Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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3 fill in the blank 25 points given △jkl with points j(1, -2), k(4, -1)…
\( J'(-2, 1) \) \( K'(-1, 4) \) \( L'(-3, 3) \)
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if the measure of angle 6 = 75 and the measure of angle 7=3x, what is t…
35
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2 fill in the blank 25 points given △jkl with points j(1, -2), k(4, -1)…
\(J'(-3, -2)\) \(K'(-6, -1)\) \(L'(-5, -3)\)
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fill in the blank 25 points given △jkl with points j(1, -2), k(4, -1), …
\(J'(1,2)\) \(K'(4,1)\) \(L'(3,3)\)
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22. the measure of $\\angle g$ is six more than twice the measure of $\…
\( 28^\circ \) ### Problem 23
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transversal vocabulary what is the relationship of the angles? diagram:…
(Assuming the question is about the angle relationship with two parallel lines and a transversal, and the correct option is "Alternate interior" (if that's the intended correct on…
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options: vertical, alternate interior (selected), alternate exterior, c…
The problem is about identifying the type of angles formed by a transversal with two parallel lines. From the options and the context (likely a geometry problem), the selected opt…
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given ( a = \begin{bmatrix} -1 & -2 & 3 \\ 4 & 8 & -6 \\ 0 & 1 & 5 end{…
The correct option is the second matrix: \(\begin{bmatrix}-4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3\end{bmatrix}\) (the one with the radio button not selected initially). So the ans…
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transversal vocabulary if two are parallel, then alternate interior ang…
The correct option is the one labeled with "congruent" (the last option, assuming the options are ordered as complementary, supplementary, disconnected, congruent). So, if we assu…
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read and try to solve the problem below. what is the approximate area o…
The approximate area of the circle is \( 12.56 \) (or \( 4\pi \) or \( \frac{88}{7}\approx 12.57 \)) square units.
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the following inequality and graph the solution. 3(x + 5) - 6 > -2(x - …
The solution of the inequality is \(x > 2\), and the correct graph is the one (e.g., OB) that shows an open circle at \(x = 2\) and the arrow pointing to the right.
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a recipe for lemon bars calls for a 14\ × 13\ pan. how many 1\ × 1\ bar…
16
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21. ∠u and ∠w are vertical angles. if m∠u = 6x + 11 and m∠w = 10x − 9, …
\( 41^\circ \)
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when 2 parallel lines are both intersected by a transversal, these angl…
The angles described are called corresponding angles.
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ahron j vav date ______ lg: i can classify real numbers into the correc…
Irrational: X (Rational: no X) ### Problem 2: Classify $2.878787\cdots$
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what is the converse of the alternate interior angles theorem? if p and…
If angle \( D \) is congruent to angle \( E \), and \( r \) is a transversal, then \( p \) and \( q \) are parallel.
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what is the perimeter of the figure shown if the smallest side is 1.5 u…
\(22\)
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what is the perimeter of the figure shown if the slanted side is 10.6 u…
44.6
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what is the perimeter of the figure shown if the slanted side is 10.6 u…
46.6
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what is the area of the figure shown? the area is □ square units. (type…
\(90\) (The answer may vary depending on the actual dimensions of the figure from the grid. If you can provide the exact number of grid squares for the base and height, we can get…
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6. determine the correct answer. determine the coordinates for c after …
\((-3, -1)\) ### Problem 8:
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for each image, match the correct ordered pair. (4 points) 2. determine…
(Problem 2): The coordinates of \(A'\) after reflection over the x - axis is \(\boldsymbol{(0, 3)}\) (matches with the given \((0,3)\) on the right).
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use the equation to solve for the area of the inner square. start by fi…
The area of the inner square is 32 square units. The area of the outer square is 64 square units, the sum of the areas of the 4 triangles is 32 square units, and the area of the i…
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what is the area of the figure shown? the area is □ square units. (type…
64
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start by writing a subtraction equation you could use to find the area …
area of outer square - sum of the areas of the 4 triangles = area of inner square
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if ∠tqr is a right angle, m∠rqs = 10°, and m∠tqs = (8x)°, find each ang…
\( x = 10 \) \( m\angle TQR=90^\circ \) \( m\angle TQS = 80^\circ \)
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if m∠iut = 42°, m∠iuv = (51x - 1)°, and m∠vut = (-1 + 72x)°, find the a…
\( x = 2 \) \( m\angle IUV = 101^\circ \) \( m\angle VUT = 143^\circ \)
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if ∠dfe is a right angle, m∠cfd = (4x)°, m∠cfe = (9x − 14)°, find each …
\( x = 8 \) \( m\angle DFE = 90 \) \( m\angle CFD = 32 \) \( m\angle CFE = 58 \)
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m∠gfe is a straight angle, m∠gfb = (160x)°, and m∠efb = (19x + 1)°, fin…
\(x = 1\) \(m\angle GFE = 180^\circ\) \(m\angle GFB = 160^\circ\) \(m\angle EFB = 20^\circ\)
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m∠uvz = 30° and m∠zvw = 78°. find m∠uvw w v z u m∠uvw= ° need help with…
\( 108 \)
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read the excerpt from the crab that played with the sea... then the lit…
The group of sentences: "And the Eldest Magician said, 'How wise are little children who see and are silent! What was the beast like?' And the little girl - daughter said, 'He was…
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use the figure to identify another name for ∠3. options: o a) ∠acd o b)…
B) \(\angle ADC\), \(\angle CDA\)
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use the picture to name four rays. o a) $overrightarrow{st}$, $overrigh…
C) \(\overrightarrow{ST}\), \(\overrightarrow{TU}\), \(\overrightarrow{TV}\), \(\overrightarrow{TW}\)
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on a scale drawing, a rectangular area has a length of 25 feet and a wi…
120 feet (corresponding to the option "120 feet")
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highlighter which pairs of lines are perpendicular to each other? selec…
B. \(\overleftrightarrow{AE}\) and \(\overleftrightarrow{FC}\), C. \(\overleftrightarrow{DG}\) and \(\overleftrightarrow{BG}\)
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solve two rectangular fields, both measured in yards, are modeled below…
\( x = 12 \)
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the scale factor of a large oil container to a small oil container is 0…
\( 60.75\space cm^{3} \) (corresponding to the option "60.75 \( cm^{3} \)")
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the scale factor of the blueprint of a wall to the actual wall is 0.07.…
\( 0.1764\space ft^2 \) (corresponding to the option: 0.1764 \( ft^2 \))
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in words, type what kind of angle is formed. • ∠bgc forms an angle. • ↔…
To solve this, we analyze each angle based on their measures (acute < 90°, right = 90°, obtuse > 90° < 180°, straight = 180°): ### For ∠BGC: The angle between BG and GC is less th…
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a travel guide has dimensions 8 in. by 10 in. what scale factor should …
1.5
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which transformations map the strip pattern onto itself? ppppp a horizo…
a horizontal translation only
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use the figure to identify another name for ∠cad. figure: points a, b, …
B) \( \angle 1 \), \( \angle DAC \)
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given △abc with points a(-2, 3), b(1, 0), and c(-3, 1), graph it, and i…
- \( A' \): \( (3, -2) \) - \( B' \): \( (0, 1) \) - \( C' \): \( (1, -3) \) - \( A'' \): \( (1, 2) \) - \( B'' \): \( (-2, 5) \) - \( C'' \): \( (-1, 1) \)
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a 4 in. by 5 in. photo is enlarged so that its width (shorter dimension…
6.25 in.
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exercise #2: find the measure of ∠b. 1)
\(112^\circ\)
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kurt enlarges a 24 cm by 30 cm photo to a 60 cm by 75 cm photo. what is…
2.5 (corresponding to the option "2.5")
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classify each figure as a line, ray, or line segment. then, show how to…
Type: line; How to write it: $\overleftrightarrow{JK}$ ### Part (b)
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fill in the blanks 10 points given △abc with points a(-2, 3), b(1, 0), …
- \( A' \): \( (3, -2) \) - \( B' \): \( (0, 1) \) - \( C' \): \( (1, -3) \) - \( A'' \): \( (0, 0) \) - \( B'' \): \( (-3, 3) \) - \( C'' \): \( (-2, -1) \)
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kurt enlarges a 24 cm by 30 cm photo to a 60 cm by 75 cm photo. what is…
2.5 (corresponding to the option "2.5")
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what type of angle does ∠fdc form? a) straight angle b) right angle c) …
A) Straight angle
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use the figure to name the vertex of ∠1. options: a) c, b) a, c) d, d) b
B) A
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d. the bike never started moving which choice describes how to identify…
d. The line curves or changes direction, not remaining a straight line ### For the question "Which type of graph would best illustrate seasonal changes in temperature over a year?"
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#4: solve the area a of a sector of a circle with radius r and angle-me…
\( r = \sqrt{\frac{360A}{\pi S}} \)
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use the figure to complete each part. (a) name the sides of ∠tqr. and (…
$\overrightarrow{QT}$ and $\overrightarrow{QR}$ ### Part (b)
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name another look! additional practice 1-4 count 4 and 5 home activity …
### Problem 1: # Explanation: ## Step1: Count the dots on the die. The die has 4 dots. ## Step2: Draw 4 counters (circles) in the box. So we draw 4 dashed - like circles (similar …
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which angle is formed by $overrightarrow{ed}$ and $overrightarrow{ef}$?…
B. $\angle 3$, D. $\angle DEF$
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find the volume of the shape below:
The volume of the rectangular prism is \( 208.8 \) cubic inches.
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mathematical connections in exercises 11 and 12, find the dimensions of…
The side length of the cube is \( 4 \) inches. ### Exercise 12:
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classify ∠mpr as right, acute, or obtuse. then identify the most approp…
\(\angle MPR\) is obtuse. A possible angle measure is \(105^\circ\) (the exact measure depends on the diagram's proportions, but it is an obtuse angle, so measures like \(100^\cir…
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classify ∠rpn as right, acute, or obtuse. then identify the most approp…
\(90^\circ\), right
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classify ∠rpn as right, acute, or obtuse. then identify the most approp…
\(120^\circ\), obtuse
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use the figure to name the sides of ∠4. figure with points a, b, c, d, …
C. $\overrightarrow{CA}$, $\overrightarrow{CD}$
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find the value of x.
\(30\)
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2. find the area of the shape below. break the larger shape into smalle…
The area of the shape is \(200.55\) square meters.
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find the value of x. triangle with angles 66°, 36°, and x° x = blank box
\(78\)
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find the value of x.
\(34\)
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classifying angles sheet 1 classify each angle as acute, obtuse, right,…
To solve this, we use the definitions of angle types: - **Acute Angle**: Less than \( 90^\circ \) (and greater than \( 0^\circ \)). - **Right Angle**: Exactly \( 90^\circ \). - **…
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point x is the circumcenter of δabc. what is the length of mb? ○ 1.5 cm…
\(2.5\) cm (corresponding to the option "2.5 cm")
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using transformations and rectangle abcd above, explain why segments ad…
Los segmentos \( AD \) y \( BC \) son congruentes porque se pueden mapear uno al otro mediante una **transformación rígida** (reflexión o traslación), que preserva la longitud. Po…
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three friends want to meet at a place that is the same distance from ea…
B. Bisect each of the angles with vertices at their houses.
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point y is the circumcenter of triangle def. which statement is true ab…
Point Y is the center of the circle that passes through points D, E, and F.
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quadrilateral abcd is a rhombus. complete the statement below using the…
Rotate ### Part B (First Statement: Translating a copy of the figure down 3 units)
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quadrilateral abcd is a rhombus. part a complete the statement below us…
over segment \(AC\)
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quadrilateral abcd is a rhombus. part a complete the statement below us…
Rotate ### Part B (Assuming a common valid/invalid case for angle mapping in rhombus)
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angle stv is a straight angle. the measure of angle stw is 130°. the me…
\(50\)
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why are translations, reflections, and rotations rigid transformations?
Translations, reflections, and rotations are rigid transformations because they preserve the shape and size of a figure (i.e., the pre - image and image are congruent). Translatio…
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translate segment ab 6 units left and 3 units downs. the coordinate of …
The coordinate of point \(A'\) is \((-5,0)\) The coordinate of point \(B'\) is \((-2,-2)\)
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in 8th-grade math, a ______ is an imaginary line that acts like a mirro…
line of reflection
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angle pqr is a right angle. the measure of angle sqr is 40°. the measur…
\( x = 50 \)
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when you apply two or more rigid motions—translations (slides), rotatio…
B. Sequence of Transformations
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image is the original geometric figure or object before a transformatio…
B. False
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angle pqr is a right angle. the measure of angle sqr is 40°. the measur…
\( 50 \)
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which angles in the picture are not supplementary? options: 1 and 2, 2 …
1 and 3; 2 and 4 (the third option in the list of choices)
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which figure shows a line tangent to the circle?
The third figure (the one with radius 3, segment 5, and tangent segment 4) shows a line tangent to the circle.
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2. which statement about the picture below is not true? ∠1 and ∠2 are c…
A. ∠1 and ∠2 are congruent.
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4 which expression cannot be used to name the angle below? diagram: two…
$\angle HGK$
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the perimeter of a rectangle is 50 inches. the length of the rectangle …
Solve for \( w \) in the equation \( 2(w + 10) = 50 \)
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cb is tangent to ⊙a at point c. find the radius. cb ⊥ ac by the radius-…
\(\frac{39}{10}\)
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graph the compound inequality on a number line. x ≥ 1 or x > 4 use the …
To graph \( x \geq 1 \) or \( x > 4 \) on the number line: 1. Place a closed circle (filled dot) at \( x = 1 \) (because \( x \geq 1 \) includes 1). 2. Shade the region to the rig…
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what is a reflection?
In geometry (a subfield of Mathematics), a reflection is a transformation that maps a figure over a line (the line of reflection) such that each point of the figure has a correspo…
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what does it mean when two figures are congruent? a they are similar in…
B. They have the same shape and size
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determine the expression for the width of a rectangle the area, a, of a…
\( 10x - 6 \) (the option with \( 10x - 6 \))
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what is a rotation? a sliding a figure in a straight line b turning a f…
B. Turning a figure around a fixed point
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2 what is a translation? a a turn around a point b a flip over a line c…
C. A slide from one position to another
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1 what is a rigid transformation? a a change that stretches or shrinks …
C. A transformation that does not change (preserves) the size and shape of a figure
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when constructing a direct proof for the theorem \for all integers n, i…
Assume \( n \) is an integer and \( n \) is even. ### Question 5 (For the statement...):
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4. (2 + 6x)° (2x + 2)° relationship: ______ x= ______
Relationship: Supplementary angles (since they form a linear pair, sum to \(180^\circ\)) \(x = 22\) (Step-by-step for reference: The two angles \((2 + 6x)^\circ\) and \((2x + 2)^\…
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11. list all information given by the marks on the diagram. // anota to…
- \( \angle RUV \), \( \angle UVT \), and \( \angle UTS \) are right angles ( \( \angle RUV = 90^\circ \), \( \angle UVT = 90^\circ \), \( \angle UTS = 90^\circ \) ), so \( RU \pe…
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3. relationship: ________ b= ________ (diagram shows intersecting lines…
\( b = 53^\circ \) (Relationship: Vertical angles are equal)
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graph the inequality ( x > -3 ) on a number line. use the tools to ente…
(Open circle at -3, arrow pointing to the right on the number line)