Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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2 practice problems 3 what is the weight of a square if a triangle weig…
El peso del cuadrado es \( 8 \) gramos.
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given m ∥ n, find the value of x and y. (4y-7)° (6x+9)° m (2x+3)° n
\(x = 21\) and \(y = 13\)
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1 which of the changes keeps the hanger in balance? select all that app…
B. Adding two triangles to each side
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given the two concentric circles with center h below, fh = 14. find the…
The area of the shaded region is approximately \( 301.6 \).
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given ( m parallel n ), find the value of ( x ). (there is a diagram sh…
\(x = 5\)
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lesson 2 practice problems 1 which of the changes keeps the hanger in b…
B. \(2x = 0.5\), E. \(4x+2.5 + 2.5+3 + 3=2x+2.5 + 3+3 + 3\)
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find the measure of the exterior angle. the measure of the exterior ang…
\(140\)
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find the measure of the exterior angle. the measure of the exterior ang…
\(130\)
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question find the area of the figure below, composed of a rectangle and…
\( 198.5 \)
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given $m \\parallel n$, find the value of x. (2x - 29)° on line m, (7x …
\(x = 23\)
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use the figure below to answer the following question. triangle abc is …
\(40^{\circ}\)
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question find the area of the figure below, composed of an isosceles tr…
120.1
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i) consider the following figure, if pqrs is a quadrilateral inscribed …
\(x = 98\) degrees and \(y = 112\) degrees.
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find the values of the variables indicated below. m = degrees. k = degr…
\(m = 120\) degrees. \(k = 60\) degrees.
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in the diagram, $\\triangle pqr$ is inscribed in a circle. the ratio of…
\(80\)
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find the value of x . (image of a right triangle with segments: st = 5 …
\(x = 2\)
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question given ( m parallel n ), find the value of ( x ). (there is a d…
38
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consider the figure shown below. find the value of each variable mentio…
\( b = 22^{\circ} \), \( a = 26^{\circ} \), \( c = 42^{\circ} \)
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find the area of this parallelogram. be sure to include the correct uni…
\( 165 \, \text{m}^2 \)
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find the value of x . (image of a large right triangle and a smaller si…
\(3\)
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quadrilateral abcd is inscribed in circle o, as shown. what is the valu…
\(y = 97\)
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find the area of this parallelogram. be sure to include the correct uni…
\( 140 \, \text{in}^2 \)
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question 33 solve. a lot is in the shape of a right triangle. the short…
B. 120 meters
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17 determine whether \\(\\overline{ab}\\) is tangent to the circle with…
For the first circle: Yes. For the second circle: No.
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question given ( m parallel n ), find the value of ( x ). (there is a d…
20
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find the value of x in ⊙q. 5x - 6 2x + 9 x =
\(5\)
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find the lengths of r, s, t, and u shown in the figure below if s + t =…
# Explanation: ## Step1: Analyze the smaller right triangle (with side 4) In the smaller right triangle, we have an angle of \(29^\circ\), the opposite side to \(29^\circ\) is \(s…
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15 in the figure shown below, find the values of the angles given in th…
\(2 = 77\), \(3 = 85\), \(4 = 103\)
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find the value of x . f 8 in. e a x in. 12 in. d b 6 in. c x = \\square
\(9\)
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question 31 unique id 0663 if a || b || c and m∠9 = 72°, find the measu…
\(m\angle1 = 73^{\circ}\) \(m\angle2 = 107^{\circ}\) \(m\angle3 = 73^{\circ}\) \(m\angle4 = 107^{\circ}\) \(m\angle5 = 73^{\circ}\) \(m\angle6 = 107^{\circ}\) \(m\angle7 = 73^{\ci…
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2 δpqr: p(-7, -1), q(4, 9), r(-2, -5), δxyz: x(-11, 4), y(0, -6), z(-1,…
No, the triangles are not congruent. Because the lengths of corresponding sides (\( QR \) & \( YZ \), \( PR \) & \( XZ \)) are not equal, so SSS congruence condition is not met.
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what equation does the hanger show now? $x = 3$ $x = 7$ $x + 3 = 4$ $x …
\(x + 3=7\)
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xz = \\sqrt{(11 - 4)^2 + (4 - 8)^2}
If the correct expression inside the square root is \((11 - 4)^2+(8 - 4)^2\), then \(XZ=\sqrt{49 + 16}=\sqrt{65}\approx 8.06\). If we take the original (with possible typo) as \((…
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find the area of the shape. (sides meet at right angles.) image of a co…
17
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find the lengths of r, s, t, and u shown in the figure below if s + t =…
# Explanation: ## Step1: Analyze the smaller right triangle In the smaller right triangle with height \( s \) and base \( r \), and the angle \( 29^\circ \), we know that \( \tan(…
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two rigid transformations are used to map δabc to δxyz. the first is a …
a rotation about point \(A\)
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find the area of the shape. (sides meet at right angles.) 5 in 2 in 2 i…
19
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in the diagram below, m∠cih = 104° and m∠bgd = 41°. find m∠ahf. step an…
63°
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find the area of the shape. (sides meet at right angles.) 3 cm 2 cm 2 c…
18
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find the lengths of w, x, y, and z shown in the figure below if xy = 63…
\( w = 8.3 \), \( x = 8.6 \), \( y = 7.3 \), \( z = 23.2 \) (all rounded to nearest tenth, matching the given values after verification).
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r(-2, -5), δxyz: x(-11, 4), y(0, -6), z(-1, 3) xy = \\sqrt{(0 + 11)^2 +…
If we simplify the expression \(\sqrt{(0 + 11)^2+(-6 - 4)^2}\), we get \(\sqrt{121 + 100}=\sqrt{221}\approx14.87\) (or \(\sqrt{221}\) exactly). So the length of \(XY\) is \(\sqrt{…
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pr = \\sqrt{(-7 + 2)^2 + (-1 + 5)^2} \\quad xz =
\(\sqrt{41}\) (or approximately \(6.403\) if a decimal approximation is needed)
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find the lengths of w, x, y, and z shown in the figure below if xy = 63…
\( w \approx 8.3 \), \( x \approx 8.6 \), \( y \approx 7.3 \), \( z \approx 23.2 \) (Note: Depending on the exact figure and angle placement, there might be a different interpreta…
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find the length of the missing side of the right triangle. round to thr…
D. \(b = 12\)
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find the lengths of a, b, c, and d shown in the figure below if a + b =…
\( a \approx 4.5 \), \( b \approx 22.5 \), \( c \approx 5.4 \), \( d \approx 23.1 \)
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qr = \\sqrt{(4 + 2)^2 + (9 + 5)^2}
If we want the simplified radical form, the answer is \(2\sqrt{58}\); if we want the decimal approximation, the answer is approximately \(15.23\). (Or following the original expre…
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in order to circumscribe a circle on a triangle, which line must you co…
E. perpendicular bisector
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how would you start to find the incenter of δabc? a draw a line paralle…
D. Construct two angle bisectors that divides the opposite sides into two proportional segments.
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which diagram shows $\\triangle rst$ rotated $120^\\circ$ counterclockw…
The bottom diagram
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identify the fourth step in constructing a circle that circumscribes a …
C. Draw the circle with radius from the circumcenter that passes through all three vertices.
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a ladder leans against the side of a house. the top of the ladder is 12…
15
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place the steps in correct order for constructing the circle that inscr…
Step 1: Draw the triangle Step 2: Draw the angle bisector for each angle of the triangle Step 3: Draw a line perpendicular to any side that passes through the intersection point S…
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the image represents what geometric construction? a copy an angle const…
C. Angle Bisector Construction
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the length of a shadow of a building is 30 m. the distance from the top…
\(19.9\)
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more comparing decimals & fractions page 2 of 2 3 write these numbers a…
3a: 2.83 3b: 1.06 4: six and nine hundredths 5a: > 5b: < 5c: =
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which construction correctly shows how to bisect ∠x? a diagram of angle…
C.
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which construction is being shown in the diagram? a copy an angle b cop…
D. Construct the bisector of an angle
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given: \\(\\overline{eh}\\) bisects \\(\\overline{dg}\\)\ \\(\\overline…
For step 4, the statement is \( \triangle DFE \cong \triangle GFH \) and the reason is "ASA Congruence" (or if moving to the final proof, statement \( \overline{DE} \cong \overlin…
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which tool(s) are needed to construct a perpendicular bisector of a lin…
C. A straight edge and a compass.
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using structure 31) quadrilateral defg has vertices d(-1,2), e(-2,0), f…
E'(-3,-4), F'(-2,-5), G'(0,-1)
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after striking a pair of arcs from each endpoint of a line segment, wha…
C. Use a straight edge to draw a vertical line between the points where each pair of arcs intersect.
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given that the images represent 4 steps in the construction of a perpen…
A.
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gerardo is using geometric constructions to help him understand the pos…
C. Option C shows the correct geometric construction for bisecting an angle.
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a 9-ft ladder leans against the side of a house. the bottom of the ladd…
\(7.5\)
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which sequence of transformations will verify that $\\triangle xyw$ and…
B. \(\triangle XYW\) is moved onto \(\triangle X'Y'W'\) after translating \(-16\) units horizontally, and then reflecting across the \(y -\)axis.
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review & refresh find the value of x. 1. 2. 3.
1. \(x = 60\) 2. \(x = 45\) 3. \(x = 113\)
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which sequence of transformations will verify that $\\triangle efg$ and…
D. \(\triangle EFG\) is moved onto \(\triangle E'F'G'\) after rotating \(180^{\circ}\) counterclockwise around the origin and reflecting across the line \(y = 3\)
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which diagram shows δstu rotated 45° counterclockwise about u?
The Top Diagram
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given: eh bisects dg de || gh prove: de ≅ gh step statement reason 2 de…
Vertical Angles Property
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the figure below has a point marked with a large dot. first, translate …
Point in original figure: \( (4, -2) \) Point in final figure: \( (4, 3) \)
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find s. write your answer as a whole number or a decimal. do not round.…
\(16\)
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select the sequence of transformations that will carry rectangle a onto…
C. rotate \(90^{\circ}\) clockwise, reflect over \(x\) - axis, then reflect over line \(x = 5\)
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the archway of the main entrance of a university is modeled by the quad…
D. (1,5) and (5.25,3.94)
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solve the problem. if necessary, round to the nearest tenth. a car deal…
B. \(47.9m\)
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find k. write your answer as a whole number or a decimal. do not round.…
\(k = 24\) feet
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which diagram shows quadrilateral stuv rotated 120° counterclockwise ab…
The Upper Graph
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write your answer as a whole number or a decimal. do not round. x = fee…
\(21.33\)
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which diagram shows δqrs rotated 150° counterclockwise about s?
The lower diagram (with the hand icon)
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in the diagram below, $\\triangle ijk \\sim \\triangle lmk$. find $r$. …
\(r = 15\) meters
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which diagram shows δuvw rotated 90° counterclockwise about w?
The Top Diagram
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find x. write your answer as a whole number or a decimal. do not round.…
\(x = 5.33\)
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find u. write your answer as a whole number or a decimal. do not round.…
\(15\)
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find d. write your answer as a whole number or a decimal. do not round.…
\(d = 6\) feet
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5. different words, same question which is different? find \both\ answe…
The question “Are \(\triangle PQR\) and \(\triangle TSR\) the same size and shape?” is different. The other three questions (about similarity, dilation, and scale - drawing) are r…
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in the diagram below, $\\triangle edc \\sim \\triangle bac$. find $n$. …
\(10\)
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use the diagram below to classify each pair of angles. answer angle 6 a…
Angle 6 and Angle 8: Vertical angles Angle 1 and Angle 8: Alternate exterior angles Angle 6 and Angle 7: Consecutive interior angles Angle 2 and Angle 7: Alternate interior angles…
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solve each exercise. then rate your understanding of the success criter…
The triangles are similar.
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26. represent copy this rectangle on your paper, and shade two thirds o…
\(\frac{5}{6}=\frac{20}{24}\)
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try it 3. can you determine whether △pqr and △tsr are similar? explain.
Yes, \(\triangle PQR\sim\triangle TSR\) by the AA (Angle - Angle) similarity criterion.
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the hypotenuse of an isosceles right triangle is 21 centimeters longer …
One leg: $21(1 + \sqrt{2})$ cm Other leg: $21(1 + \sqrt{2})$ cm Hypotenuse: $21(2 + \sqrt{2})$ cm
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$\\angle 1$ and $\\angle 2$ are vertical angles. if $m\\angle 1 = (5x +…
\(64^{\circ}\)
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25. (40) \\(\\frac{5}{6} = \\frac{?}{24}\\) 26. (28) represent copy thi…
105 students ride the bus.
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the varners live on a corner lot. often, children cut across their lot …
21 feet
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use these numbers to form another facts. 24. (5) \\(\frac{2 cdot 3 cdot…
For problem 24: \(6\); For problem 25: \(20\)
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so, the triangles are not similar. try it tell whether the triangles ar…
1. The triangles are not similar. 2. The triangles are similar.
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express tan o as a fraction in simplest terms. answer attempt 1 out of …
\(\frac{7}{24}\)
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express sin q as a fraction in simplest terms. answer attempt 1 out of …
$\frac{12}{13}$
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express cos y as a fraction in simplest terms. answer attempt 1 out of …
\(\frac{3}{5}\)
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express tan p as a fraction in simplest terms. (there is a right triang…
$\frac{15}{29}$
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find the value of tan v rounded to the nearest hundredth, if necessary.…
\( 1.33 \)