幾何
三角形、円、座標幾何、証明問題。
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problem 14: (first taught in lesson 48) read the true statement below a…
Converse: False; Inverse: False; Contrapositive: True
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problem 12: (first taught in lesson 30) find the measures of the angles…
\(10^{\circ},80^{\circ},90^{\circ}\)
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what is a rule for the translation that maps △rst to △rst?
\((x,y)\to(x - 8,y+3)\)
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problem 11: (first taught in lesson 30) find the measures of the angles…
\(32^{\circ},32^{\circ},116^{\circ}\)
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in the diagram, ( g parallel h ), ( mangle1=(4x + 36)^{circ} ), and ( m…
\(120^{\circ}\)
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problem 7: (first taught in lesson 45) tell whether each set of numbers…
a. No b. Yes
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sketch the graph of the function using a window that gives a complete g…
Assuming that option \(B\) has a horizontal line \(y = 3\) with an open - circle at \(x = 2\) and a horizontal line \(y=-3\) with a closed - circle at \(x = 2\), the answer is \(B…
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which words have horizontal reflection symmetry? select all that apply.…
D. TOOT
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name symmetry of regular polygons investigation use tracing paper to ma…
- Lines of symmetry for the triangle: 3 - Vertex - matching turns for the triangle: 3 - Rotation angle for the triangle: \(120^{\circ}\) - Lines of symmetry for the figure \(KLMNO…
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letters a, b, c, and d are angles measures. which equation is enough in…
\(a = d\), \(c = d\), \(b + c=180^{\circ}\)
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problem 1: (first taught in lesson 45) the sum of the lengths of any tw…
False
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which set of equations is enough information to prove that lines a and …
\(m\angle1 = 110^{\circ}\) and \(m\angle3 = 70^{\circ}\) (the third option)
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rectangle pqrs with vertices p(5,15), q(15,15), r(15,10), and s(5,10): …
\(P'(4,12)\), \(Q'(12,12)\), \(R'(12,8)\), \(S'(4,8)\)
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parallel lines e and f are cut by transversal b. what is the value of x…
\(25\) (the third option)
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identify the scale factor used to graph the image below. k =____
\(k = 3\)
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quadrilateral abcd with vertices a(-4,1), b(-2,3), c(0,-2), and d(-5,-2…
\(A'(-12,3)\), \(B'(-6,9)\), \(C'(0,-6)\), \(D'(-15,-6)\)
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given: \\( \\overline { p q } \\cong \\overline { p r } \\), \\( \\over…
5. \( \angle3=\angle4\) 6. \( \angle1 = \angle3\), \( \angle2=\angle4\) 7. \( \angle1=\angle2\); If two angles of a triangle are equal, then the sides opposite those angles are eq…
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find the area of the triangle below. be sure to include the correct uni…
\(52.5\) square yards
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2 rotate point ( p(-2,-3) 90^{circ} mathrm{cw} ) using the rule ( (x, y…
\(P'(-3,2)\)
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find the area of the triangle below. be sure to include the correct uni…
\(6\) square feet
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given: \\( \\overline { p q } \\cong \\overline { p r } \\), \\( \\over…
2. \( \angle3\cong\angle4\) 4. \( \angle1\cong\angle3,\angle2\cong\angle4\); 4. Corresponding Angles Postulate
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find the area of the triangle below. be sure to include the correct uni…
\(210\) square feet
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an artist draws a stained - glass window to scale. the actual window wi…
\(4\)
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find the area of the triangle below. be sure to include the correct uni…
\(112.5\) square feet
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what must be the value of x so that lines a and b are parallel lines cu…
20
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1 write the line of reflection shown and give the coordinates of the im…
Line of reflection: \(x = 1\); \(A'(-2,3)\)
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given: ij = kj prove: il ≠ lm (using the indirect method)
6. \(IL eq LM\) 7. \(m\angle K>m\angle1\) 8. Assumption \(IL = LM\) is false; Contradiction
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24) 30) 29)
24) \(x\approx9.56\) 29) \(x\approx3.42\) 30) \(x\approx4.94\)
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given: ij = kj prove: il ≠ lm (using the indirect method) 5. m∠k > m∠2 …
By the indirect method (proof by contradiction), since assuming \(IL = LM\) leads to contradictions with the given \(IJ = KJ\) (\(\angle J=\angle K\)) and \(m\angle K>m\angle2\) (…
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is \\( \\triangle k l m \\) congruent to \\( \\triangle n o p \\)? just…
Yes, a reflection can map \( \triangle KLM \) onto \( \triangle NOP \)
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reflect the vector $\\langle - 11,4\ angle$ across the y - axis. $\\lan…
\(\langle11,4 angle\)
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is △stz congruent to △xyz? justify your answer using rigid motions. yes…
Yes, a reflection can map \( \triangle STZ \) onto \( \triangle XYZ \)
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rotate the vector $langle 0,2 angle$ $270^{circ}$ degrees counterclockw…
\(\langle2,0 angle\)
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which two triangles are congruent by the sss theorem? * △qpr is congrue…
\(\triangle QPR\) is congruent with \(\triangle HGI\)
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tan x find tanx 40/24 24/32 32/24 32/40
\(\frac{32}{24}\)
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reflect the vector $\\langle -3,5\ angle$ across the x - axis. $\\langl…
\(\langle-3,-5 angle\)
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given: ij = kj prove: il ≠ lm (using the indirect method) 1. ij = kj 1.…
3. \(\angle2 = \angle1\) 4. Exterior Angle Inequality 5. \(m\angle2>m\angle K\)
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find the distance between point i and point j.
\( 6 \)
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test review: slope and similar triangles solve the following problems. …
1. For problem 1: The slope is \(\frac{1}{3}\) (because the ratio of the vertical side to the horizontal side for similar triangles is constant). 2. For problem 2: The slope is \(…
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solve for x. round to the nearest tenth of a degree, if necessary. answ…
\(26.6^{\circ}\)
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given the information in the diagram, which theorem best justifies why …
converse alternate exterior angles theorem
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given: \\( \\angle t = \\angle v ; \\overline { s t } \\parallel \\over…
2. Alternate - Interior Angles Theorem; 4. Transitive Property of Congruence; 5. Converse of the Alternate - Interior Angles Theorem.
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solve for x. round to the nearest tenth of a degree, if necessary. answ…
\(40.9\)
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given: (angle 1congangle 3) prove: (pparallel q) complete the missing p…
1. Given (or the converse of the alternate - interior angles theorem, since \(\angle1\) and \(\angle3\) are alternate - interior angles for lines \(l\) and \(m\) with an appropria…
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solving algebraically for unknown values find the values of x and y tha…
\(x = 80\), \(y = 50\)
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use the figure to complete each part. (a) name the sides of ∠2. □ and □…
(a) \( \overrightarrow{FH}\) and \( \overrightarrow{FE}\) (b) \( \angle GFE\) and \( \angle F\) (c) \(F\)
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solving for unknown angle measures if angle 1 is 110°, what would the o…
Angle 2 = \(110^{\circ}\) Angle 3 = \(70^{\circ}\) Angle 4 = \(70^{\circ}\)
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level 5 enter an axis of symmetry to reflect the tetronimo such that it…
\(x = 6\)
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6. what is the formula for the volume of a cylinder? a. $\\pi r^{3}$ b.…
D. $\pi r^{2}h$
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applying angle relationships to justify paralle which lines are paralle…
Lines \(p\) and \(q\) are parallel because alternate exterior angles are congruent.
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9 triangles lmn and fgh are shown. select whether each statement is tru…
- \(\frac{NM}{LN}=\frac{HG}{FH}=2\): FALSE - \(LM + MN+NL=FG + GH+HF\): FALSE - Triangle \(LMN\) is similar to triangle \(FGH\): TRUE
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letters x, y, and z are angle measures. which equations would guarantee…
\(x = z\), \(x + z=180^{\circ}\)
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dilate the given triangle by a magnitude of 3. \\( \\begin{bmatrix} 3 &…
The completed matrix is \(\begin{bmatrix}9&18&9\\-9&9&9\end{bmatrix}\). So the green box (top - middle) is \(18\), the bottom - middle is \(9\), the top - right is \(9\), and the …
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for the diagram shown, which angles are alternate interior angles? ○ ∠3…
$\angle3$ and $\angle6$
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level 4 enter the horizontal and vertical translation and rotation to p…
Translation: \((x - 3,y - 9)\), Rotation: \(90^{\circ}\)
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18. triangle jkl is shown on the coordinate plane below. triangle jkl i…
C. \( (4,1) \)
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rotate the given triangle $90^{circ}$ clockwise about the origin. $\\le…
The completed matrix is \(\begin{bmatrix}0&1&2\\0&3&- 5\end{bmatrix}\). So the green box (first - row, third - column) is \(2\), the first gray box (second - row, second - column)…
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rotate the given triangle $90^{circ}$ clockwise about the origin. $\\be…
\(1\)
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directions. for each of the following items, circle the letter of the c…
21. A. incentive 22. C. postulates 23. E. stringent 24. D. pivotal 25. E. militant 26. D. postulated...retributions 27. D. compliances...incentive 28. D. implacable...stringent 29…
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19 rectangles zyxw and zyxw are shown in the coordinate plane below. wh…
D. Dilate rectangle \(ZYXW\) with a scale factor of \(2\) about the origin, followed by a translation \(14\) units up and \(12\) units to the left.
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in the figure below, ( mangle4 = 98^{circ} ). find ( mangle1 ), ( mangl…
\( m\angle1 = 98^{\circ} \) \( m\angle2 = 82^{\circ} \) \( m\angle3 = 82^{\circ} \)
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solve for x. round to the nearest tenth of a degree, if necessary. answ…
\(45\)
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a gardener makes a new circular flower bed. the bed is ten feet in diam…
circumference \( = 10\pi\) feet, area \( = 25\pi\) square feet (the first option)
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find the perimeter and area of the polygon shown below. 13 ft 20 ft p =…
\(P = 80\) feet, \(A = 368\) square feet (the first option)
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in the figure below, \\( \\overline{ab} \\cong \\overline{ad} \\) and \…
\(x = 12\) and the length of \(\overline{AC}\) is \(167\).
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in the figure below, \\( \\triangle a b c \\) is similar to \\( \\trian…
\(11.25\)
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which statement about the two triangles is correct? (\triangle abcsim\t…
\(\triangle ABC\sim\triangle DEF\) because \(\frac{6}{4}=\frac{12}{8}=\frac{9}{6}\) (first option)
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the parallel lines x and y are cut by transversal z. the measures of tw…
\(125^{\circ}\)
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10. which congruency statement would not result in △bcd ≅ △qrs? (1 poin…
B. \(\angle D\cong\angle S\) forms the Angle - Side - Angle Congruence Theorem
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find the ratio of squares to triangles in the diagram below. unsimplifi…
\(3:15\)
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use the image provided which two angles when added together equal the m…
\(\angle9+\angle4\)
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can one of the triangle congruence theorem listed below be used to show…
D. None of the theorems listed can be used to show congruence
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find the ratio of triangles to total shapes in the diagram below. unsim…
\(4:14\)
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line segment (overline{op}) has a length of 2 units and has been plotte…
\(2\) units
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1. classify the triangles based on their side lengths and angle measure…
Scalene acute triangle, Scalene right - triangle, Scalene obtuse triangle, Equilateral acute triangle.
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reflect the given triangle over the line ( y = -x ). \begin{bmatrix} 3 …
The completed matrix is \(\begin{bmatrix}3&-3&-3\\-3&-6&-3\end{bmatrix}\)
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find the measure of \\( \\angle h \\) 34 degrees 45 degrees 56 degrees …
56 degrees
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8. in the problem below, \\( \\triangle a b c \\cong \\triangle a d c \…
\(x = 5\) and the length of \(BC\) is \(45\).
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what is a simplified expression for the perimeter of the polygon? compl…
\(86\)
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given △abc is located on the coordinate plane ∠a measures 78° if the tr…
\(78^{\circ}\)
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7. state the additional congruency statement(s) needed to prove ( \tria…
a. \(AB = FG\) b. \(\angle C=\angle H\)
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reflect the given triangle over the line y = -x. \\( \\begin{bmatrix} 0…
\(1\)
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rotate the given triangle $90^{circ}$ counterclockwise about the origin…
\(2\)
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given: \\( \\angle 1 \\cong \\angle 2 \\) prove: \\( p \\parallel q \\)…
**Statements**: \(p\parallel q\) **Reasons**: converse of corresponding angles theorem
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trapezoid midsegment homework pg. 105, #2 - 3, 6 - 10 find each measure…
2. \(120^{\circ}\) 3. \(68^{\circ}\) 6. \(28\) 7. \(11\) 8. \(13\) 9. \(13\) 10. \(20.6\)
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rotate the given triangle 90° counterclockwise about the origin. \\( \\…
The value in the green box (the first element of the second column of the rotated matrix) is \(1\), and the second element of the second column is \(2\).
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solve for z. round to the nearest tenth of a degree, if necessary. answ…
\(59.3\)
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using angle relationships to find variable find the value of x that mak…
a. Alternate interior angles. b. \(9x + 11=74\) c. \(x = 7\)
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6. (overline{ac}) is the perpendicular bisector of (overline{gh}). dete…
a. \(GH=GB + HB=8 + 8=16\); b. \(CH = 12\)
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margaret needs to put a new gutter on one side of her roof. the shape o…
\(220\)
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solve for x. round to the nearest tenth of a degree, if necessary. answ…
\(56.4\)
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using angle relationships to find the variable find the value of x that…
a. Same - side interior angles b. \((10x - 23)+137 = 180\) c. \(x = 6.6\)
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margaret needs to put a new gutter on one side of her roof. the shape o…
\(306.36\space ft\)
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look at this shape: which image shows a reflection?
C.
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using angle relationships to find a variable find the value of x that m…
a. Alternate - interior angles b. \(8x - 77=3x + 38\) c. \(23\)
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look at this shape: which image shows a translation? a b c
A.
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look at this shape:which image shows a rotation?
B
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look at this shape: which image shows a reflection?
B
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given: \\( \\angle 1 \\cong \\angle 2 \\) prove: \\( p \\parallel q \\)…
| Statements | Reasons | |--|--| | $\angle1\cong\angle3$ | Vertical angles are congruent | | $\angle2\cong\angle3$ | Transitive property of congruence ($\angle1\cong\angle2$ (give…
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look at this shape: which image shows a translation? a b c
B.