Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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26. if one angle of a triangle measures 90°, what is the sum of the oth…
\(90^{\circ}\) (the fourth option)
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25. what is the sum of the angles in any triangle regardless of its typ…
\(180^{\circ}\)
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1.- en los ejercicios, halla ( mangle1 ) y ( mangle2 ). di cuál teorema…
\(m\angle1 = 117^{\circ}\), \(m\angle2 = 117^{\circ}\) (using Alternate Interior Angles Theorem for \(\angle1\) and Corresponding Angles Theorem for \(\angle2\))
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give one pair of supplementary angles and one pair of vertical angles s…
# Explanation: ## Step1: Recall the definition of supplementary angles Supplementary angles are two angles that add up to \(180^{\circ}\). In the figure, \(\angle1\) and \(\angle2…
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25. what is the sum of the angles in any triangle regardless of its typ…
\(180^{\circ}\)
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24. given △abc with angles ∠a = 40° & ∠b = 70°, what is the measure of …
\(70^{\circ}\) (the second option)
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23. a triangle has interior angles measuring 80° and 70°. what is the m…
\(30^{\circ}\)
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22. if a triangle has one angle of 45° and another of 60°, what is the …
\(75^{\circ}\) (the third option)
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21. what is the sum of the interior angles of a triangle? 360° 90° 180°…
180°
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19. the sum of the exterior angles of a triangle = 360° true false
A. True
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18. why is $mangle4 + mangle5 + mangle6 = 360^{circ}$? addition propert…
Exterior Angle Theorem
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18. why is ( mangle4 + mangle5 + mangle6 = 360^{circ} )? addition prope…
None of the options provided are correct. The sum of the exterior angles of a triangle (or any polygon) is \(360^{\circ}\) which is a general geometric exterior - angle - sum prop…
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17. why is $mangle1 + mangle2 + mangle3 + mangle4 + mangle5 + mangle6 =…
Exterior Angle Theorem
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16. the sum of the interior angles of a triangle is 180° true false que…
True
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15. each pair of int. and ext. angles sum is 180° true false question 1…
True
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14. each pair of int. and ext. angles form a linear pair true false
True
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12. why is \\( \\angle 3+\\angle 4=180^{\\circ} \\) ? the exterior angl…
Definition of a Linear Pair
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exterior angle theorem the sum of the remote interior angles is equal t…
Definition of a Linear Pair.
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11. why is $\\angle1+\\angle2+\\angle3 = 180^{circ}$? the exterior angl…
The Triangle Sum Theorem
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10. why is $(\\angle1+\\angle3)+\\angle2 = 180^{circ}$ they are complem…
They are a Linear Pair
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9. why is ∠dca ≅ ∠1 and ∠ecb ≅ ∠2? alt. int. angles are congruent alt e…
Alt. Int. Angles are congruent
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8. you can draw a line through a point ii to another line. true false
True
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and exterior angles of a triangle 6. supplementary angles... +180° +90°…
\(+180^{\circ}\)
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5. why is the angle formed, where the green transversal intersects the …
Alt. Int. Angles are Congruent
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4. why is the angle opposite the intersection x? adjacent angles can be…
Vertical Angles are Congruent
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directions: choose the correct answer. encircle the letter of your choi…
1. c. Which 2. c. These 3. a. mine 4. d. Whose 5. b. and 6. c. hers 7. c. but 8. c. or 9. a. so 10. b. What
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3. why is the angle on the top right of the intersection x? alt. int. a…
Alt. Ext. Angles are Congruent
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use the drop - down menus below to state the sequence of transformation…
A translation followed by a reflection. The two figures are congruent because rigid - transformations (translation and reflection) are used to map Figure M onto Figure N.
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2. what symbol is used in a diagram to say that lines are parallel? the…
The same number of arrow heads on each line.
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1. parallel lines form 4 right angles at their intersection point inter…
Never intersect
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figure 1 and figure 2 below are congruent. which point corresponds to p…
\(O\)
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write equations for the horizontal and vertical lines passing through t…
horizontal line: \(y = 8\) vertical line: \(x=0\)
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edwards grandmother used to make him pannukakku when he was little. he …
A pan with a radius of \(6\) in.
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edwards grandmother used to make him pannukakku when he was little. he …
\(117\ \text{in}^2\)
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reese needs a new bike mirror. her old mirror was a rectangle with a le…
The first circular mirror (with radius \(4\space cm\)) has an area approximately equal to the area of the old rectangular mirror. So Reese should buy the circular bike - mirror wi…
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the chalk circle around the pitchers mound has a diameter of 16 ft. wha…
\(64\pi\) \(ft^{2}\)
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what is the area of the pitchers circle? a = ? ft² the chalk circle aro…
\(200.96\) \(ft^{2}\)
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a group of tibetan monks create a sand mandala at an art museum. the ma…
\(12.56\)
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a group of tibetan monks create a sand mandala at an art museum. the ma…
$0.785$
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describe the rotation where △rfb is the preimage and △cxl is the image,…
180 degrees, two quadrants
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the measures of the exterior angles of an octagon are (2x^{circ}), (3x^…
\(80^{\circ}\)
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the measures of the exterior angles of a quadrilateral are ( x^{circ}, …
The measure of the smallest exterior angle is \(30^{\circ}\).
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the measures of the exterior angles of an octagon are ( x^{circ}, 2x^{c…
\(x = 10\)
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how many sides does a regular polygon have if each interior angle measu…
The regular polygon has \(30\) sides.
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how many sides does a polygon have if the sum of the interior angles is…
\(n = 25\)
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determine the relationship between the two triangles and whether or not…
The two triangles are related by **SAS (Side - Angle - Side)**, so the triangles **are congruent**.
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determine the correct description quadrilaterals gsvy, kwnt, and hbrx a…
For the translation from \(KWN T\) (pre - image) to \(HBRX\) (image): right \(2\), up \(5\). For the translation from \(XRBH\) (pre - image) to \(GSVY\) (image): left \(10\), down…
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determine the relationship between the two triangles and whether or not…
The two triangles are related by reflection, so the triangles are congruent.
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question determine the relationship between the two triangles and wheth…
The two triangles are related by **ASA (Angle - Side - Angle)**, so the triangles **are congruent**.
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question determine the relationship between the two triangles and wheth…
The two triangles are related by SSS (Side - Side - Side), so the triangles are congruent.
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find the value of x. 148° x = ?°
\(16\)
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which two inferences about lady bracknell are best supported by the int…
- She values social status and keeps careful track of who is eligible to marry into her circle. - She equates ignorance with charm and prefers people not to question social tradit…
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are these lines parallel? yes no
no
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find the measure of angle x. x = ?°
\(78\)
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given ( m parallel n ), find the value of ( x ).
\(x = 13\)
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solve the inequality and graph the solution on the line provided. 8x - …
Inequality Notation: \(x > 1\) For the number - line: Draw an open circle at \(x = 1\) (because the inequality is strict, \(x eq1\)) and shade the line to the right of \(1\) to r…
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figure b is the result of a transformation on figure a. which transform…
A reflection over the \(y\) - axis.
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question name the figure below in two different ways. symbol: and answe…
\(\overrightarrow{YX}\) and \(\overrightarrow{Y\cdots X}\)
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the diagram shows a triangle. what is the value of z? z = square ^{circ…
\(30\)
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identify two segments that are marked congruent to each other on the di…
$GK$ is congruent to $IK$
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nombra la figura a continuación de dos maneras diferentes. simbolo: and
# Explicación breve: Una línea recta se puede nombrar utilizando dos puntos que la forman. En este caso, los puntos son A y I, y también se pueden usar otros puntos como G, pero l…
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what is the volume of this sphere? round your answer to the nearest hun…
\(9202.77\)
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el radio, r, de una esfera es 9.2 mm. calcular el volumen de la esfera,…
$3260.1$ mm$^{3}$
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a plot of land is in the shape of a triangle. if one side is x meters, …
\(13x - 7\)
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find the distance between the pair of points $(4\\sqrt{3},\\sqrt{7})$ a…
The distance between the given points is \(\sqrt{187}\) units. A. The distance between the given points is approximately \(13.67\) units.
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noah is baking a two - layer cake, in which the bottom layer is a circl…
\(AC = 6\) inches
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give the center and radius of the circle described by the equation and …
Domain: \([-7,-3]\) Range: \([4,8]\)
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a four - sided figure is resized to create a scaled copy. the lengths o…
\(\frac{1}{3}\)
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the measures of the angles of a triangle are shown in the figure below.…
\(x = 6\)
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in the figure below, x lies between w and y. find the location of x so …
\( 28 \)
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solve the inequality and graph the solution on the line provided. 8x - …
Inequality Notation: \(x > - 6\) On the number - line, we draw an open circle at \(-6\) (because the inequality is strict, \(x eq - 6\)) and shade to the right of \(-6\) since \(…
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an athlete whose event is the shot put releases a shot. when the shot w…
The maximum height is \(24.4\), which occurs \(30\) feet from the point of release.
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draw the reflection of the following quadrilateral over the line x.
The reflected quadrilateral is drawn by reflecting each vertex across the line \(x = 3\) (using the rule \((a,b)\to(6 - a,b)\)) and then connecting the new vertices.
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solve the inequality and graph the solution on the line provided. 8x - …
Inequality Notation: \(x > - 6\) For the number - line: Draw an open circle at \(-6\) (because the inequality is \(>\), not \(\geq\)) and draw an arrow to the right of \(-6\) on t…
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the measures of the angles of a triangle are shown in the figure below.…
\(80^{\circ}\)
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analyzing statements about a reflection which are true if figure defg i…
- D(0, 4) → D’(0, -4) - E(-2, 0) → E’(-2, 0) - The perpendicular distance from G’ to the x - axis will equal 2 units.
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the measures of the angles of a triangle are shown in the figure below.…
\(94^{\circ}\)
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triangle xyz is shown on the coordinate plane. if triangle xyz is trans…
\((3,-10)\)
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what is the image of the point $(-7,-8)$ after a rotation of $270^{circ…
\((-8,7)\)
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3. the triangles are congruent. which sequence of rigid motions will ta…
A. Translate \( XYZ \) using directed line segment \( YC \). Rotate \( X'Y'Z' \) using \( C \) as the center so that \( X'' \) coincides with \( B \). Reflect \( X''Y''Z'' \) acro…
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the right triangle below is dilated by a scale factor of $\\frac{1}{2}$…
Perimeter of given right triangle: $180$ units Area of given right triangle: $1080$ units² Perimeter of dilated right triangle: $90$ units Area of dilated right triangle: $270$ un…
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find the measure of the missing angle. answer attempt 1 out of 2 a =
\(49\)
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the diagram shows a triangle. what is the value of s? write your answer…
\(14.5\)
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a container built for transatlantic shipping is constructed in the shap…
The total weight of the contents is \( 22\) pounds (rounded to the nearest pound).
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would you use sss or sas to prove the triangles congruent? use only the…
B. \(\triangle ABC\cong\triangle DEF\), SAS
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find the x - and y - intercepts of the line. enter each answer as an or…
The x - intercept is \((1,0)\) and the y - intercept is \((0,-10)\)
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7. when triangle abc is reflected across line ab, the image is triangle…
A. Corresponding parts of congruent figures are congruent.
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graph the points and find the distance between each set of points. when…
6. The distance is approximately \(7.6\) 7. The distance is \(10\)
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name period date part ii - constructed response find the value of x in …
1. \(x = 4\) 2. \(x = 10\) 3. The board will reach \(8\) feet high. 4. She will bike approximately \(2.2\) miles. 5. The length of the longest diagonal is approximately \(18\) inc…
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question given ( m parallel n ), find the value of ( x ) and ( y ).
\(x = 19\), \(y=94\)
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3. in the figure shown, lines f and g are parallel. select the angle th…
C. Angle 7 ### Problem 4
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find the area. 12 cm 10 cm a =? cm²
\(60\)
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find the perimeter. 15 cm 25 cm 20 cm p =? cm
\(60\)
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what is the surface area of this cylinder? round your answer to the nea…
\(37.70\)
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the perimeter of a rectangle is 16 inches. the equation that represents…
7 in.
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graph the image of \\( \\triangle t u v \\) after a reflection over the…
Plot the points \(T'(-5,6)\), \(U'(5,6)\), \(V'(-4,8)\) and connect them.
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example 4 proof write a two - column proof. 8. given: \\( \\angle 5 \\c…
| Statements | Reasons | | --- | --- | | 1. $\angle 5\cong\angle 7$ | Given | | 2. $\angle 7\cong\angle 8$ | Vertical angles are congruent | | 3. $\angle 5\cong\angle 8$ | Transit…
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for each part below, use the figure to fill in the blank. if necessary,…
(a) \( HI = 7 \) (b) \( m\angle K=100^{\circ} \)
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the rectangle below has an area of $x^{2}-15x + 56$ square meters and a…
\(x - 8\)
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suppose that the function f is defined, for all real numbers, as follow…
Graph a horizontal line \(y = - 5\) with an open - circle at \((0,-5)\) and a closed - circle at the point \((0,-2)\).