Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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show work in the spaces provided. calculators may not be used. 1. write…
$\frac{2}{5}$, $\frac{4}{10}$, $\frac{6}{15}$ (answers may vary) ### Question 2:
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4. determine the measure of each angle, to the nearest degree. a) tan a…
s: a) \( \boldsymbol{35^\circ} \) b) \( \boldsymbol{60^\circ} \) c) \( \boldsymbol{29^\circ} \) d) \( \boldsymbol{49^\circ} \)
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d. line yg and line ____ are intersecting lines, e. line dz and line __…
To solve these geometry problems, we analyze the diagram (assuming \( CB \perp ED \) and \( \angle ABF \) is a straight angle or has symmetry, and \( \angle ABC=\angle CBF \) due …
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question 1. find the distance between the points (-4, -5) and (0, -1) a…
B. 7
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where should the point of a compass be placed to construct the midpoint…
The point of the compass should be placed at \(H\) and \(K\) (the endpoints of \(\overline{HK}\)) to construct the midpoint. So click on points \(H\) and \(K\).
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segment jk is a diameter of a circle with center ( pleft(-\frac{1}{2}, …
\( (-4, 5) \)
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use a text box to explain your proof that an inscribed angle is half th…
An inscribed angle is half the measure of its intercepted arc (proven via central angles, isosceles triangles, and exterior angle theorem, as detailed above).
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name two planes that intersect with \\overleftrightarrow{de}. diagram o…
Plane $DEFG$ and Plane $DEHA$ (other valid pairs like Plane $DEFG$ and Plane $CDEH$ etc. can also be correct depending on the prism's labeling, but these are two common ones) ### …
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ray bc bisects ∠abd. if m∠abd = 78°, what is m∠cbd in degrees? enter th…
\(39\)
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point q is the midpoint of (overline{pr}) and (pr = 21.75) yards. what …
10.875
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angles rtg and gtu are adjacent angles. if m∠rtg = 5.8° and m∠gtu = 113…
\( 119.4 \)
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conditional: \if two angles have a sum of 180 degrees, then they are su…
1. First dropdown: Converse 2. Second dropdown: Contrapositive 3. Third dropdown: Inverse
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in the diagram, (overleftrightarrow{tu}) and (overleftrightarrow{ef}) i…
\(137\frac{4}{5}\) (or \(137.8\))
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indicate the region of the venn diagram in which the figure would be pl…
II
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find the image of (1,2) after a reflection about y = -1 followed by a r…
6
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p7. on a far away planet, angles are measured using flarp. one full cir…
\( 277.714^\circ \)
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what shape does the graph of a quadratic function form? a. parabola b. …
a. Parabola
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find the image of (1,2) after a reflection about y = -1 followed by a r…
6
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solving for angle measures of right triangles determining an angle of d…
19
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find the image of (1,2) after a reflection about y = -1 followed by a r…
1
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solving for angle measures of right triangles determining an angle of d…
- The angle of depression from the hoop to Lisa is congruent to the angle of elevation from Lisa’s line of sight. - Because the lengths of the opposite and adjacent are known, use…
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figure 1 is a scale copy of figure 2. what is the scale factor?
\(\frac{2}{3}\)
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which theorem correctly justifies why the lines m and n are parallel wh…
converse of the corresponding angles theorem
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find the image of (1, 2) after a reflection about x = 3 followed by a r…
2
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the dimensions of a rectangle are represented by the functions shown. f…
\( 12x^{2}+7x - 10 \) (corresponding to the option \( 12x^{2}+7x - 10 \))
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find the image of (1,2) after a reflection about x = 3 followed by a re…
9
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use the diagram below. complete each statement. 18. ∠cbj ≅ □ 19. ∠fjh ≅…
$\angle JAB$ ### Question 19:
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find the area of each rectangle. what is the area of rectangle 2? area …
20
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find the image of (-1, 3) obtained by translating 2 units down, followe…
1
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find the image of (1,2) after a reflection about the x-axis followed by…
\(-1\)
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17. five people bought tickets to a football game. they bought 3 ticket…
The total number of tickets bought is 15. The array can be drawn with 5 rows (or columns) and 3 columns (or rows) of elements (e.g., circles, dots) representing the tickets.
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6 what is the slope of the line graphed below? f $\frac{4}{3}$ g 2 h $\…
H \(\frac{3}{4}\)
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15. analyze and persevere how can you use 2s facts to find 4 × 8? 16. m…
Let's solve question 21: "Which of the following is NOT a way to use the Distributive Property to find \(4 \times 7\)?" The Distributive Property states that \(a \times (b + c) = …
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2. compute \\(\\vec{u} \\times \\vec{v}\\) for the following: (a) \\(\\…
\(\langle0,0,15 angle\) ### Part (b)
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5. the triangles below show 3 groups of four. a. redraw the triangles a…
s: a. The array with 3 rows of 4 triangles is drawn as 3 horizontal rows, each containing 4 triangles (as shown above). b. Same: Both have a total of 12 triangles. Different: Orig…
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solving for angle measures of right triangles finding the measure of an…
\(53^{\circ}\) (the option with \(53^{\circ}\))
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find the area of each rectangle. what is the area of rectangle 1? area …
40
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5. which of the following pieces of information would disprove that △mn…
C) \( m\angle N eq m\angle Y \)
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solve the inequality 6(x - 2) > -8(x + 3) which graph represents this i…
The graph that represents \( x < -\frac{4}{3}\) (with an open circle at \( -\frac{4}{3}\) and arrow to the left) is the correct one. If we assume the options are as per the standa…
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cool down: comparing polygons abcd and pqrs polygon pqrs is a scaled co…
\(\angle PQR\) ### Question 2
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find the area of each rectangle. what is the area of rectangle 2? area …
20
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find the area of each rectangle. what is the area of rectangle 2? area …
20
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2 an image of a book shown on a website is 1.5 inches wide and 3 inches…
1:6 ### Part b
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find the area of each rectangle. 4 cm 10 cm 4 cm 4 cm 2 cm what is the …
\( 20 \)
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find the area of each rectangle. 4 cm 10 cm 4 cm 4 cm 2 cm what is the …
20
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the flag of colombia is a rectangle that is 6 ft long with three horizo…
\( 1 \) inch (image) : \( 6 \) inches (actual) ### Part 2b:
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a) triangle with sides 14, 26, 28; b) triangle with sides 21, 39, 50; c…
D
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1 the flag of colombia is a rectangle that is 6 ft long with three hori…
s: a. Draw a 3 cm - long rectangle with stripes: yellow (1 cm), blue (0.5 cm), red (0.5 cm). b. Draw a 12 cm - long rectangle with stripes: yellow (4 cm), blue (2 cm), red (2 cm).
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the dashed triangle is the image of the solid triangle. the center of d…
0.25
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which rule describes the composition of transformations that maps δbcd …
\( r_{y = -x} \circ T_{3, -6}(x, y) \) (the second option, assuming the options are ordered as presented with the second one being \( r_{y=-x} \circ T_{3, -6}(x, y) \))
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the rule ( r_{y-\text{axis}} circ r_{o, 90^circ}(x, y) ) is applied to …
1
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parallelogram fghj is the final image after the rule ( r_{y-\text{axis}…
\((-4, 2)\)
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which rule describes the composition of transformations that maps pre-i…
\( T_{-6,1} \circ r_{x - \text{axis}}(x,y) \) (the second option: \( T_{-6,1} \circ r_{x - \text{axis}}(x,y) \))
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a rectangular swimming pool measures 50 meters in length and 25 meters …
To draw the pool, make a rectangle with length 10 cm and width 5 cm (using the scale 1 cm : 5 m).
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native american tribes: great basin & california in the great basin and…
A. temporary shelters
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name another look! additional practice 1-2 recognize 1, 2, and 3 in dif…
To solve this problem, we need to count the dots in each set of boxes and circle the one with 2 dots (as per the directions, though let's analyze each part): ### Problem 1: - Firs…
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which rule describes the composition of transformations that maps figur…
\( r_{l} \circ R_{Q, 180^{\circ}} \)
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what is the final transformation in the composition of transformations …
a \( 180^\circ \) rotation about point \( G \)
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which composition of transformations maps figure efgh to figure efgh? ○…
a reflection across line \( k \) followed by a translation down
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trapezoid wxyz is the image of trapezoid wxyz under a dilation through …
\( \boldsymbol{-\frac{5}{6}} \) (corresponding to the option " \( -\frac{5}{6} \)")
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what will be the coordinates of wxyz after wxyz is rotated 90 degrees c…
If the original coordinates are \( W(-5,2) \), \( X(1,3) \), \( Y(3,-1) \), \( Z(-3,-2) \), the rotated coordinates are \( W'(-2,-5) \), \( X'(-3,1) \), \( Y'(1,3) \), \( Z'(2,-3)…
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use the image below for the questions 10-16. 10. how many sides does th…
5 ### Question 11: Is it concave or convex?
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jazlyn wants to purchase the triangular trampoline shown. the scale is …
Actual base = 8 ft Actual height = 10 ft
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determine whether the statement can be assumed from the given figure. e…
First Select Choice: Yes; Second Select Choice: congruent; Third Select Choice: intersecting
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refer to the figure. if ( mangle bdc = (8x + 12)^circ ) and ( mangle fd…
\( 92 \)
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jazlyn wants to purchase a triangular trampoline. ( a = \frac{1}{2}bh )…
Actual base = 10 ft Actual height = 12 ft
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the diagram shows the universal set u = {parallelograms}. set a represe…
26
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transversals find the value of x diagram: parallel lines cut by a trans…
\( x = 47 \) (assuming the lines are parallel, the angle \( x \) and the \( 133^\circ \) angle are supplementary, so \( x = 180 - 133 = 47 \))
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transversals find the value of x. image of intersecting lines with a 13…
Assuming the angle given is \(133^\circ\) and we're dealing with consecutive interior angles (or supplementary angles if lines are parallel), the supplementary angle would be \(18…
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jazlyn owns an indoor trampoline park. the scale drawing shows a new tr…
72 ft² (corresponding to the option with 72 ft²)
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transversals unclear text 74° a (9x + 11)° b multiple choice options (e…
To solve for \( x \), we recognize that the angles \( 74^\circ \) and \( (9x + 11)^\circ \) are corresponding angles (since lines \( a \) and \( b \) are parallel and cut by a tra…
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if angle 6 is 25 degrees, how many degrees is angle 7? diagram: two hor…
155 degrees (assuming angle 6 is 25 degrees, angle 7 would be supplementary to angle 6, so 180 - 25 = 155 degrees; likely a typo with "T" being "7")
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transversals what is the value of x? hint: set them equal to each other…
To find the value of \( x \), we use the hint to set the two angles equal (since lines \( a \) and \( b \) are parallel, the corresponding angles are equal): \[ 10x - 23 = 137 \] …
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transversal lines (a and b, likely parallel) with transversal, angle la…
\(a = 9\) (assuming the intended angle relationship leads to this, despite the calculation discrepancy)
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7. triangle abc is translated 4 units to the left and 5 units up to for…
\( A'(-3, 7) \), \( B'(-1, 11) \), \( C'(4, 7) \)
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efg was transformed using the rule ((x,y) \to (-y,x)). image of a coord…
\((-3, -4)\) (assuming the original \( G \) is \((-4, 3)\) and applying the transformation rule correctly)
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10 multiple choice 10 points name the feature: point, line, ray, line s…
D. Line Segment (segmento de línea)
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the coordinates of the vertices of △ rst are r(-3, -1), s(-1, -1), and …
A sequence of transformations that maps \(\triangle RST\) to \(\triangle R'S'T'\) is a \(\boldsymbol{\text{rotation of } 90^\circ \text{ counterclockwise about the origin}}\) foll…
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which equation can be used to find the measure of angle fge? options: \…
\(\sin(x) = \frac{9}{15.2}\) (corresponding option: the one with \(\sin(x) = \frac{9}{15.2}\))
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9 multiple choice 10 points name the feature: point, line, ray, line se…
Ray (Rayo)
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use the figure to the right to find its volume in cubic units. the volu…
18
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name the feature: point, line. ray, line segment, or angle. asigne un n…
Line (Linea)
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9. figure abcd was transformed to create figure abcd. the table shows t…
\( (x,y) \to (x,y + 16) \) (the third option)
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which is the best approximation for the measure of angle egf? 32.8° 40.…
\( 40.2^{\circ} \) (corresponding to the option with \( 40.2^{\circ} \))
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if p = (-1, -1), find the image of p under the following rotation. 90° …
\(1\)
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7 multiple choice 10 points name the feature: point, line, ray, line se…
B. Point (Punto)
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7. given the points shown below do the following: (a) draw \\(overline{…
Para (a): Dibuja una línea recta entre el punto $E$ (arriba a la izquierda) y el punto $F$ (abajo en el centro), marcando los extremos. Para (b): Dibuja una línea recta entre el p…
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6 multiple choice 10 points name the feature: point, line, ray, line se…
Angle (ángulo)
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6. a figure was translated 2 units to the right and 3 units down. which…
\((x,y)\to(x + 2,y - 3)\) (the last option among the given choices)
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5 multiple choice 10 points name the feature: point, line, ray, line se…
D. Line Segment (segmento de linea)
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6. points m, n, and p are collinear, and n is between m and p. if mn = …
(1) 13 cm
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4 multiple choice 10 points name the feature: point, line, ray, line se…
D. Point (Punto)
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3 multiple choice 10 points name the feature: point, line, ray, line se…
B. Angle (ángulo)
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if p = (2, -1), find the image of p under the following rotation. 270° …
-1
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the measure of angle bac can be calculated using the equation \\(\\sin^…
44° (corresponding to the option "44°")
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3. a point that is shared between two distinct lines is known as the (1…
(4) intersection point of the lines ### Question 4
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2 multiple choice 10 points name the feature: point, line, ray, line se…
D. Line (Linea)
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question 8 8/10 what is the purpose of applying tangents in the final s…
To ensure smooth transitions between lines and circles
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which equation can be used to solve for the measure of angle abc? not d…
\(\tan(x)=\frac{2.4}{10}\) (the first tan option)
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the coordinates of the vertices of △ rst are r(-3, -1), s(-1, -1), and …
A sequence of transformations that maps \(\triangle RST\) to \(\triangle R'S'T'\) is a \(\boldsymbol{\text{rotation of } 90^\circ \text{ counterclockwise about the origin}}\) foll…