几何
三角形、圆、解析几何与证明题。
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the smallest of the three circles with center d has a radius of 8 inche…
\( 464\pi \) in.² (the option with \( 464\pi \) in.²)
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line segment wx is the radius of circle x, and line segment zy is the r…
324π units² (the option with 324π units²)
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the diagram shows one way to develop the formula for the area of a circ…
\( A=\frac{1}{2}(2\pi r)(r) \) (the third option: \( A = \frac{1}{2}(2\pi r)(r) \))
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in circle g, r = 3 units. maria draws a circle with double the area of …
\( 18\pi \) units² (the option with \( 18\pi \) units²)
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what is the slope of this line? simplify your answer and write it as a …
\(-\frac{1}{4}\)
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5. \\begin{cases} 2x - 6y = 30 \\\\ y = \\dfrac{1}{3}x + 1 \\end{cases}
The system of equations has no solution.
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what is the slope of this line? (-12, 18) (0, 0) simplify your answer a…
\(-\frac{3}{2}\)
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what is the slope of this line? simplify your answer and write it as a …
\(\frac{2}{5}\)
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what is the slope of this line? simplify your answer and write it as a …
\(\frac{1}{4}\)
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Question was provided via image upload.
Statement 4: \( \triangle QST \cong \triangle RSQ \); Reason: ASA (Angle - Side - Angle) Congruence Postulate (and then by CPCTC, \( \overline{QT} \cong \overline{RS} \))
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$\\angle twu \\cong \\angle rvx$, $\\overline{uv} \\cong \\overline{wx}…
The reasons for each statement are: 1. Given 2. Given 3. Given 4. Segment Addition Postulate 5. Segment Addition Postulate 6. Substitution Property 7. Transitive Property 8. AAS C…
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what is the slope of this line? simplify your answer and write it as a …
\(-\frac{2}{5}\)
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c) a reflection in the line y = -1 point a is 4 units above y = -1, so …
1) Reflected vertices: \(A'(-3,3)\), \(B'(-7,2)\), \(C'(-4,1)\) (graph by plotting these and original points). 2) Reflected vertices: \(A'(1,3)\), \(B'(5,4)\), \(C'(2,5)\) (graph …
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7. find the value of x if the two triangles are similar. (x + 2) 45 ft …
34
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6. if a tree cast a 24 ft shadow at the same time a yardstick (3ft) cas…
36
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5. a horse is sighted on the other side of a canyon. find the width of …
75
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4. if manny the martian’s shadow is 17.5 ft. in length and the shadow o…
7
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$\\angle y \\cong \\angle z$, $\\overline{vy} \\cong \\overline{wz}$, a…
The statement for step 5 is $\boldsymbol{\triangle VYW \cong \triangle ZWX}$ with reason "ASA (Angle - Side - Angle) Congruence Criterion" (and then by CPCTC we get $\overline{VW}…
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3. if the trapezoids shown are similar to each other, what is length of…
2.7
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2. if triangles lmp and lno are similar, fill in the missing proportion…
C. NO
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click a line to delete it (image of a coordinate plane with a line and …
The equation of the line is \(y =-\frac{5}{4}x - 5\) (or in decimal form \(y=-1.25x - 5\))
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1. if δabc is similar to δdef, what must be the length of \\(\\overline…
15
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$\\overline{tw} \\cong \\overline{sw}$ and $\\overline{uw} \\cong \\ove…
Statement 4: \( \overline{SV} \cong \overline{TU} \) Reason 4: Corresponding Parts of Congruent Triangles are Congruent (or \( \triangle SWV \cong \triangle TWU \) by SAS, so \( \…
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i is the midpoint of \\(\\overline{eg}\\). complete the proof that \\(\…
1. Given 2. Given (from diagram, parallel lines indicated by arrows) 3. Alternate Interior Angles Theorem (due to $\overline{FG} \parallel \overline{EH}$ and transversal $\overlin…
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△suv ≅ △tvu. complete the proof that ∠tsu ≅ ∠stv. (image of a geometric…
- Statement 2 Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - Statement 4 Reason: Reflexive Property of Congruence - Statement 6 Reason: CPCTC (Correspo…
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complete the proof that \\(overline{xz} \\cong overline{wy}\\). image o…
- Statement 4 Reason: Additive Property of Angle Measure - Statement 6 Reason: Substitution (using $\angle YVZ\cong\angle WVX$) - Statement 9 Reason: CPCTC (Corresponding Parts of…
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solve the following system of equations graphically on the set of axes …
The solution to the system of equations is \( x=-1,y = - 4 \), or the point \( (-1,-4) \)
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complete the proof that \\(\\overline{rw} \\cong \\overline{tu}\\). (im…
- Step 4 Reason: Additive Property of Length - Step 7 Reason: Transitive Property of Equality - Step 8 Reason: AAS (Angle - Angle - Side) Congruence Criterion
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△ghk ≅ △ihj. complete the proof that ∠gjk ≅ ∠ikj. (image of a geometric…
Substitution Property of Equality
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△ghk ≅ △ihj. complete the proof that ∠gjk ≅ ∠ikj. image of a geometric …
# Explanation: ## Step1: Analyze Step 5 and Step 3 From Step 3, we know \( \overline{GH} \cong \overline{HJ} \), so \( GH = HJ \)? Wait, no, Step 3 is \( \overline{GH} \cong \over…
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complete the proof that \\(\\overline{ux} \\cong \\overline{sw}\\). | s…
Transitive Property of Equality (or Substitution, recognizing both equal \( VW + WX \))
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find the x- and y-intercepts of the line $y = -\frac{6}{11}x$. write yo…
x-intercept: \( 0 \) y-intercept: \( 0 \)
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find the lateral surface area and surface area of a cone with a slant h…
(a) lateral surface area: \( 150.72 \) square inches (b) surface area: \( 200.96 \) square inches
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for each of the triangles below, find: \\(\\sin (a), \\cos (a), \\tan (…
\( \sin(A) = \boldsymbol{\frac{9\sqrt{106}}{106}} \), \( \cos(A) = \boldsymbol{\frac{5\sqrt{106}}{106}} \), \( \tan(A) = \boldsymbol{\frac{9}{5}} \), \( \sec(A) = \boldsymbol{\fra…
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triangle abc is shown below. determine whether each statement is true o…
1. First statement: False 2. Second statement: False 3. Third statement: True (Mark False for first two, True for third in the table)
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triangle lmn is shifted according to the translation shown in the table…
L' \((-1, -1)\) M' \((-2, 0)\) N' \((-7, 3)\)
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a right triangle has height h centimeters and length m centimeters. wha…
\(\frac{hm}{2}\) (corresponding to the option with \(\frac{hm}{2}\))
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$\\angle g \\cong \\angle h$. complete the proof that $\\triangle fgh \…
1. Reason: Given 2. Reason: Reflexive Property of Congruence 3. Reason: AAS (Angle - Angle - Side) Congruence Criterion
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find the slope of the line, $y = \\frac{7}{12}x - 11$. write your answe…
\(\frac{7}{12}\)
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$\\angle qpu \\cong \\angle rst$, $\\overline{tu} \\cong \\overline{qr}…
1. Reason for \( \angle QPU \cong \angle RST \): Given 2. Reason for \( \overline{TU} \cong \overline{QR} \): Given 3. Reason for \( \angle PUQ \cong \angle RTS \): Given 4. Reaso…
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∠qpr ≅ ∠pqs, ( overline{qs} cong overline{pr} ), and ( overline{pq} par…
- Step 4 Reason: Alternate Interior Angles Theorem - Step 6 Reason: Transitive Property of Congruence - Step 7 Reason: Transitive Property of Congruence
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19/20 if the area of a square is 36, what is the value of x? 3x 10 8 6 2
2 (the option with value 2)
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complete the proof that $\\triangle qsu \\cong \\triangle qtr$. (image …
- Step 6 Reason: Substitution Property of Equality - Step 8 Reason: AAS (Angle - Angle - Side) Congruence Criterion
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complete the proof that $\\triangle uvw \\cong \\triangle xst$. (image …
- Statement 5 Reason: Additive Property of Length - Statement 6 Reason: Substitution Property of Equality - Statement 8 Reason: ASA (Angle - Side - Angle) Congruence Postulate
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if the length l of a rectangle is 3 less than twice the width w, which …
\( L = 2W - 3 \) (the option with this equation, likely the last one in the list as per the given options: \( L = 2W - 3 \))
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graph the line with the equation $y = -\frac{1}{2}x - 6$.
To graph the line \(y =-\frac{1}{2}x-6\): 1. Plot the y - intercept at \((0, - 6)\). 2. Use the slope \(-\frac{1}{2}\) to find another point (e.g., from \((0,-6)\), move down 1 an…
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5/20 the two triangles are similar, what is the value of x? 7 7.5 8 8.5
7.5
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minor arc kl measures 135°. which is the radian measure of central angl…
\( \frac{3\pi}{4} \) radians (corresponding to the option: \( \boldsymbol{\frac{3\pi}{4}} \) radians)
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consider circle t with radius 24 in. and $\\theta = \\frac{5\\pi}{6}$ r…
20π in
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in circle o, the length of radius ol is 6 cm and the length of arc lm i…
14.2 cm (corresponding to the option "14.2 cm")
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circle o has a circumference of approximately 250π ft. what is the appr…
250 ft (the option with "250 ft")
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the diameter of a circle is 48 meters. what is the angle measure of an …
\(\frac{75}{2}\) (or \(37.5\))
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an arc on a circle measures 295° the measure of the central angle, in r…
\( \frac{3\pi}{2} \) to \( 2\pi \) radians (the last option: \( \frac{3\pi}{2} \) to \( 2\pi \) radians)
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the radius of a circle is 2 miles. what is the length of a 126° arc? gi…
\( \frac{7}{5}\pi \) (or \( \frac{7\pi}{5} \))
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circle o has a circumference of approximately 44 in. what is the approx…
14 in (corresponding to the option "14 in")
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the diameter of a circle is 50 inches. what is the angle measure of an …
\(\frac{756}{5}\) (or \(151.2\))
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$\\angle u \\cong \\angle x$, $\\overline{uv} \\cong \\overline{wx}$, a…
Statement 6 Reason: Substitution (using $\overline{UV} \cong \overline{WX}$ to replace $WX$ with $UV$ in $VX = WX + VW$) Statement 7 Reason: Transitive Property of Equality (or Su…
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in circle m, diameters jl and hk each measure 16 centimeters. what is t…
6.9 cm (corresponding to the option "6.9 cm")
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arc cd is \\(\frac{2}{3}\\) of the circumference of a circle. what is t…
\(\frac{4\pi}{3}\) radians (corresponding to the option " \(\boldsymbol{\frac{4\pi}{3}}\) radians")
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since all circles are similar, a proportion can be set up using the cir…
Because \( \frac{\pi}{1}=\frac{C_2}{2r}, C_2 = 2r\pi \)
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the radius of a circle is 48 centimeters. what is the angle measure of …
\( \frac{345}{2} \) (or \( 172.5 \) or \( 172\frac{1}{2} \)) degrees
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the radius of a circle is 8 feet. what is the angle measure of an arc π…
\( \frac{45}{2} \) (or \( 22.5 \))
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point d (7, 8) was rotated about the origin, creating point d (-8, 7). …
counter - clockwise
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the radius of a circle is 25 meters. what is the length of a 144° arc? …
\( 20\pi \)
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point d (7, 8) was rotated about the origin, creating point d (-8, 7). …
\(90^\circ\)
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the radius of a circle is 20 inches. what is the length of a 180° arc? …
\( 20\pi \)
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which of the following statements is not true about $\\triangle abc$ an…
The interior angles of \( \triangle ABC \) have twice the measure of the interior angles of \( \triangle A'B'C' \).
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the diameter of a circle is 48 centimeters. what is the angle measure o…
\( \frac{285}{2} \) (or \( 142.5 \)) degrees
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if $\\triangle abc \\cong \\triangle def$, then angle $\\angle a \\cong…
CPCTC.
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question in the diagram below, \\(\\overline{ac} \\parallel \\overline{…
\(m\angle HBC = \boldsymbol{65^\circ}\)
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the diameter of a circle is 50 kilometers. what is the angle measure of…
\( \frac{108}{5}^\circ \) (or \( 21.6^\circ \))
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the rule for any glide reflection over the y-axis is: (x, y) → x + a, -…
\((x,y)\to[-(x + a),y + b]\)
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does the graph show a reflection of triangle abc? image of coordinate p…
No, the graph is not a reflection.
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if segment ab has coordinates a(3, 2) and b(4, 5) and the segment glide…
\(A'(-1,-1), B'(0,2)\) (the second option)
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in the graphic below, $\\triangle ghj \\cong \\triangle klj$ by: image …
AAS.
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the radius of a circle is 15 kilometers. what is the length of a 180° a…
\( 15\pi \)
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when writing a formal two - column proof, the reasoning for the first s…
A. False
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a reflection and a glide are the same thing. true false
B. False
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in the graphic below, δlae ≅ δkea by: image of a quadrilateral with tri…
A. AAS
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the diameter of a circle is 10 meters. what is the angle measure of an …
\( 72 \)
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angle-angle-angle (aaa) is not a congruency of triangles theorem. true …
True
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are triangles hto and cdl congruent? options: ○ yes, by aas ○ yes, by a…
Yes, by AAS
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the diameter of a circle is 8 kilometers. what is the angle measure of …
\( 45 \)
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in the graphic below, $\\triangle sta \\cong \\triangle ays$ by: image …
SSS
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the parallelogram will be rotated 90° clockwise about the origin. draw …
To draw the rotated parallelogram, plot the vertices obtained by rotating each original vertex \((x, y)\) 90° clockwise (using \((y, -x)\)): \((7, 1)\), \((5, 0)\), \((0, 0)\), \(…
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in the graphic below, $\\triangle mat \\cong \\triangle mht$ by: image …
SAS
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a glide reflection is a transformation that is a combination of a glide…
True
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the diameter of a circle is 6 inches. what is the length of a 90° arc? …
\(\frac{3}{2}\pi\) (or \( \frac{3\pi}{2} \))
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in the graphic below, $\\triangle tri \\cong \\triangle nlg$ by: two tr…
AAS.
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after proving two triangles are congruent, then one can prove parts of …
True
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$\\overline{bc} \\cong \\overline{cb}$ is an example of the reflexive p…
True
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question 11 of 50 the value of x is: two triangles with angle and congr…
\(66^{\circ}\)
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the radius of a circle is 9 inches. what is the length of a 150° arc? g…
\( \frac{15}{2}\pi \) (or \( 7.5\pi \)) inches
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△abc is rotated 90° clockwise about the origin to create △abc. what are…
(2, -3)
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the perimeter of a figure is the total length of all of its sides. ○ fa…
True
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cpctc means the corresponding parts of congruent triangles are congruen…
True
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the diameter of a circle is 2 miles. what is the length of a 180° arc? …
\(\pi\)
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the congruency theorem angle-side-angle (asa) proves two triangles are …
B. False
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if polygon cold is congruent to polygon warm, and the area of polygon w…
28 square feet
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in the graphic below, $\\triangle abc \\cong \\triangle def$ by: image …
SSS