Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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question 2 of 10 the blue segment below is a radius of ⊙o. what is the …
C. 19.6 units
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text 2. as they opened, a single delicate - sheet of paper bravely sail…
Part A: B. Sentence 1: Words such as frigid, clutched, and shuffled create an alarmed tone. Sentence 2: Words such as delicate, bravely, and stagger create a comical tone. Part B:…
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question 1 of 10 which of the following segments is a diameter of ⨀o? a…
D. $\overline{UF}$
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3 given: ∠1 and ∠2 form a right angle; m∠1 + m∠3 = 90° prove: ∠2 ≅ ∠3 s…
2. Definition of complementary angles 3. Given 4. Definition of complementary angles 5. Congruence of complementary angles
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select the triangle congruence theorem that proves these two triangles …
B. SAS
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question 10 of 10 true or false? if a radius of a circle intersects a c…
B. False
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select the triangle congruence theorem that proves these two triangles …
SSS
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question 9 of 10 if the blue radius below is perpendicular to the green…
B. 18 units
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question 8 of 10 if the blue radius below is perpendicular to the green…
C. 17.4 units
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question 7 of 10 if the blue radius below is perpendicular to the green…
B. 17 units
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question 6 of 10 true or false? in ⊙o, radius $overline{op}$ intersects…
A. True
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9 here is a construction of a construction are shown. explain how to co…
Use the angle - bisecting tool in the digital construction software to bisect the central angles of the given inscribed hexagon. The intersection points of the angle - bisectors a…
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question 5 of 10 true or false? the blue radius is perpendicular to the…
B. False
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question 4 of 10 a radius of a circle is perpendicular to a chord if an…
C. bisects that chord
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question 3 of 10 if the blue radius below is perpendicular to the chord…
A. 8 units
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question 2 of 10 true or false? the blue radius is perpendicular to the…
A. True
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question 1 of 10 true or false? the segment $overline{ab}$ is congruent…
A. True
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question 10 of 10 fill in the blank. given ⊙e below, you can conclude t…
B. \(\overline{AB}\)
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question 9 of 10 what is the length of chord $overline{vi}$ in $odot c$…
D. 9.4 units
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question 8 of 10 what is the length of the blue segment in ⊙a below? a.…
A. 6.47 units
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yes, by the vertical angles congruence theorem, m∠feb = 123°. so, ac an…
yes, By the Linear Pair Postulate, $m\angle DEB = 57^{\circ}$. So, $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel by the Corresponding Angles Converse.
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1. complete the proof by justifying each statement. given: ∠gij and ∠ki…
For the first proof: | Statements | Answers | Reasons | |--|--|--| | $\angle GIJ$ and $\angle KIH$ are vertical $\angle$s | H | Given | | $\angle GIJ\cong\angle KIH$ | R | Vertica…
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question 6 of 10 fill in the blank. given ⊙o below, you can conclude th…
A. \(\overline{AO}\)
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question 5 of 10 what is the length of chord $overline{an}$ in $odot o$…
A. 14.4 units
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which set of transformations will map figure stuvw onto figure mnopq? a…
C. a 90 - degree counter - clockwise rotation about the origin, and then a reflection across the y - axis
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find the missing side of each triangle. write your answers as decimals …
1. **For the first right - triangle with sides 10.9 in and 6.5 in**: - # Explanation: - ## Step1: Identify the Pythagorean Theorem The Pythagorean Theorem for a right - triangle i…
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3.2 extra practice in exercises 1 and 2, find m∠1 and m∠2. 1.
$m\angle1 = 41^{\circ}, m\angle2 = 41^{\circ}$
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8 here is a construction of a regular hexagon inscribed in a circle. no…
To construct an equilateral triangle inscribed in the circle centered at $A$ using the given regular - hexagon inscribed in the circle: Select a vertex of the hexagon. Then, using…
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3.2 extra practice in exercises 1 and 2, find m∠1 and m∠2. 1. in exerci…
$m\angle1 = 41^{\circ}$, $m\angle2 = 41^{\circ}$
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6 given: $ywcong yz$, $xy = vy$ prove: $overline{xz}congoverline{vw}$ s…
2. Definition of congruent segments 3. Segment - addition postulate 4. Substitution property 5. Segment - addition postulate 6. Transitive property of equality 7. Definition of co…
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8 here is a construction of a regular hexagon inscribed in a circle. no…
To construct an equilateral triangle: Select a point on the circle, use the radius of the circle to mark off other points on the circle with the compass - like tool and connect th…
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are ac and df parallel? explain your reasoning. yes; by the vertical an…
yes; By the Linear Pair Postulate, $m\angle DEB = 57^{\circ}$. So, $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel by the Corresponding Angles Converse.
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question 4 of 10 fill in the blank. given ⊙m below, you can conclude th…
C. $\overline{MA}$
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decide whether there is enough information to prove m||n. yes no if so,…
No; cannot
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decide whether there is enough information to prove (mparallel n). if s…
Yes
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triangle xyz is rotated 90° counterclockwise about the origin to form t…
A. ∠J
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question 3 of 10 fill in the blank. if two chords of a given circle are…
A. be equidistant from the center of the circle
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question 2 of 10 which is a true statement about any two chords that ar…
B. They are congruent.
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triangle xyz has coordinates x(5, 3), y(3, 2), and z(3, 4). the triangl…
C. $X'(3,-5),Y'(2,-3),Z'(4,-3)$
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question 1 of 10 a chord of a circle is any line segment whose endpoint…
A. True
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given: $overline{ym}congoverline{yz}$, $overline{xz}congoverline{vm}$, …
The proof is completed by using the segment - addition postulate and substitution of equal - length segments to show that \(\overline{XZ}\cong\overline{VW}\) based on the given co…
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ml || rt, where fw is a transversal. given m∠rhw=(x + 20)° and m∠mgf=(9…
$144.5^{\circ}$
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you start at (5, 1). you move left 2 units and up 2 units. where do you…
$(3,3)$
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complete the statement. 1. two angles are complementary if the sum of t…
1. 90 2. 180 3. adjacent 4. theorem 5. Supplementary, adjacent 6. Neither, adjacent 7. Neither, non - adjacent 8. \(50^{\circ}\) 9. \(78^{\circ}\) 10. \(26^{\circ}\) 11. \(5^{\cir…
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angles a and b are supplementary. if a = 112°, what is the value of b? …
B. $68^{\circ}$
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you move down 4 units. you end at (-1, 0). where did you start?
$(-1,4)$
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a (3x - 35)^0 b o 130^0 c d
$x = 55$
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you start at (-2, -4). you move down 1 unit and up 4 units. where do yo…
(-2, -1)
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find the missing side lengths in the 45 - 45 - 90 triangles. leave your…
# Explanation: ## Step1: Recall right - triangle trigonometry and special - right - triangle ratios For a 45 - 45 - 90 triangle, the ratio of the sides is $a:a:a\sqrt{2}$, where t…
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you start at (0, -1). you move left 4 units and down 3 units. where do …
$(-4,-4)$
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140° 6x + 20 solve for x
$x = 20$
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you move left 5 units. you end at (-5, -3). where did you start?
$(0,-3)$
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you start at (-4, 0). you move left 1 unit and right 6 units. where do …
$(1,0)$
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consider the diagram shown. complete the statements. if the measures of…
If the measures of ∠6 and ∠8 are equal, then lines r and s are parallel. If the measures of angles ∠6 and ∠10 add up to 180°, then lines r and s are parallel.
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you start at (4, -1). you move right 1 unit. where do you end?
$(5,-1)$
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given: k is the mid - point of jl, m is the mid - point of ln, jk = mn.…
2. Definition of mid - point 3. Given 4. Substitution (using \(JK = KL\) and \(JK = MN\) and \(LM = MN\)) 5. Substitution 6. Symmetric property of equality 7. Definition of congru…
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complete the statements. the congruent - complements theorem implies th…
60; 20
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1. ∠cpn and ∠plh are supplementary. given 2. m∠cpn + m∠hlp = 180°. defi…
The proof is complete as shown above to prove that $\overleftrightarrow{CK}\parallel\overleftrightarrow{PH}$.
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part 3: quick check circle the correct answer: 1. a student council is …
a) Formal group
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given: ∠cpn and ∠plh are supplementary. prove: (overleftrightarrow{ck}p…
The proof is completed as above to show that $\overleftrightarrow{CK}\parallel\overleftrightarrow{FH}$ based on the given information and geometric properties.
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given: k is the mid - point of jl, m is the mid - point of ln, jk = mn.…
The proof is complete as shown above to prove \(\overline{KL}\cong\overline{LM}\).
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if ∠a and ∠b are supplementary and ∠a = 5x - 7, ∠b = 3x + 15, what is t…
22
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3. kl = lm 4. l is the mid - point of km 5 given: $overline{pq}congover…
6. Transitive property of equality 7. Definition of congruent segments
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the diagram below is a right rectangular prism. all the angles shown me…
Plane ABCD and plane ABFE
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the diagram below is a right rectangular prism. all the angles shown me…
Planes FEG and GCD are perpendicular.
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angles a and b are supplementary. if a = 2x + 10 and b = 3x - 20, what …
$x = 38$
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we start at (-1, -1). you move right 5 units and down 8 units. where do…
$(1,-12)$
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2 given: $overline{kl}congoverline{ln}$, $overline{lm}congoverline{ln}$…
| Statements | Reasons | |--|--| | 1. $\overline{KL}\cong\overline{LN},\overline{LM}\cong\overline{LN}$ | 1. Given | | 2. $KL = LN, LM = LN$ | 2. Definition of congruent segments …
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use the drawing tools to form the correct answer on the number line. gr…
The solution of the compound - inequality is $-5 < x\leq6$. On the number line, there is an open circle at $x=-5$ (because $x > - 5$) and a closed circle at $x = 6$ (because $x\le…
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you start at (1, -4). you move right 3 units. where do you end?
(4, - 4)
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determine the correct set up to find the area of the rectangle. $4x + 8…
$A=(4x + 8)(2x + 3)$
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special right triangles find the missing side lengths. leave your answe…
1. **For a 45 - 45-90 triangle**: - The ratio of the side lengths is \(a:b:c = 1:1:\sqrt{2}\), where the legs (the sides opposite the 45 - degree angles) have the same length, and…
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given m∠3=(3x + 2)° and m∠7 = 104°, find the value of x so that l || m …
$34$
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what angle is alternate interior to ∠2? o ∠7 o ∠1 o ∠2 o ∠3 o ∠4 o ∠5 o…
∠7
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what angle is alternate interior to ∠2? ∠7 ∠1 ∠2 ∠3 ∠4 ∠5 ∠6
∠7
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how are ∠1 and ∠5 related? corresponding angles alternate interior angl…
A. Corresponding Angles
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how are ∠3 and ∠6 related? corresponding angles alternate interior angl…
Alternate Interior Angles
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the graph shows triangles jkl and opq. is jkl similar to opq? justify y…
Yes, because a dilation by a scale factor of 2 centered at point \(J\) maps \(JKL\) onto \(OPQ\).
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the graph shows quadrilaterals qrst and vwxy. is qrst similar to vwxy? …
No, because \(\frac{VW}{QR}\) is not equal to \(\frac{XY}{ST}\)
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1. triangle abc has vertices a(-2,5), b(1,0), and c(6,-2). what are the…
1. **Explicación paso a paso**: - **Paso 1: Regla de reflexión en el eje \(y = x\)** - La regla para reflejar un punto \((x,y)\) en la recta \(y = x\) es \((y,x)\). Dados los vért…
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read the excerpt from daughter of invention. \sticks and stones dont br…
word usage
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given: $overline{su}$ bisects $angle tsw$ prove: $mangle usv + mangle v…
| Statement | Justification | |--|--| | 1. $\overline{SU}$ bisects $\angle TSW$ | Given | | 2. $m\angle TSU=m\angle USW$ | Definition of angle - bisector | | 3. $\angle USW=\angle…
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jk has endpoints at j(20, 17) and k(16, 16). find the mid - point m of …
$(18,16.5)$
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r(-13, 7) and s(-17, -12) are the endpoints of a line segment. what is …
$(-15,-2.5)$
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b(1, 16) and c(13, - 4) are the endpoints of a line segment. what is th…
$(7,6)$
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a(4, 3) and c(2, 11) are the endpoints of a line segment. what is the m…
$(3,7)$
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geometry proofs using definitions and postulates name: date: class: 1 g…
| Statement | Justification | |--|--| | 1. $m\angle KOL = m\angle MON$ | Given | | 2. $m\angle KOL=m\angle KOM + m\angle MOL$, $m\angle MON=m\angle MOL + m\angle LON$ | Angle - ad…
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tu has endpoints at t(18, 16) and u(8, 11). find the mid - point m of t…
$(13,13.5)$
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kl has endpoints at k(3, 5) and l(3, 7). find the midpoint m of kl. wri…
$(3,6)$
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gh has endpoints at g(-5, 8) and h(5, -8). find the mid - point m of gh…
$(0,0)$
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tu has endpoints at t(4, 6) and u(10, 8). find the midpoint m of tu. wr…
$(7,7)$
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you move left 1 unit. you end at ( - 1, 5). where did you start?
(4, 5)
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a line segment has the endpoints c(2, 6) and d(6, 0). find the coordina…
$(4,3)$
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select all of the sets of side lengths that will form a triangle. 7, 6,…
7, 6, 11; 9, 5, 13; 5, 5, 9
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you start at (2, 2). you move up 1 unit. where do you end?
(2, 3)
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a line segment has the endpoints v(10, 7) and w(8, 9). find the coordin…
$(9,8)$
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you start at (3, -3). you move up 3 units and right 1 unit. where do yo…
(4, 0)
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find the value of n. 126° your answer
18
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question 10 of 10 a radius is an angle that connects any point on the c…
B. False
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question 7 of 10 what is the center of the circle shown below?
B. J