Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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when graphing the line $y = \\frac{1}{2}x - 1$, how do you move from on…
1 unit up, 2 units to the right
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6.2.ap-4 reasoning one image of δabc is δabc how do the x-coordinates o…
B. The x - coordinates of the vertices are the same distance away from the y - axis but in the opposite direction.
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which is an equation of line (ell)? (\bigcirc) (x = 2) (\bigcirc) (x = …
D. $y = 2$
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what is the slope of the line shown?\\(\\frac{1}{4}\\)\\(-\\frac{1}{4}\…
B. $-\frac{1}{4}$
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when graphing the line $y = 2x + 1$, how do you move from one point to …
2 units up, 1 unit to the right
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what is the slope of this line?
2
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the unknown side length b. p = 1,000 m x m 150 m x = 350 mber side leng…
$w = 3$ m, $l = 12$ m (or $w = 12$ m, $l = 3$ m) --- For the top problem (verification):
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9. given: \\(\\overline{ab} \\cong \\overline{ed}\\), \\(\\overline{ab}…
s: ### Problem 9 (Table): | Statements | Reasons | | --- | --- | | 1. $\overline{AB} \cong \overline{ED}$ | Given | | 2. $\overline{AB} \parallel \overline{DE}$ | Given | | 3. $C$…
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simplify your answer and write it as a proper fraction, improper fracti…
The slope of the line is $\frac{5}{6}$, and the equation of the line is $y = \frac{5}{6}x - 1$
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battle of the shakespearean insults! using the generator below develop …
To solve this, we'll create Shakespearean insults by combining words (assuming common Shakespearean insult word lists for the columns: Column 1: reeky, fusty, mangled, warped; Col…
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lesson (eng) lección (esp) 9 - 12. for each figure below, determine if …
The two triangles are congruent (e.g., \(\triangle ABC \cong \triangle ACB\) or specific names), and \(x = 2\). ### 9-12 b.
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the image of $\\triangle abc$ after a reflection across $\\overleftrigh…
The correct option (assuming the notation and options are as per the problem's intended meaning, after correcting for possible typos) is the one stating: "F is the midpoint of \(\…
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finding perimeter and area find the perimeter and the area of the figur…
Perimeter: \(\boldsymbol{42}\) meters, Area: \(\boldsymbol{92}\) square meters ### Problem 16:
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do you know how? 4. chrissie says the equation of the line shown on the…
George is correct. The line has a y - intercept of 5 (crosses y - axis at (0, 5)) and a negative slope (\(m = -\frac{1}{2}\)) calculated from points like (0, 5) and (6, 2). The eq…
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which graph represents the graph of the equation $x = 2$? (four coordin…
The fourth graph (the one with a vertical line passing through x=2 on the x-axis)
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in the accompanying diagram, which is an equation of line (ell)? option…
A. $x = 3$
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what is an equation of the line whose graph is shown? y = x y = 2x y = …
y = x
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1.1 exercise set 1. fill in the blanks. a) a fraction with the denomina…
## 1. Fill in the blanks a) proper b) improper (or whole) c) equivalent ## 2. Shaded fractions a) $\frac{1}{4}$ b) $\frac{2}{3}$ c) $\frac{1}{2}$ d) $\frac{2}{5}$ e) $\frac{3}{4}$…
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on your own: applications of right triangle trigonometry on your own ap…
$52.9$ meters
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on your own: applications of right triangle trigonometry on your own ap…
24 ft
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on your own: applications of right triangle on your own applications of…
5.2 meters
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a convenience store owner plans to mount a security camera on the wall …
5.31 ft
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6. in each of the following cases, indicate if the given figures are si…
a) Not similar b) Similar c) Similar d) Not similar --- ### For Question 7:
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find the circumference. 12 cm
The circumference is \( 24\pi \, \text{cm} \) (or approximately \( 75.36 \, \text{cm} \)).
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in the accompanying diagram, which is an equation of line ( ell )? opti…
A. $x = 3$
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$overleftrightarrow{ap}$ is tangent to circle $o$ at $a$, circle $o$ ha…
2 ft
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using the figure shown, which line segment could represent a chord of a…
$\overline{LM}$
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the figure below is a drawing of a circular window in a building. circu…
A. 20
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using the figure shown, which line segment could represent a chord of t…
$\overline{QR}$
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what is the correct formula for the area of this circle? 18 a = π(9²) a…
A. $A = \pi(9^2)$
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using the figure shown, which line segment could represent a chord of a…
$\overline{PQ}$
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in circle o shown below, diameter \\(\\overline{db}\\) is perpendicular…
8
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d. find the measures of $\\angle dah$, $\\angle hab$, $\\angle bac$, an…
To solve for the measures of \(\angle DAH\), \(\angle HAB\), \(\angle BAC\), and \(\angle CAE\), we typically need a diagram (e.g., a protractor - marked angle diagram, a set of i…
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in order to create a pattern for a blanket, ming needs to use two congr…
B. 18 in.
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the area of a sector of the circle with an arc measure of 30° and with …
3π
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what is the correct formula for the area of this circle? 10 a = π + 2(1…
C. $A = \pi(5^2)$
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using the figure shown, which line segment could represent a chord of t…
$\overline{MN}$
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in the figure above, circle ( o ) is inscribed in ( \triangle abc ) so …
20
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+follow these steps to write a thesis statement for each of the prompts…
Level 1: I believe the U.S. presidential birth eligibility law should be changed to allow naturalized citizens to run for office. Level 2: The U.S. presidential birth eligibility …
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what is the measure of $\\angle x$? diagram of a circle with a triangle…
$64^\circ$
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true/false decide if each statement is true or false, and write \true\ …
true 2.
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in the diagram, $mangle c = 35$, $moverarc{bd} = 50$, $overline{de} con…
16.58 cm
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on the school playground, the slide is 4 meters due west of the tire sw…
5
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edgars school is 15 kilometers west of his house and 8 kilometers south…
40
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in circle r shown below, diameter \\(\\overline{de}\\) is perpendicular…
$\overline{RL} \cong \overline{LE}$
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use the pythagorean theorem write an equation that can be used to answe…
The ship is 10 meters from the lighthouse. Now problem 2 (How long is the wire supporting the sign?):
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8.4 cm c 4.3 cm what is the length of the hypotenuse? if necessary, rou…
9.4
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4. the diagram shows $overline{eh}$ intersecting $overline{cd}$, $overl…
The relevant angle relationship is that the sum of the right angle (\( 90^\circ \)), \( 20^\circ \), \( x^\circ \), and \( \frac{5}{3}x^\circ \) equals \( 180^\circ \) (these angl…
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find the area of the figure. 13 cm, 5 cm, 7 cm. options: 50 cm², 28 cm²…
$50 \text{ cm}^2$
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use the correct inequality symbol to complete each statement. a. if c <…
\(>\) ### Part B
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use the correct inequality symbol to complete each statement a. if $c <…
\(ac > bc\) (so the symbol is \(>\)) ### Part B (Assuming the question is \(a - c\) vs \(b - c\))
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in the diagram shown, abcd is an isosceles trapezoid with altitude \\(\…
174 units²
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$\\overleftrightarrow{cd}$ is the bisector of $\\angle c$. construct th…
The incenter is the intersection point of \( \overrightarrow{CD} \) (angle bisector of \( \angle C \)) and the angle bisector of either \( \angle A \) or \( \angle B \). When cons…
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this drawing is an example of a ______. options: translation, octagon, …
D. reflection
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jules owns a square plot of land that measures 30 yards on each side. h…
\( 30\sqrt{2} \) yd (corresponding to the option \( 30\sqrt{2} \) yd)
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7. a hockey rink is 96m by 48m draw a scale model of a hockey rink if t…
Use a ruler to draw a rectangle with a length of 8 cm and a width of 4 cm; this rectangle is the scale model of the hockey rink.
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triangle abc is an image of the other triangle. what kind of transforma…
rotation
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theorem of interior angles of a triangle theorem the sum of the interio…
a) $\boldsymbol{146^\circ}$ b) $\boldsymbol{115^\circ}$ c) $\boldsymbol{25^\circ}$ d) $\boldsymbol{52^\circ}$ e) $\boldsymbol{10^\circ}$ f) $\boldsymbol{43^\circ}$
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what is the area of the parallelogram? 16 cm 24 cm 30 cm 240 cm² 768 cm…
480 cm²
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line segment yv of rectangle yvwx measures 24 units. what is the length…
\(8\sqrt{3}\) units (the option: \(8\sqrt{3}\) units)
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which rule explains why these scalene triangles are similar? options: s…
none of the above; the triangles cannot be proven similar
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the diagram above shows a square with a side of 6 and a circle with rad…
0.60
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what is the area of $\\triangle abc$ if $h = 12$ and $ac = 5$? (options…
30
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consider triangle def. the legs have a length of 36 units each. what is…
D. \(36\sqrt{2}\) units
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which triangle is a 30°-60°-90° triangle? 10 5 $5\\sqrt{3}$ 15 5 $5\\sq…
The first triangle (with sides 5, \(5\sqrt{3}\), 10)
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the length of segment ef is 12 cm. which statements regarding triangle …
- \( \overline{EF} \) is the longest side of \( \triangle DEF \). - \( DF = 6\space cm \) - \( DE = 6\sqrt{3}\space cm \)
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the drawing shows an example of ______. a transmission a translation a …
a translation
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use the pythagorean theorem to determine the hypotenuse of a right tria…
15 in.
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triangle abc is a right triangle. which equation could be used to deter…
$x = \sqrt{15^2 - 8^2}$
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in the right triangle shown, what is the length of $overline{pq}$? 8.5 …
15 m
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find x. 2 1.5 2.5 3 1 1.5
2.5
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what is x? 21 in. 28 in. x 7 inches 49 inches 12 inches 35 inches
35 inches
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find the length of \\(\\overline{ac}\\) to the nearest tenth.\ \ \\(\\b…
12.5
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given the following triangle, \\(\\tan \\theta = \\underline{quadquad}\…
$\frac{3}{4}$
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multiple choice 1 point which of these statements, if true, is sufficie…
$\angle S \cong \angle QPR$
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given the following triangle, \\(cos \\theta =\\) ____ . the triangle i…
$\frac{4}{5}$ (corresponding to the option "4/5")
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$overline{pq}$ is parallel to $overline{xy}$. what is the length of $ov…
3
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estimate the measure of this angle within 15°.
$120^\circ$ (range: $105^\circ$ to $135^\circ$)
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for problems 1 and 2, use the diagram that shows $overleftrightarrow{ab…
$\angle AED$ and $\angle BEC$ (or $\angle AEC$ and $\angle BED$) #### b. Adjacent angles
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$overline{pq}$ is parallel to $overline{xy}$. what is the length of $ov…
\). Given \( PQ = 4 \), \( QR = 6 \), \( YR = 4 \), \( PR = 8 \). So \( \frac{PQ}{XY} = \frac{6}{4} = \frac{3}{2} \). Therefore, \( \frac{PR}{XR} = \frac{3}{2} \), so \( \frac{8}{…
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which angles are adjacent to each other? \\(\\angle 4\\) and \\(\\angle…
$\angle5$ and $\angle4$
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a triangle has sides whose lengths are 5, 12, and 13. a similar triangl…
10, 24, and 26 (the first option: 10, 24, and 26)
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5. angle (θ) opposite adjacent hypotenuse trig function
\( x \approx 4.60 \)
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find the radius of a circle with a circumference of 28.26 cm.
The radius of the circle is \( 4.5\space\text{cm} \).
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which of the following statements is incorrect? 19, x, 25°, y (right tr…
\(\boldsymbol{\cos 25^{\circ}=\frac{19}{x}}\) (the first option: \(\cos 25^{\circ}=\frac{19}{x}\))
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4. angle (θ) opposite adjacent hypotenuse trig function
If we are finding the length of \(x\) (the opposite side), the value of \(x\) is approximately \(6\). For the table: - Angle \((\theta)\): \(50.1^\circ\) - Opposite: \(x\) (or app…
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12. find the stated lengths and angle measures of rhombus fghj. round t…
$GJ = 26$ $JK = 13$ $\angle HFJ = 82^\circ$ $\angle HJF = 8^\circ$
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12. find the stated lengths and angle measures of rhombus fghj. round t…
$GJ = 26$ $JK = 13$ $\angle HFJ = 40.8^\circ$ $\angle HJF = 49.2^\circ$
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determining leg length in a 45°-45°-90° triangle the hypotenuse of a 45…
\(12\sqrt{2}\) in. (corresponding to the option: \(12\sqrt{2}\) in.)
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a right triangle has one angle that measures 60°. what is the measure o…
$30$
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one angle of an isosceles triangle measures 30°, what measures are poss…
B. $120^\circ$, C. $75^\circ$, D. $30^\circ$
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key vocabulary circle a number to rate how well you know each word. mar…
1. **belief**: - Rating example: 3 - Correct definition: an idea that you think is true - Drawing idea: A child drawing a picture of the tooth fairy under their pillow 2. **experi…
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one angle of an isosceles triangle measures 40°. what measures are poss…
40°, 70°, 100°
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determining angle/side relationships what are the angle measures in tri…
\(m\angle A = 90^{\circ},m\angle B = 60^{\circ},m\angle C = 30^{\circ}\) (the third option)
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practice with special right triangles. each leg of a 45°-45°-90° triang…
\(14\sqrt{2}\) cm (corresponding to the option: \(14\sqrt{2}\) cm)
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3. | angle (θ) | opposite | adjacent | hypotenuse | trig function | | -…
\( x\approx13.75 \) (or \( \approx13.77 \) with more precise \( \cos(37^\circ) \))
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practice solving problems involving complementary and supplementary ang…
$\boldsymbol{\angle4 \text{ and } \angle5}$, $\boldsymbol{\angle7 \text{ and } \angle5}$, $\boldsymbol{\angle3 \text{ and } \angle6}$
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a right triangle has one angle that measures 30°. what is the measure o…
$60$
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in square abcd, diagonals \\(\\overline{ac}\\) and \\(\\overline{db}\\)…
\( x = 6 \) \( y = 3 \)
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given: ∠1 and ∠2 are complements, ∠2 and ∠3 are complements, and m∠1 = …
By the **Congruent Complements Theorem**, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of **congruent** ang…