length of leg s of the triangle below? a. 16 b. sqrt{4} c. …
C. 4
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△lmn is rotated 90° clockwise around the origin to form △lmn which coor…
\(y\)-coordinate of point \(M\)
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41 quadrilateral stuv is a rectangle, su = 2p + 60, and tv = 3p + 57. w…
\(66\)
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question 5 of 10 which of the following words correctly describe a tria…
B. Right, E. Isosceles
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quadrilateral abcd is a rectangle, ae = b + 2, and de = 2b - 73. what i…
\(b = 75\)
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at which store should michael buy his new smart phone? 2. triangle xyz …
The two correct proportions are: - $\boldsymbol{\frac{8}{32}=\frac{17}{PR}}$ (second option) - $\boldsymbol{\frac{60}{15}=\frac{PR}{17}}$ (fifth option) (Note: Based on the origin…
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question 4 of 10 what are the measures of the angles in an isosceles ri…
D. \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \)
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express the area of the entire rectangle. your answer should be a polyn…
\(x^{2}+11x + 30\)
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which rotation is shown in the coordinate plane? 90° counterclockwise 1…
\(90^{\circ}\) counterclockwise
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question 2 of 10 a 10 foot ladder is leaning against a building. the la…
C. \( 5\sqrt{2} \) feet
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4) quadrilateral pqrs is a rectangle, qt = 10b + 23, and rt = 15b - 12.…
\(93\)
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what is the length of each leg of the triangle below? a. 13 b. \\( \\sq…
D. \( 13\sqrt{2} \)
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name combining like terms directions: simplify the expressions. circle …
Let's solve each problem one by one by combining like terms: ### Problem 1: \( 3x + 10 - 8 + 2x \) ## Step 1: Combine like terms for \( x \) \( 3x + 2x = 5x \) ## Step 2: Combine …
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question 10 of 10 what is the value of ( h ) in the figure below? in th…
D. 8
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which figure is a rotation of figure a? figure b figure c figure d
Figure D
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a circle representing a pool is graphed with a center at the origin. gr…
\(y = 6-\frac{x}{4}\)
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question 9 of 10 what is the length of \\( \\overline { c d } \\) ? in …
C. 4
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if cg = 2z - 53 and eg = z, find the value of z that makes quadrilatera…
\( z = 53 \)
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question 8 of 10 based only on the information given in the diagram, it…
A. True
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question 7 of 10 what is the value of x in the figure below? in this di…
C. \(\frac{45}{4}\)
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quadrilateral pqrs is a rectangle, qt = 15z + 25, and rt = 6z + 34. wha…
\(z = 1\)
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quadrilateral vwxy is a rectangle, vx = 11w + 12, and wy = 17w. what is…
\(34\)
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is parallelogram rstu a rectangle?
no
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find the value of x that makes quadrilateral ghij a parallelogram. x =
\(4\)
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find the value of s that makes quadrilateral bcde a parallelogram.
\( s = 12 \)
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find the value of s that makes quadrilateral defg a parallelogram.
\( s = 19 \)
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a circle representing a pool is graphed with a center at the origin. gr…
\(y = 6-\frac{x}{4}\)
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find the value of s that makes quadrilateral ghij a parallelogram.
\( s = 60 \)