Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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2. how many angles does a triangle have? ______ 3. does a rectangle hav…
3 ### Question 3
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use the information given in the diagram of △ghi to find the missing me…
\( m\angle G=\boldsymbol{60^\circ} \), \( \text{IM}\approx\boldsymbol{8.7} \), \( \text{GM}=\boldsymbol{5} \) (assuming \( \text{GI} = 10 \) as the hypotenuse, adjust if the side …
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4. what is the area of the grey matting in this 16” by 20” picture fram…
240 sq. in.
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1. how many sides does a nonagon have? 2. how many angles does a triang…
3
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2. what is the area of the grey matting in this 8” by 10” picture frame…
56 square inches
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1.1 practice questions 1. write the number of unit squares in each larg…
\( 2^2 \) ### Part (b)
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1. the pizza’s crust has cheese in it. how many inches around is the cr…
12.57 in
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7. how many pairs of angles are marked as congruent in the figures belo…
2
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rounded to the nearest tenth, what is the length of ln? sin(20^circ) = …
\(2.7\)
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name the marked angle in 2 different ways.
\( \angle MNL \), \( \angle N \)
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name the figure below in two different ways. figure: a line with points…
$\overleftrightarrow{ES}$ and $\overleftrightarrow{SE}$ (or Line ES and Line SE)
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which model shows the sum of 0.1 and 0.8? choose 1 answer: a image of a…
A
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name the marked angle in 2 different ways.
\( \angle ROP \), \( \angle O \)
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name the marked angle in 2 different ways.
$\angle B$, $\angle ABC$ (or $\angle CBA$)
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6. which is not a pair of congruent angles in the diagram below? diagra…
$\angle AEB \cong \angle CDB$ (the option stating $\angle AEB \cong \angle CDB$ is not a pair of congruent angles)
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name the marked angle in 2 different ways. diagram with vertices x, w, …
\( \angle W \), \( \angle XWV \)
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5. if hexagon abcdef is similar to hexagon klmnop, which of the followi…
\(\boldsymbol{\angle E \cong \angle O}\) (the option with \(\angle E \cong \angle O\))
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what are the correct trigonometric ratios that could be used to determi…
To solve this, we analyze the right triangle \( \triangle LNO \) (assuming \( O \) is the right - angled vertex? Wait, no, the right angle is at \( N \), so \( \angle N = 90^{\cir…
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the lines on a tennis court form adjacent angles with measures of $(3a …
\(a = 39\) \(b = 38\)
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4. which statement is not true based on the figures below? $overline{de…
\( \overline{CD} \cong \overline{JK} \)
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the lines on a tennis court form adjacent angles with measures of (3a -…
\(a = 39\), \(b = 38\)
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3. which is not a pair of congruent angles in the diagram below? diagra…
angles ABD and BAD
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if ( mangle abc = (3m - 15)^circ ) and ( mangle abd = (5m + 59)^circ ),…
17
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2. triangle abc is similar to triangle dbe. $overline{ac} : overline{de…
28
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in the triangular prism shown below, which lines are skew? select all t…
\(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{MO}\), \(\overleftrightarrow{OR}\) and \(\overleftrightarrow{MN}\)
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1. the following shapes are similar. $overline{ab} : overline{ij}$ is 5…
6
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rays ba and bc are perpendicular. point d lies in the interior of ∠abc.…
\( x = 14 \) \( m\angle ABD = 47^\circ \) \( m\angle DBC = 43^\circ \)
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in the cube shown below, which lines are parallel? select all that appl…
$\overleftrightarrow{SV}$ and $\overleftrightarrow{TU}$, $\overleftrightarrow{QR}$ and $\overleftrightarrow{OP}$
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protection projections projections orthographic projection projection i…
120 ### Question 10
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practice: find the perpendicular distance from the given fixed point to…
s: 1. Perpendicular distance from \( S(2, 3) \) to \( 4x + 3y - 6 = 0 \) is \( \boldsymbol{\frac{11}{5}} \) (or \( 2.2 \)). 2. Perpendicular distance from \( D(-2, -3) \) to \( 4x…
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3- a rectangular garden has a length of 16m and a width of 9m. (a) calc…
The area of the garden is \( 144 \, \text{m}^2 \). #### Part (b)
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the measure of the supplement of an angle is three times the measure of…
measure of the angle = \( 45^\circ \) measure of the angle's supplement = \( 135^\circ \)
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7. describe the shape below. a 6-sided (hexagon) convex polygon. a 7-si…
B. A 7 - sided (heptagon) concave polygon.
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←→ wx and ←→ yz intersect at point v. if m∠wvy = (4a + 58)° and m∠xvy =…
\(a = 8\) \(b = 54\)
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5. which of the following shapes is not a parallelogram? kite rectangle…
A. Kite
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given right triangle xye, what is the value of tan(y)? four option boxe…
\(\frac{\sqrt{3}}{3}\) (or \(\frac{1}{\sqrt{3}}\) depending on the exact option labels, but the value of \(\tan(30^\circ)\) is \(\frac{\sqrt{3}}{3}\))
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4. what is the shape shown? a concave nonagon a concave heptagon a conv…
A convex pentagon
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3. which of the following is not a polygon? square hexagon trapezoid el…
D. Ellipse
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9. what political principles are in the declaration of independence? ci…
- The purpose of government is to make sure people get their rights. - People have rights that no government should take away. - If a government is bad, the people should get rid …
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from winesburg, ohio all through his boyhood and young manhood george w…
4. restlessness and contentment
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trigonometric ratios given right triangle xyz, which correctly describe…
a is adjacent, b is opposite, c is the hypotenuse (the fourth option)
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1. determine the value of unknown variables. give a reason for your ans…
- For part (a): \(x = 60\) (vertical angles are equal) - For part (c): \(x = 66\) (linear pair angles sum to \(180^\circ\))
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2. name the types of polygons in the picture. image of road signs: a bl…
A. rectangle, square, octagon, square, rectangle
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20. use the image below to find the missing value. using the segment ad…
4
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handbook page p-1d click or tap on any word or words that should be fol…
The words that should be followed by a comma are "flag" and "nicknames". So we click on "flag" and "nicknames" (in the context of the interactive task, we would interact with thes…
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using the side lengths of △pqr and △stu, which angle has a sine ratio o…
$\angle P$
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1. which of the following shapes is not a parallelogram? trapezoid rect…
Trapezoid
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19. in the image, point b would be considered the ______ of segment ac.…
D. midpoint
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18. ________ lines cross at a right angle. options: - perpendicular - i…
A. Perpendicular
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assume lines p and q intersect to form adjacent angles 1 and 2. if m∠1 …
\(25\)
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17. for two right triangles to be congruent, which of the following mus…
B. Their corresponding sides and angles must be equal in measure.
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right triangle pqr is shown. what is the value of tan(q)? enter your an…
$\frac{15}{8}$
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16. in the diagram below, which two rays are opposite one another? diag…
C. $\boldsymbol{\overrightarrow{XM}}$ and $\boldsymbol{\overrightarrow{XN}}$ (Note: Assuming the third option is labeled C; adjust label based on original question's numbering if …
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7. what type of quadrilateral is shown (choose the most specific answer…
Parallelogram
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statement x = 45-40 = 5 reason vertically opposite corrections a + 63° …
\(x = 60\) (Reason: Vertically opposite angles are equal, so we set the two expressions equal and solve for \(x\).) ### Part c: Solving for \(x\) when angles are \(58^\circ\) and …
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6. why is the shape below not a polygon? it has open - ended lines. it …
A. It has open - ended lines.
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5. which of the following is not a polygon? rectangle pentagon circle t…
C. Circle
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12. how has the green figure been transformed to form the red figure? i…
A. It was translated 5 units to the right and 2 units up.
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4. which of the following is not a polygon? trapezoid square ellipse he…
C. Ellipse
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tan net trange (网) and s ta vaue of dn (的)
The area of the right - triangle is \(24\) square units.
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the diagram is a straightedge and compass construction. lines ℓ, m, and…
c. Point \( K \) is closer to point \( C \) than it is to point \( A \) or point \( B \) e. Point \( L \) is closer to point \( B \) than it is to point \( A \)
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11. based on the pattern below, what would you expect the next block to…
The third option (the cube with the blue arrow on the top face and no blue dots on any face)
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assume lines p and q intersect to form adjacent angles 1 and 2. if m∠1 …
\( 6 \)
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right triangle abc is shown. what is the value of sin(b)? enter your an…
$\frac{24}{25}$
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3. name the types of polygons in the picture. image of traffic signs op…
D. rectangle, square, octagon, square, rectangle (assuming the last option is D; if the options are labeled as per the order, the last option with "rectangle, square, octagon, squ…
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9. the picture represents a final step used in... image of segments pq,…
B. constructing congruent segments
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d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} find the distance between eac…
1. The distance is approximately \(14.04\). 2. The distance is approximately \(9.43\).
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refer to the figure. figure with points a, b, c, d, e, f; lines: vertic…
\(17\)
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given right triangle gyk, what is the value of tan (g)? options: 1/3, √…
\(\sqrt{3}\)
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2. what is the shape shown? a convex nonagon a concave pentagon a conve…
D. A concave hexagon (assuming the options are labeled A - D as per typical multiple - choice, with the last option being "A concave hexagon")
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given △def, which is not equal to cos(f)? options: tan(f), sin(d), sin(…
\(\tan(F)\)
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1. describe the shape below. a 7 - sided (heptagon) concave polygon. a …
A. A 7 - sided (heptagon) concave polygon.
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∠6 and ∠7 form a linear pair. twice the measure of ∠6 is twelve more th…
\( m\angle 6 = 122^\circ \) \( m\angle 7 = 58^\circ \)
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8. which is not a pair of congruent sides in the diagram below? options…
B. $\overline{KJ}$ and $\overline{FG}$
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6. what is the circumference of a basketball hoop’s rim that is 9 inche…
28.26 inches (corresponding to the option with "28.26 inches")
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5. a line that crosses segment at right angles while dividing the segme…
A. a perpendicular bisector
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the measure of the supplement of an angle is 60° less than four times t…
\( 40 \)
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given right triangle jkl, what is the value of cos(l)?
$\frac{5}{13}$ (corresponding to the option with $\frac{5}{13}$)
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7. which of the following is not one of euclid’s postulates? all right …
B. All complementary angles form a right angle.
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6. use the image below to answer the question. using the segment additi…
5 (corresponding to the option with value 5)
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gonometric ratios given △abc ~ △xyz, what is the value of cos(z)? optio…
\(\frac{12}{13}\) (assuming one of the options is \(\frac{12}{13}\), if the options are \(\frac{5}{12}\), \(\frac{12}{13}\), \(\frac{5}{13}\), \(\frac{12}{5}\), then the correct o…
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5. which of the following is not one the three categories of euclid’s g…
D. Conjecture
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determine whether the statement can be assumed from the given figure. e…
First "Select Choice": Yes; Second "Select Choice": are (because \(\angle 5\) and \(\angle 7\) share a common side and vertex, and their non - common sides are collinear, satisfyi…
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choose all answers that describe the polygon below. answer attempt 2 ou…
Quadrilateral, Trapezoid
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4. which answer is most likely the kind of angle that is shown here? im…
an obtuse angle
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3. use the image below to answer the question. using the segment additi…
26
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review questions for questions 1–8, circle the correct answer to each q…
(The option with text "switched to the Patriot cause") ### Question 2:
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2. use the image below to answer the question. using the segment additi…
30
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the diagram below shows a partly completed construction of a square ins…
1. Draw a line perpendicular to \( \overleftrightarrow{BC} \) through center \( A \), intersecting \( \odot A \) at \( D \) and \( E \). 2. Connect \( B \), \( D \), \( C \), \( E…
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1. use the image below to answer the question. using the segment additi…
10
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what is the volume of this triangular pyramid? 10 yd 15 yd 9 yd cubic y…
225
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1. the right triangle drawn on the road sign is 10 inches high. if the …
25 sq.in. (corresponding to the option "25 sq.in.")
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in the triangular prism shown below, which lines are parallel?
To determine which lines are parallel in the triangular prism, we analyze the structure: ### Step 1: Recall Properties of a Triangular Prism A triangular prism has two congruent t…
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which of the following factors is not a component of the fraud triangle…
All of the above are components of the fraud triangle.
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4. if a triangle has sides that measure 8cm and 12cm, which of the foll…
5 cm (the option corresponding to 5 cm)
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a line passes through the origin and the point (3,5). what is the slope…
\(\frac{5}{3}\) (corresponding to the last option)
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find the value of x. 13 10 x = ? round to the nearest tenth.
\(16.4\)
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3. which statement is true for the slopes of parallel lines?
The slopes of parallel lines are equal.
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1. how can you prove that a conjecture is false? 2. sketch the next fig…
By finding a counterexample (a specific case that satisfies the conjecture's hypothesis but not its conclusion). ### Question 2 (Sketching the next figure)
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2a. sally constructed ∠aob with \\overrightarrow{oc} as an angle bisect…
\( 42 \) degrees