Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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find the value of x.
$45$
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graph. x > -530 plot the endpoints. select an endpoint to change it fro…
Plot an open circle at \(-530\) on the number - line and draw a ray extending to the right from that open circle.
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2. select the inequality that relates kl and yz in (\triangle jkl) and …
\(KL>YZ\)
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1. select all the inequalities that relate the sides of the figure show…
A. \(b > a\), C. \(b < c\), D. \(a < b < c\)
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statements reasons 1. ( mangle acb = 48^{circ}, mangle chi = 132^{circ}…
A. Vertical Angles Theorem. B. If consecutive - interior angles are supplementary, then the lines are parallel. C. If alternate - interior angles are congruent, then the lines are…
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examine the triangle below. which equation can be used to determine the…
B. \(125 + x = 180\)
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two sides of a triangle measure 5 in. and 12 in. which could be the len…
10 in.
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compare the given dimensions of four triangles. which triangle is possi…
The triangle with side lengths of \(5\) ft, \(12\) ft, and \(13\) ft is possible to construct.
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tinh has a triangle with side lengths 12 mm, 15 mm, and 18 mm. he wants…
Tinh's reduction is incorrect; he should have only divided the side lengths by 3.
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two sides of a triangle measure 8 cm and 15 cm. which could be the leng…
18 cm
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sarkis wants to draw a triangle with sides measuring 4 ft, 10 ft, and 1…
Sarkis cannot draw a triangle with these side lengths.
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which dimensions cannot create a triangle? three angles measuring 40°,7…
three angles measuring \(40^{\circ}\), \(70^{\circ}\), and \(65^{\circ}\)
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which dimensions can create more than one triangle? three sides measuri…
three angles measuring \(25^{\circ}\), \(65^{\circ}\), and \(90^{\circ}\)
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spiral review 18. complete each figure so it is congruent to the figure…
The triangle was translated \(1\) unit to the right and \(2\) units up.
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which dimensions can create only one unique triangle? three sides measu…
three sides measuring \(5\) in., \(12\) in., and \(14\) in.
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test prep 13. what missing value would make the equation have infinitel…
C. 6
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aziza has a triangle with two sides measuring 11 in. and 15 in. she cla…
Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.
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which dimensions can create more than one triangle? three sides measuri…
three angles measuring \(75^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\)
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which dimensions can create more than one triangle? three sides measuri…
three angles measuring \(75^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\) and three angles measuring \(40^{\circ}\), \(50^{\circ}\), and \(60^{\circ}\)
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under which condition could a triangle exist? 1 acute angle, 1 right an…
2 acute angles, 1 right angle
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in exercises 9 - 14, tell whether the triangle is a right triangle. exa…
- Exercise 9: Right - triangle - Exercise 10: Not a right - triangle - Exercise 11: Not a right - triangle - Exercise 12: Right - triangle - Exercise 13: Not a right - triangle - …
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identifying dimensions that create two triangles which dimensions will …
The dimensions with angles \(45^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) will create an unlimited number of triangles.
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gerry wants to construct a triangle with segments that are 4, 6, and 11…
Gerry cannot construct a triangle with these side lengths.
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ted has the following triangle dimensions. • side length of 8 • side le…
He cannot construct a triangle.
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10. examine the diagram below. (figure is not drawn to scale.) what are…
D. \(75^{\circ}\) and \(105^{\circ}\)
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finding missing measurements consider the triangle. angle ( a = 60 ^ { …
\(5\sqrt{3}\)
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the rectangle cdef, shown below, is reflected across the x - axis to fo…
\(C'(-3,-10)\), \(D'(-3,-6)\), \(E'(-10,-6)\), \(F'(-10,-10)\)
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8. modeling real life television sizes are measured by the lengths of t…
Since \(41.3>40\), you should purchase the television.
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consider the triangle. angle a= angle b = 30° angle c = 90° ab = 10 ac …
Angle \(A = 60^{\circ}\), \(BC=5\sqrt{3}\)
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5. the measures of the angles of a triangle are given. a. the measure o…
D. 26
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finding a missing angle a student drew a triangle with a side length of…
\(30^{\circ}\)
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the rectangle cdef, shown below, is reflected across the x - axis to fo…
\(C'(-10,3)\), \(D'(-6,3)\), \(E'(-6,9)\), \(F'(-10,9)\)
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7. modeling real life find the distance between the two platforms of th…
The distance between the two platforms is approximately \(14.1\) ft.
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from which set of dimensions could a triangle be constructed? side leng…
side length of \(2\), side length of \(6\), side length of \(7\)
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a student is constructing a triangle with the following dimensions: • s…
21 inches, 35 inches
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1. what are the measures of \\( \\angle 1 \\) and \\( \\angle 2 \\)? a.…
D. \(m\angle1 = 75^{\circ}\); \(m\angle2 = 51^{\circ}\)
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the rectangle lmno, shown below, is reflected across the x - axis to fo…
\(L'(2,9)\), \(M'(4,9)\), \(N'(4,13)\), \(O'(2,13)\)
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lara has a triangle that has side lengths of 26, 34, and 58. she wants …
Lara should have only divided the side lengths by 2 in order to reduce the triangle.
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an architect designs a diagonal path across a rectangular patio. the pa…
D. \(x^{2}+(x + 5)^{2}=841\)
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give the coordinates of the image of triangle abc under a reflection ab…
\(A'=(-16,7)\), \(B'=(2,3)\), \(C'=(11,-3)\)
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drag a vertex of the triangle to change its shape. double - click or do…
One unique triangle (since the sum of angles is \(180^{\circ}\) and we are given three angle measures, and by the Angle - Angle - Angle (AAA) similarity criterion, but when we con…
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drag a vertex of the triangle to change its shape. double - click or do…
One unique triangle
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6. which list contains a multiple of both 3 and 5? a) 21, 25, 30 b) 3, …
C. 15, 30, 45
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drag a vertex of the triangle to change its shape. double-click or doub…
Exactly one triangle
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d is the midpoint of \\( \\overline { a c } \\) reason: given \\( \\ove…
SAS
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in exercises 1 - 4, find the value of x. then tell whether the side len…
1. \(x=\sqrt{7^{2}+11^{2}}=\sqrt{49 + 121}=\sqrt{170}\approx13.04\), not a Pythagorean triple. 2. \(x=\sqrt{16^{2}+30^{2}}=\sqrt{256+900}=\sqrt{1156}=34\), is a Pythagorean triple…
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a rectangles length is 5 inches more than twice its width. its area is …
\( w(2w + 5)=50 \) (the third option)
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the rectangle cdef, shown below, is translated 3 units to the right and…
\(C'(4,1)\), \(D'(4,-6)\), \(E'(-3,-6)\), \(F'(-3,1)\)
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3 write the correct quadrilateral name in the boxes that match each des…
1. Parallelogram 2. Rhombus 3. Rectangle 4. Square
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for #1 - 5, given that m || n, state the name of the angle pair. then c…
1. Equation: \(\angle4\cong\angle8\) 2. Equation: \(\angle6+\angle7 = 180^{\circ}\) 3. Equation: \(\angle5\cong\angle7\) 4. Equation: \(\angle5\cong\angle1\) 5. Equation: \(\angle…
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3. circle all of the following that are not true. a. lincoln believed s…
B. Lincoln believed that slavery should end and all races were equal; D. Douglas and Lincoln agreed on popular sovereignty
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kitchen triangle in exercises 27 and 28, use the following information.…
No, a triangle with side lengths 9 feet, 3 feet, and 5 feet cannot exist. Because when applying the triangle - inequality theorem (\(a + b>c\) where \(a = 3\), \(b = 5\), \(c = 9\…
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the rectangle jklm, shown below, is translated 3 units to the right and…
The coordinates of the vertices of \(J'K'L'M'\) are \(J'(9,-2)\), \(K'(9,-7)\), \(L'(-1,-7)\), \(M'(-1,-2)\)
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14. the length of a rectangle is three times the width. the sum of the …
A. 5
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for questions 12 and 13, determine the best method to solve the system …
12. B. elimination using addition 13. A. substitution
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the rectangle lmno, shown below, is translated 5 units to the right and…
\(L'(7,3)\), \(M'(7,-8)\), \(N'(-1,-8)\), \(O'(-1,3)\)
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evaluate algebraic expressions given the formula for the area of a trap…
\(30\)
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a substitution c elimination using subtraction b elimination using addi…
\(x = 0,y = 0\)
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florian and michelle are trying to construct a triangle. florian says t…
Florian has the correct side lengths because the measurements fit the triangle inequality rule.
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andia says she can find the area of the polygon shown by adding the are…
12
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kitchen triangle in exercises 27 and 28, use the following information.…
The side - angle relationships do not follow the Law of Sines.
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drag a vertex of the triangle to change its shape. double - click or do…
Obtuse triangle
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the length of a rectangle is equal to one more than twice the width. wh…
The width of the rectangle is \( 14.5 \) centimeters and the length is \( 30 \) centimeters.
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cube a has side lengths of 3 cm. the expression 6 × 3² can be used to f…
Cube \(A = 54\space cm^{2}\) Cube \(B = 150\space cm^{2}\)
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drag a vertex of the triangle to change its shape. double - click or do…
Each angle of the triangle measures \(60^{\circ}\)
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w is the midpoint of ( overline{uv} ) and ( overline{tv} cong overline{…
# Explanation: ## Paso 1: Identificar la congruencia de segmentos Como \(W\) es el punto medio de \(\overline{UV}\), por definición de punto medio, \(\overline{UW}\cong\overline{V…
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drag a vertex of the triangle to change its shape. double - click or do…
No, those interior angle measures do not add up to \(180^{\circ}\).
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drag a vertex of the triangle to change its shape. double - click or do…
A. \(3,4,5\), B. \(9,12,15\), C. \(5,12,13\)
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drag a vertex of the triangle to change its shape. double - click or do…
\(90^{\circ}\)
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drag a vertex of the triangle to change its shape double - click or dou…
\(45^{\circ}\)
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w is the midpoint of \\( \\overline{uv} \\) and \\( \\overline{tv} \\co…
3. Definición de punto medio 4. Propiedad reflexiva de la congruencia 5. Criterio SSS (lado - lado - lado) 6. Ángulos correspondientes de triángulos congruentes
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consider \\( \\triangle p q r \\) in the coordinate plane. a. what are …
Coordinates of \(P'\): \((-9,3)\) Coordinates of \(Q'\): \((-4.5,6)\) Coordinates of \(R'\): \((-1.5,6)\)
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p(square,square)
\((3,-5)\)
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∠h ≅ ∠i and ↔{hi} ⊥ ↔{gj}. complete the proof that ↔{ij} ≅ ↔{hj}.
1. Dato 2. Dato 3. Todos los ángulos rectos son congruentes 4. Propiedad reflexiva de la congruencia 5. AAS 6. Lados correspondientes de triángulos congruentes son congruentes
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26. taking a shortcut look at the diagram shown. suppose you are walkin…
This route is shorter than staying on the sidewalks because of the triangle inequality theorem. The sum of the lengths of the two sidewalk paths (the two sides of a right - angled…
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j is the midpoint of \\( \\overline{hi} \\). complete the proof that \\…
6. \( SAS\)
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in △jkl, (overline{lj}congoverline{kl}) and (mangle k = 10^{circ}). fin…
\(85^{\circ}\)
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the shape is made of unit squares. what is the area of the shape? squar…
4
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j is the midpoint of ( overline{hi} ). complete the proof that ( overli…
Definición de punto medio
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the shape is made of unit squares. what is the area of the shape? squar…
\(3\)
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find the value of x, y, and z in the rhombus below.
\(x = 13\), \(y=-109\), \(z =-115\)
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find the value of ( x ), ( y ), and ( z ) in the rhombus below. answer …
\(x=-34\), \(y = - 68\), \(z=-118\)
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eh bisects ∠feg and ef ≅ eg. complete the proof that gh ≅ fh. 1 eh bise…
5. \( SAS \) 6. \( CPCTC \)
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find the value of x. then find the measure of each angle and write the …
\(x = 11\); \(37^{\circ}\); \(80^{\circ}\); \(117^{\circ}\)
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eh bisects ∠feg and ef ≅ eg. complete the proof that gh ≅ fh.
3. Definición de bisectriz de ángulo 5. SAS (\( \text{Side - Angle - Side} \)) 6. Lados correspondientes de triángulos congruentes son congruentes.
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plot the image of point a under a dilation centered at the origin with …
The coordinates of the image of point \(A\) are \((-6,-6)\)
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ezras dad is building a cover for his sandbox. the sandbox is in the sh…
12 square feet
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area of special quadrilaterals what is the area of the kite? 21 square …
42 square feet
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area of special quadrilaterals what is the area of the kite? 20 square …
40 square meters
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a kite was broken into two triangles. what is the height, h, of one of …
\(8\) ft
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area of special quadrilaterals 10 cm 16 cm 12 cm what is the area of th…
\(176\space cm^{2}\)
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find the unknown angle measures. m∠b=□° m∠c=□°
\(m\angle B = 54.5^{\circ}\), \(m\angle C = 54.5^{\circ}\)
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two tables, congruent trapezoids, are placed together to make a corner …
20 square feet
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t is the midpoint of \\( \\overline{rs} \\). complete the proof that \\…
Para la razón de la tercera línea (\(\overline{RT}\cong\overline{ST}\)) es "Definición de punto medio".
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using algebra in exercises 24 and 25, solve the inequality ab + ac > bc…
\(x<7\)
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a window is in the shape of a kite. caleb wants to apply a layer of pla…
18 inches in width and 7 inches in height
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verona is finding the area of a kite. she breaks up the figure into two…
Yes, each triangle has a base of 10 meters and a height of 3 meters.
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a trapezoid was broken into a rectangle and a triangle. what is the len…
\(2\) cm
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using algebra in exercises 24 and 25, solve the inequality ab + ac > bc…
\(\frac{1}{3}<x<7\)
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step 1: break the figure into rectangles and triangles. step 2: find th…
The area of the triangle in Step 3 should be doubled since there are 2 triangles.