Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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a reflection across \\(\\overline{qr}\\) followed by a rotation \\(180^…
- The position of point Q is the same as the position of point Q'. - $\triangle QRS \cong \triangle Q'R'S'$ - $\overline{Q'R'} \cong \overline{R'S'} \cong \overline{S'Q'}$
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lottie needs to put gypsy moth caterpillar tape around the circumferenc…
7.85 feet (or approximately \( 2.5\pi \) feet if we leave it in terms of \( \pi \))
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the browns are putting a rock border around the circumference of their …
They need approximately \( 62.8 \) feet of rock (or \( 20\pi \) feet if we leave it in terms of \( \pi \)).
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if the diameter of a circle is 5 kilometers, what is the circumference?
The circumference of the circle is \( 5\pi \) kilometers (or approximately \( 15.7 \) kilometers).
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solve for x to the nearest tenth. (image of a geometric figure with sid…
\( x \approx 14.4 \)
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instructions solve the following problem and select your answer from th…
6
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point t is located at (-1, 1) on the coordinate plane. point t is refle…
\(T'(1,1)\)
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complete the following sentence. the figure below has rotational symmet…
\( 72 \)
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point m is located at (-4, 4) on the coordinate plane. point m is refle…
\(M''(4,-4)\)
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the triangle on the right is a scaled copy of the triangle on the left.…
$\frac{1}{2}$
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the rectangle on the right is a scaled copy of the rectangle on the lef…
\(\frac{9}{8}\)
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which terms describe this shape? choose all that apply. kite rhombus pa…
A. kite, B. rhombus, C. parallelogram, D. quadrilateral (assuming the options are labeled as such with these terms)
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which terms describe this shape? choose all that apply. shape image squ…
quadrilateral, rhombus
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a triangle with side lengths 17, 10, 21 and height 8 (with a right angl…
$84$ square feet
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6. $\\triangle rst \\sim \\triangle ysz$; find $yz$ (image of triangle …
\(YZ = 28\)
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use a trigonometric ratio to solve for d. round to two decimal places a…
$34.89$
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5. a parallelogram with base 12 inches, height 26 inches, and side leng…
312 square inches
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use a trigonometric ratio to solve for a. round to two decimal places a…
$16.29$
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find the measure of angle a in degrees. round to two decimal places as …
$54.46^\circ$
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use a trigonometric ratio to solve for d. round to two decimal places a…
$20.24$
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find the measure of angle y in degrees. round to two decimal places as …
$66.42^\circ$
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use a trigonometric ratio to solve for c. round to two decimal places a…
$18.86$
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practice period date example 1 practice • spiral review • extra practic…
1. $\triangle TRS \sim \triangle XWS$ (SAS Similarity, vertical angle + congruent sides) 2. $\triangle ABC \sim \triangle QPR$ (SSS Similarity, all sides in $\frac{4}{3}$ ratio) 3…
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use a trigonometric ratio to solve for z. round to two decimal places a…
$10.17$
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12. directions first, select the line a button to graph the line and ch…
1. Set Line Type to **Dashed** (not solid). 2. Graph the dashed line through intercepts $(6, 0)$ and $(0, -2)$. 3. Shade the region above this dashed line to represent the solutio…
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1. directions first, select the line a button to graph the line and cho…
1. Set the line type to **Dashed** (not Solid). 2. Graph the dashed line through intercepts $(10, 0)$ and $(0, -5)$. 3. Shade the region above this dashed line to represent the so…
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6. directions first, select the line a button to graph the line and cho…
1. Plot the solid line through points $(0, 6)$ and $(9, 0)$. 2. Shade the region below this solid line.
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the length of a rectangle is twice its width. if the perimeter of the r…
length: 12 m width: 6 m
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which point is a reflection of point p in the mirror line marked m? ima…
A. Point A
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which point is a reflection of point p in the mirror line marked m? ima…
B
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triangle qrs is dilated according to the rule $d_{0,2}(x,y)$. what is t…
- \( D_{O,2}(x,y)=(2x,2y) \) - The distance from \( Q' \) to the origin is twice the distance from \( Q \) to the origin. - Side \( Q'S' \) lies on a line with a slope of - 1. (If…
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consider the system of equations.\\begin{cases}x^{2}+y^{2}=49\\\\x=-y -…
The solutions are the points \((-7, 0)\) and \((0, -7)\). To graph the line \( x = -y - 7 \) (or \( y = -x - 7 \)): find two points (e.g., when \( x = 0 \), \( y = -7 \); when \( …
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below are two parallel lines with a third line intersecting them. x = \…
\(x = 92\)
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the point where two lines intersect on a graph is called the ______. th…
intersection point ### 2. The form of a linear equation written as \( y = mx + b \) is known as... form.
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the point where two lines meet or cross is called the ________. when th…
intersection point ### Second Question:
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12 8a - 4b + 7 = 6c explain why a, b and c cannot all be integers. 13 i…
Since \(8a-4b\) is even (as \(8a\) and \(4b\) are even, and even - even = even), \(8a - 4b+7\) is odd (even + odd = odd). But \(6c\) is even (as \(6c = 2\times3c\)). An odd number…
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in the diagram, $overline{kg}$, $overline{jf}$, $overline{ae}$ and $ove…
- $\overrightarrow{AE}$ is perpendicular to the horizontal line through $A$, creating a $90^\circ$ right angle. - The angles $\angle JAK$, $\angle KAE$, and the right angle $\angl…
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in the diagram, \\( \\overleftrightarrow{kj} \\), \\( \\overleftrightar…
- Vertical angles: $\angle EAK \cong \angle JAH$ - Complementary angles: $\angle JAH + \angle HAG = 90^\circ$, $\angle EAK + \angle KAJ = 90^\circ$ - Supplementary angles: $\angle…
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a water sprinkler sprays water over a distance of 30 feet while rotatin…
1021.02
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find the length s and area a. (there is a circle with a sector, radius …
$s = 2.094$ feet $A = 2.094$ square feet
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find the area a of the sector of a circle of radius 60 miles formed by …
300 miles²
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find the central angle θ which subtends an arc of length 18 inches of a…
$\frac{3}{7}$ radians (or approximately 0.429 radians)
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the pythagorean theorem (coloring activity) name: date: per: directions…
The missing side (hypotenuse) is approximately \(\boldsymbol{15.8}\) meters, corresponding to Dark Blue in the coloring activity.
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graph the image of trapezoid stuv after a dilation with a scale factor …
To graph the dilated trapezoid \( S'T'U'V' \): 1. Find the original coordinates: \( S(-3, -3) \), \( T(3, -3) \), \( U(3, 3) \), \( V(0, 3) \). 2. Apply dilation (scale factor 3, …
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for problems 18-26, solve and graph each inequality. 18. $-3(x + 6) < -…
\(x > 1\) (Graph: Open circle at 1, arrow to the right) ### Problem 19: Solve \(60 < 6(x + 8)\)
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2. write out the steps of your snowflake algorithm below. you may skip …
1. **Step 1: Define base shape** Start with an equilateral triangle (each side is a straight line segment of length $L$). 2. **Step 2: Segment division** For every straight line s…
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△ear is rotated 180° about the origin. draw the image of this rotation.
The image $\triangle E'A'R'$ has vertices at $E'(5, 6)$, $A'(5, -4)$, and $R'(2, -2)$. When plotted and connected on the coordinate grid, this forms the 180° rotation of $\triangl…
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pentagon abcde is the image of pentagon abcde under a dilation with a s…
2 units
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draw the image of $\\triangle abc$ under a translation by 5 units to th…
The vertices of the translated triangle are $A'(-6, 1)$, $B'(-4, -3)$, $C'(-2, 0)$. When plotted and connected, this forms the image of $\triangle ABC$ translated 5 units left.
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quadrilateral abcd is the image of quadrilateral abcd under a dilation.…
$\frac{1}{2}$
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plot the image of quadrilateral abcd under a reflection across the y-ax…
The reflected quadrilateral $A'B'C'D'$ has vertices at $(-1, -3)$, $(-2, -6)$, $(-4, -4)$, and $(-3, -2)$. When plotted and connected, this is the image of $ABCD$ reflected across…
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△abc is the image of △abc under a rotation about the origin, (0,0). gra…
B. $90^\circ$ counterclockwise D. $270^\circ$ clockwise
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find the midpoint of the segment with the following endpoints. (-2, 3) …
$(3, \frac{1}{2})$
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quadrilateral k is the image of quadrilateral k under a dilation. what …
D. \(D\)
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draw the line of reflection that reflects quadrilateral abcd onto quadr…
The line of reflection is $\boldsymbol{x=\frac{5}{2}}$ (or $x=2.5$), a vertical line passing through $x=2.5$ on the coordinate plane.
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draw the image of quadrilateral abcd under a translation by 2 units to …
The coordinates of the translated quadrilateral $A'B'C'D'$ are: $A'(-2, -4)$, $B'(5, -6)$, $C'(6, -4)$, $D'(-3, -2)$ (When drawn on the grid, connect these four points to form the…
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point ( a(2, 3) ) is the image of ( a(3, -4) ) under a translation. det…
A translation by 1 units to the left and 7 units up
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graph the inequality below on the number line. (a > -8) (there is a num…
To graph \( a > -8 \): - Place an **open circle** at \(-8\) (since \( a eq -8 \)). - Draw an arrow starting at the open circle and pointing **to the right** (towards values grea…
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find the area. a = ? ft² (there is a parallelogram with base 12 ft, hei…
\( 168 \)
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graph the inequality below on the number line. $b < 4$ number line from…
To graph \( b < 4 \) on the number line: - Place an open circle at \( 4 \) (since \( 4 \) is not included in the solution). - Draw a ray (line with an arrow) starting from the ope…
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name: date: 1-4-26 per: 7th unit 8: special right triangles day 3: spec…
\(a = 9\), \(b = 9\sqrt{2}\) ### Problem 2:
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express the interval using two different representations. 0 ≤ x ≤ 7 ans…
Interval Notation: $[0, 7]$ Number Line: A number line with closed (filled) circles at 0 and 7, and a solid green line segment connecting the two circles.
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3 numeric 1 point if the scale factor of figure a to figure b is 4:5, f…
12
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2 fill in the blank 1 point the pairs of polygons below are similar. gi…
$\frac{1}{2}$
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which is the best way to complete the text? francis scott key penned th…
Fort McHenry; he
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1. when the versailles treaty was signed, germany still had troops occu…
Belgium (the option with "Belgium" as the text, which was marked with the yellow circle in the original question's interface)
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instruction: determine the mirror image of the following with respect t…
### For Problem 1 (Mirror Image over Vertical Dashed Line) #### Step 1: Identify Key Points of the "L" Shape Let's denote the vertices of the "L" shape. Let the bottom - left corn…
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find the value of b in the diagram below. diagram: four rectangles each…
$5$
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exploring the properties of reflections explore the properties of refle…
\( CL = \boxed{2.8} \) units, \( LC' = \boxed{2.8} \) units
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in the coordinate plane, points a, b, and c have coordinates (1,2), (4,…
1. The figure is a right triangle. 2. $\frac{9}{2}$ (or 4.5) 3. The coordinates of point $D$ are $(1, -1)$. When plotted, $AD$ is vertical (matches the vertical side $BC$) and $CD…
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a net for a three - dimensional figure is shown on grid paper. each squ…
72
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slumbers trapped base nest poisoned comes cycle fair mordor entangled i…
1. Nest 2. Trapped 3. Slumbers 4. Comes 5. Poisoned
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given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠abc = m∠ghi (there is a box…
The statement $\boldsymbol{\angle ABC \cong \angle DEF}$ should be added with the reason "given". Then, using the transitive property of congruence (and the fact that congruent an…
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darryl organized his old school supplies into pencil boxes. he put 5 pe…
$4$
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a circular fountain has a diameter of 16 meters. what is its area? a. 2…
a. 200.96 m²
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if you slice a circle into 4 equal sectors, what is the area of one sec…
a. $16\pi$ cm²
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a circular fountain has a diameter of 16 meters. what is its area? a. 2…
a. $200.96\ \text{m}^2$
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the radius of a circular garden is 9 meters. what is its area? a. $81\\…
a. $81\pi \text{ m}^2$
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challenge - can you practice all 14 works of mercy? circle the works of…
1. I shared my treasure (money) to purchase the snacks for my sisters. 2. I saw the image of Jesus as a caring provider who looks after the needs of those in his care, especially …
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from the top of a 38 metre tall building, i look down to the street bel…
The car is moving away from the building.
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page 187: a weekend challenger... from the top of a 38 metre tall build…
The car is moving away from the building. (Sketch: Vertical building, two horizontal lines from top, two lines of sight with \(67^\circ\) and \(22^\circ\) angles to horizontal, in…
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which angles are adjacent to each other? select all that apply. image o…
$\angle5$ and $\angle6$, $\angle11$ and $\angle12$
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find the value of x. (there is a triangle with angles 45°, 53° and x°) …
\(x = 82\)
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find the value of x. (there is a right triangle with one angle 58°, one…
\(32\)
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progress: question id: 1063986 the movement of the progress bar may be …
The correct option is the fourth one: I read “Gone with the Wind,” but I have not seen the movie. (The option with the blue circle, which punctuates the title by using quotation m…
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rectangles q and r are similar. if the area of rectangle q is 294, what…
The area of rectangle R is \( 2.94 \).
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rectangles e and f are similar. if the area of rectangle e is 12, what …
The area of rectangle F is \( 9.72 \).
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use the given information to complete the proof of the following theore…
| Statement | Reason | |-----------|--------| | 1. $ABCD$ is a parallelogram | Given | | 2. $\overline{AB} \parallel \overline{DC}$ | Definition of a Parallelogram | | 3. $\overli…
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writing a two-column proof given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠…
2. $\angle GHI \cong \angle DEF$ 2. given 3. $\angle ABC \cong \angle GHI$ 3. transitive property 4. $m\angle ABC = m\angle GHI$ 4. definition of $\cong$ angles
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writing a two-column proof given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠…
**Statements**: $\angle ABC \cong \angle DEF$, $\angle GHI \cong \angle DEF$, $m\angle ABC = m\angle GHI$ **Reasons**: Given, Given, Transitive Property of Congruence (and Definit…
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algebra 1 semester review equations, inequalities, linear functions, an…
1. A. -27 2. A. -17 3. C. x < 4 4. D. x ≥ -16 5. B. 4 days 6. C. {0,2,3,4} 7. B. {-2,0,1,3} 8. D. -2 ≤ y ≤ 4
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write an equation of the line below. try again your answer is incorrect.
\(y=\frac{1}{2}x + 2\)
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name: shinu kiru area of a fox directions: find the area of each shape,…
To find the total area of the fox, we calculate the area of each shape (rectangles and triangles) and sum them up. ### Step[SSE onError error]
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in parallelogram pqsr, what is pq? options: 2 cm, 5 cm, 6 cm, 9 cm the …
9 cm
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what is the measure of angle l in parallelogram lmno? options: 20°, 30°…
B. 40°
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what is the missing reason in step 6? statements\treasons 1. \\(\\overl…
CPCTC
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what is the missing reason in step 6? statements 1. $overline{ad} \\con…
CPCTC
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multiple choice circle the correct answer. 1. solve for x: 2(3x - 5) = …
1. D. x = 8 2. A. -6x + 10 3. C. 15
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multiple choice circle the correct answer. 1. solve for x: 2(3x - 5) = …
1. D. x = 8 2. A. -6x + 10 3. C. 15
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write an expression that represents the perimeter of the figure below. …
$8k + 2j$