Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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d) a 6.0 cm b (right angle) 5.0 cm c 2.0 cm d (right angle) i statement…
The length of \(i\) is \(2.4\space cm\)
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modeling with polynomials quick check (1 point) the equation ( a(w) = w…
A. A(w) increases as w increases when \( w > 0 \)
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rotation spinning a shape around a certain point
The problem here is about the geometric transformation of rotation (spinning a shape around a point). To analyze or perform a rotation, we can use the following general steps for …
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a triangle is rotated 90° about the origin. which rule describes the tr…
(x, y) → (-y, x)
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what is the value of s?
\( 26 \)
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△rst ~ △nmo. what is an? (not drawn to scale) triangles shown: blue △rs…
\(4\)
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the diagram shows two similar pentagons. the shortest side of the large…
B. 42 cm
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use the diagram shown to answer the question. right triangle with right…
C. $19\sin33^\circ$
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what is the value of s? diagram: right triangles ghi (right angle at h)…
\( 26 \)
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the triangles are similar, and the angle bisectors are drawn from corre…
\(28\)
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what is tu? diagram with points w, v, t, u, right angles, segment label…
\( 40 \)
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problems 1–6: here is a coordinate plane 1. write the coordinates of ea…
| Point | Coordinates | |-------|-------------| | V | (4, 2) | | W | (-2, 4) | | X | (-5, -5) | | Y | (3, -3) | | Z | (-5, 0) | ### Problem 2: Plot and label point A at (-2, 1)
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the triangles are similar, and the angle bisectors are drawn from corre…
\(28\)
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what is... 40 x+21 m∠...
\( x = 7 \)
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the area of the parallelogram below is 280 m². what is its height? (not…
The height of the parallelogram is \( 14 \, m \).
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if m∠qrt = m∠srt = 51° and st = 45, what is qt? qt = (diagram shows poi…
\( 45\)
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y-value tells you to move left,right up,down
The \( y \)-value tells you to move \(\boldsymbol{\text{up, down}}\) (matching the blue "up, down" box).
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if eh = gh = 4 and m∠gfh = 53°, what is m∠efh? m∠efh = \\boxed{}°
\( 37 \)
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problem 20: (lesson 26) decide whether this definition passes the rever…
A. If a person plans buildings and oversees their construction, then he/she is an architect; converse is not true and the definition does not pass.
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if $\\angle efh \\cong \\angle gfh$, $eh = s + 6$, and $gh = 2s$, what …
12
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the graphs represent a rotation around a fixed point. pre-image (graph)…
B. \( 90^\circ \) clockwise rotation around the point \( (1, 1) \)
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what is the value of a? diagram: points r, s, p, q with right angles at…
\( 20 \)
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if $overline{ad} cong overline{cd}$ and $mangle abd = 66^circ$, what is…
\( 132 \)
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∠a and ∠b are supplementary. if m∠a = 6x + 17 and m∠b = 3x + 10, find m…
113
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what is wx? wx =
\( 8 \)
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problem 16: (first taught in lesson 12) if \\(\\overrightarrow{ce}\\) b…
48
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if m∠wyx = m∠wyz = 45°, wx = u + 46, and wz = 3u, what is the value of …
\( 23 \)
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for exercises 1–18, give the coordinates of each point. then name the q…
\((-5,5)\), II ### Problem 3: Point C
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what is the value of t?
\(24\)
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a classroom board is 18 inches wide and 16 inches tall. kenji is puttin…
68
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the diameter of a circle is 14 meters. what is its radius? a 7 m b 3.5 m
A. 7 m
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if m∠tvu = m∠tvw = 41°, tu = x + 50, and tw = 3x, what is the value of …
\( 25 \)
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(b) problem 13: (first taught in lesson 23) given \\(\\overline{kl} \\p…
32
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problem 12: (first taught in lesson 17) given that $overleftrightarrow{…
A. Interior angles on the same side of the transversal; supplementary
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problem 11: (first taught in lesson 23) given that $overrightarrow{ba} …
A. Corresponding angles; congruent
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what is m∠bce? m∠bce = \\boxed{^\\circ}
\( 64 \)
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problem 10: (first taught in lesson 24) given that $overleftrightarrow{…
A. Alternate exterior angles; congruent
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mateo made the model below to represent the number of miles he swims in…
For the first drop - down: number of columns (or number of groups/rectangles) For the second drop - down: number of shaded blocks per column (Note: Since the exact drop - down opt…
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if m∠acb = m∠acd = 66° and ad = 10, what is ab? diagram of triangle wit…
$10$
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a coordinate grid with x - axis (ranging from -5 to 5) and y - axis (ra…
D. U
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if rs = ru = 71 and m∠rtu = 65°, what is m∠stu? m∠stu = □° submit
\( 130 \)
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what is uv? uv = \\boxed{} submit
\( 33 \)
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use the coordinate plane at the right for exercises 1-18. for exercises…
\((-5,5)\), II ### 3. Point C
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1. alphabetize the following list of vocabulary words and add three to …
Alphabetized list: bow, convert, dimension, dowel, parallel, rectangle, savage (noun), stern. Added words: apple, banana, cat, dog, elephant.
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what is the perimeter of the square below? (the square has a side lengt…
The perimeter of the square is 36 inches.
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from this given statement, select the definition, property, postulate, …
(Note: The provided option A is incorrect for this proof. The correct theorem is the "Congruent Complements Theorem" which states that if two angles are complementary to the same …
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what is m∠uvw? diagram with points x, u, v, w; right angles at w and u;…
\( 127 \)
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which figure is missing in the pattern?
The missing figure is a grid with 5 rows (vertical) and 4 columns (horizontal) (a 5×4 grid of blue squares, following the pattern where each subsequent figure increases the number…
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what is m∠uvw? diagram: right angles at w (xw ⊥ wv) and u (xu ⊥ uv), se…
\( 66 \)
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if $\\angle bce \\cong \\angle dce$ and $be = 10$, what is $de$? diagra…
$10$
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problem 7: (first taught in lesson 24) from this given statement, selec…
(Note: Since the full options B - E are not provided, but based on the context, the correct concept should be "If two parallel lines are cut by a transversal, then consecutive int…
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the lines intersect to form a square pyramid. which pair of lines are p…
A. \(\overleftrightarrow{AD}\) and \(\overleftrightarrow{BC}\)
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problem 6: (first taught in lesson 12) complete this sentence with the …
B. midpoint
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each square on the grid in problem 1 measures 5 ft by 5 ft. use the len…
(for problem 3 table, filling scaled lengths and possible original lengths): | original side length (ft) | 6 | 2 | 3 | 5 | |---------------------------|---|---|---|---| | scaled s…
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problem 5. (lesson 18) complete this sentence with the best of the choi…
E. congruent
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what is the area of the rectangle? 2 cm (height of rectangle), 3 cm (ba…
A. \( 6 \, \text{cm}^2 \)
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the area of the rectangle? cm 3 cm a 6 cm² b 23 cm² c 17 cm² d 31 cm²
A. $6\ cm^2$
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circle the even numbers: 2 8 9 15 90 13 100 3 22 14 50 104 201 46
The even numbers to circle are: 2, 8, 90, 100, 22, 14, 50, 104, 46
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problem 3: (first taught in lesson 26) complete this sentence with the …
To solve this, we recall the Alternate Interior Angles Theorem (or its converse). The converse of the Alternate Interior Angles Theorem states that if two lines are cut by a trans…
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square on the grid in problem 1 measures 5 ft by 5 ft. use the length o…
First Table Scaled Side Lengths: 1, 2, 3, 4 (for original 5, 10, 15, 20) Second Table Scaled Side Lengths: 24, 8, 12, 16 (for original 6, 2, 3, 4; or other originals with scale fa…
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an angle is bisected, forming two new angles. each new angle has a meas…
\(34^{\circ}\)
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on the grid in problem 1 measures 5 ft by 5 ft. use the length of c the…
### First Table (Original to Scaled, Scale Factor Calculation) #### Explanation: We know that the grid square is 5 ft by 5 ft. Let's assume the first row is the original length (l…
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if st = 11x + 17, tu = 7x − 19, and su = 19x − 19, what is tu? diagram:…
\( 100 \)
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if uv = x - 2, vw = 3x - 13, and uw = 9, what is vw? diagram: u---v---w…
\( 5 \)
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if fg = 3x, gh = 9x - 5, and fh = 11x + 8, what is fg? simplify your an…
39
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given: ( angle e cong angle g ), ( overline{de} parallel overline{fg} )…
To prove \( \overline{EF} \parallel \overline{GH} \): 1. **Given**: \( \angle E \cong \angle G \), \( \overline{DE} \parallel \overline{FG} \) 2. **Alternate Interior Angles Theor…
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circle letters that need to be capitalized and add the missing punctuat…
### Part 1: Capitalization and Punctuation 1. **"wow, i loved that movie"** - Capitalize "W" (start of sentence) and "I" (first - person pronoun). - Add an exclamation mark (!) as…
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if st = x + 11, tu = 20, and su = 7x - 17, what is su? diagram: line se…
39
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if kl = 2x, lm = 6x - 16, and km = 4x + 8, what is km? simplify your an…
34
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if uv = 12, vw = x - 6, and uw = 2x - 6, what is uw? u ---- v ---- w (w…
18
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on a line segment, u is between t and v. if tu = 12x, uv = 10x - 11, an…
84
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on a line segment, u is between t and v. if tu = 13x, uv = 10x - 11, an…
52
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on a line segment, q is between p and r. if pq = 6x + 8, qr = x + and p…
5
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f is a point on segment eg. if ef = 3x, fg = x + 9, and eg = 5(2x - 7),…
11
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complete the proof given: ( t ) is the midpoint of ( overline{su} ) dia…
\( x = 5 \)
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if ef = 2x, fg = x - 2, and eg = 2x + 16, what is ef? diagram: e---f---…
36
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chapter 1 worksheet please fill in the blank with correct word or words…
\(x = 11\)
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if kl = 11x, lm = 18x - 20, and km = 20x + 7, what is km? diagram of k-…
67
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a triangle has sides a = 2 and b = 5 and angle c = 40°. find the length…
\(3.699\)
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a triangle has sides a = 6 and b = 2 and angle c = 60°. find the length…
\(2\sqrt{7}\)
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if kl = 11x, lm = x + 14, and km = 16x + 2, what is lm? k l m 11x x + 1…
\( 17 \)
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practice: find the equation of the circles with the given pairs of coor…
To find the equation of a circle when the endpoints of its diameter are given, we use the **diameter form of the circle's equation**: If \((x_1, y_1)\) and \((x_2, y_2)\) are the …
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if de = x - 5, ef = 18, and df = 3x - 19, what is df? diagram: line seg…
29
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solve for the angle θ where 0 ≤ θ ≤ 2π. sin 2θ - √2 cos θ = 0 θ = (use …
\(\frac{\pi}{4},\frac{3\pi}{4},\frac{\pi}{2},\frac{3\pi}{2}\)
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if uv = x - 8, vw = 7, and uw = 2x - 17, what is uw? diagram of u---v--…
15
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if ef = 7x + 15, fg = 8x, and eg = 17x - 11, what is ef? diagram: e---f…
106
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solve for the angle θ, where 0 ≤ θ ≤ 2π. $sin^2 \theta = \frac{3}{4}$ $…
\(\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\)
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if rs = 20, st = 17x, and rt = 19x + 14, what is rt? diagram: line segm…
71
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if bc = x - 4, cd = 11, and bd = 2x - 12, what is bc? diagram: points b…
15
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what is the length of the hypotenuse? if necessary, round to the neares…
6.2
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if fq = 8, qh = x + 10, and fh = 10x, what is qh? diagram: line segment…
12
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if de = x + 5, ef = 4, and df = 10x, what is de? d---e---f (with de lab…
\(6\)
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4. if a rectangle is 3 inches by 5 inches, what is its area?
The area of the rectangle is 15 square inches.
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if tu = x + 3, uv = 5x, and tv = 9, what is uv? diagram: line segment t…
5
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4. what is the ordered pair of point x on this graph?
\((8, 10)\)
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complete the proof that ∠ptq ≅ ∠rts. diagram with points s, r, t, q, p …
Statement: \( m\angle PTQ = m\angle RTS \) Reason: Subtraction Property of Equality (Then, to get \( \angle PTQ \cong \angle RTS \), the next step would use the Definition of Cong…
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given: lines p and q are parallel and r is a transversal. prove: ∠2 ≅ ∠…
# Explanation: ## Step1: Analyze Statement A (Reason: Vert. ∠’s ≅) Vertical angles are congruent. Looking at the diagram, ∠2 and ∠3? No, wait, ∠2 and ∠3 are adjacent, but ∠2 and ∠…
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given: lines p and q are parallel and r is a transversal. prove: ∠2 ≅ ∠…
A: Angle 2 is congruent to angle 3 B: Angle 3 is congruent to angle 7
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3. define in your own words what it means when two figures are congruen…
Two congruent figures have identical shape and size; corresponding sides/angles are equal, and one can be transformed (moved/rotated/reflected) to match the other exactly.
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dominic used his younger sisters pattern blocks to spell out his name. …
\( 90^\circ \)