Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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determine whether each statement about the triangles is true. choose tr…
To solve this, we analyze each statement using triangle congruence, similarity, and transformation rules: ### 1. $\boldsymbol{\triangle ABC \text{ is congruent to } \triangle A''B…
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draw the size of the actual wall of the birdhouse by dilating the figur…
The dilated figure has vertices at \((0, 14)\), \((8, 8)\), \((8, 2)\), \((4, 2)\) (plotted using the Polygon tool as per the steps).
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the graph of x = 5 is a ______ line with an intercept at ______. choose…
D. vertical; \((5,0)\)
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multiple-choice question why is it called \counter-clockwise?\ the rota…
A. The rotation goes the opposite direction than the hands of a clock
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multiple-choice question why is it called \clockwise?\ the rotation goe…
B. The rotation follows the hands of the clock (assuming the second option is labeled B; if the first was A and the second B, then the correct one is the second option with the la…
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the scale factor of a figure and its enlargement is 6. what is the new …
18 cm
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read the original short story and answer the questions. the garden at d…
a. Simile
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when you get all the way back around to the starting point on a rotatio…
B. 360 (assuming the options are labeled as A. 270, B. 360, C. 300)
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graph the image of kite tuvw after a rotation 180° clockwise around the…
The rotated kite has vertices at \( T'(-6, 9) \), \( U'(-9, 6) \), \( V'(-6, 2) \), \( W'(-2, 6) \) (graph by plotting these points and connecting them).
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two triangles (pink labeled height, base and blue labeled height, base)…
$\boldsymbol{\frac{\text{original height}}{\text{original base}} = \frac{\text{reduction height}}{\text{reduction base}}}$ (the first option)
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all of the other quotients choose... is ✔ is not therefore, the quotien…
First dropdown: is not Second dropdown: all (Note: There may be a wording error in the problem, as "all of the quotients are equivalent" would imply it IS a dilation. Correctly, i…
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consider the reduction of the rectangle. 2.3 ft 16.8 ft x ft 4.5 ft not…
0.6 feet
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therefore, the quotients of the corresponding side lengths of the figur…
First blank: is Second blank: all (Note: If the original problem’s first blank is forced to "is not", it would be incorrect, as "all quotients equivalent" implies dilation. The co…
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choose one option from each drop-down menu to answer the question. in f…
all of the other quotients
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which is the scale factor proportion for the enlargement shown? (image:…
$\boldsymbol{\frac{1}{x}=\frac{2}{6}}$ (First option)
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multiple-choice question in which direction does counterclockwise turn?…
around to the left
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the quotients of the corresponding side lengths in figures jklm and pqr…
- The quotient of sides \(JK\) and \(PQ\) is not equivalent to all of the other quotients. - Therefore, the quotients of the corresponding side lengths of the figures show that fi…
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find the perimeter or circumference and area of each figure. round answ…
### Problem 4 (Triangle) #### Step 1: Identify base and height Points \( A(0,9) \), \( B(4,9) \), \( C(0,1) \). Base \( AB \): distance between \( A \) and \( B \). Since \( y \)-…
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circle a has a radius of 6 meters. what is the area of the shaded secto…
\( 5\pi \)
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multiple-choice question if a coordinate system has an x and y axis tha…
the x and y axis make right angles (90 degrees)
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determine whether each statement about the design from the rug is true.…
To determine the correctness of each statement, we analyze the properties of dilation: ### 1. "The center of dilation for figures 1 and 2 is point \( Y \)." The center of dilation…
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reflection across x = -1
To solve the reflection of the triangle across the line \( x = -1 \), we first need to determine the coordinates of the original vertices \( A \), \( B \), and \( C \). Let's assu…
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in the diagram, ab = 10 and ac = 2√10. what is the perimeter of △abc? ○…
\(20 + 2\sqrt{10}\) units (the option: 20 + 2√10 units)
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homework ~ unit 1 lesson 3: scale drawing 3.) here is an original figur…
To draw the scaled copy: 1. Identify the vertices of the original trapezoid. 2. Multiply the horizontal and vertical distances of each vertex from a reference point (e.g., the bot…
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in the diagram, kl = 2√2, lm = √5, and mn = √2. what is the perimeter o…
\( 3\sqrt{2} + 2\sqrt{5} \) units (corresponding to the option " \( 3\sqrt{2} + 2\sqrt{5} \) units")
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consider the original triangle and the enlargement. 2 cm 3 cm 8 cm a fi…
12
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use the compass and straightedge to construct a segment congruent to \\…
Constructed segment \( \overline{PQ} \) (where \( Q \) is on the arc from \( P \) with radius \( RS \)) congruent to \( \overline{RS} \).
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the scale factor of a figure and its enlargement is 4. what is the new …
18 cm
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two rectangles have equal area, in square feet. • rectangle x has a wid…
\( w = 4 \)
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which proportional relationship is key to deriving the pythagorean theo…
b. \( AC^{2} = AB \cdot AD \) and \( BC^{2} = AB \cdot BD \)
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d(-2,5) c(-5,1) a(1,1) b(-2,-3) what is the perimeter of rhombus abcd? …
20 units
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in △pqr, the angle bisector of ∠pqr intersects pr at s. if ps = 5, sr =…
a. 12 ### Second Question (Similarity Criterion)
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what is the perimeter of △lmn? ○ 8 units ○ 9 units ○ 6 + √10 units ○ 8 …
$8 + \sqrt{10}$ units (the option: 8 + √10 units)
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if a line is drawn parallel to one side of a triangle, it divides the o…
d. Proportionally ### Second Question:
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in △lmn, the angle bisector of ∠l intersects mn at p. if lp is the angl…
b. 12 ### Second Question:
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top 3/4\ 1-1/4\ 3/4\ 3/4\ front 1/4\ 1/2\ 1-1/4\ 1/2\ side orthographic…
The total length (horizontal) from the top view is \( \boldsymbol{2''} \).
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b. draw a scaled copy of the polygon with a scale factor \\(\\frac{1}{2…
Yes, Polygon \( A \) is a scaled copy of Polygon \( B \). The scale factor that takes \( B \) to \( A \) is \( 2 \).
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in the diagram, $overline{dg} parallel overline{ef}$. diagram with poin…
\(\boldsymbol{\overline{DE}\cong\overline{GF}}\) (The option corresponding to this is the first option among the given choices, i.e., the option with \(\overline{DE}\cong\overline…
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in the diagram, wz=√26. what is the perimeter of parallelogram wxyz? ○ …
\( 2\sqrt{26}+8 \) units (corresponding to the option \( 2\sqrt{26}+8 \) units)
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a right triangle with one leg labeled 12 yd, another leg labeled 15 yd …
The area of the right triangle is \( 90 \) square yards.
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the vertices of a quadrilateral in the coordinate plane are known. how …
A. Use the distance formula to find the length of each side, and then add the lengths.
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in the diagram, zy = wx = 2\\sqrt{10}. what is the perimeter of rectang…
\( 6\sqrt{10} \) units (corresponding to the option "6√10 units")
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a grid map marks the plot of harold’s garden in meters. the coordinates…
46
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find the measure of the missing angles. answer d = \\boxed{}^\\circ \\q…
# Explanation: ## Step1: Find angle \( d \) Angles on a straight line sum to \( 180^\circ \). So, \( d + 131^\circ = 180^\circ \). \( d = 180^\circ - 131^\circ = 49^\circ \) ## St…
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reflection across x = -1 rotation 90° counterclockwise about the origin
To solve problems related to geometric transformations (reflection and rotation) of the given triangles, we analyze the coordinates of the vertices and apply the transformation ru…
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3. which sequence of transformations takes δa to its image, δb? image o…
B. reflection over the \( y \) - axis and translation 2 units down
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which statement proves that quadrilateral hijk is a kite? ∘ $overline{h…
B. \( IH = IJ = 3 \) and \( JK = HK = \sqrt{29} \), and \( IH eq JK \) and \( IJ eq HK \)
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problem 3 polygon b is a scaled copy of polygon a. a. what is the scale…
2 (since 5 ÷ 2.5 = 2, so the scale factor is 2) #### b. Missing Lengths in B
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6) the volume of a square pyramid can be represented by the formula giv…
\( h = \frac{3V}{s^{2}} \)
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in the following graph, in what order did the transformations occur? im…
A. reflected, then translated
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graph each image given the transformation. use correct notation! 1. tra…
The translated figure has vertices at \( T'(-5,-4) \), \( W'(-4,-2) \), \( V'(-2,-2) \), \( U'(-2,-3) \) (and the figure is formed by connecting these points). To graph it, plot t…
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prove that the diagonals of kite uvwx are perpendicular. step 1: determ…
To solve this, we first identify the coordinates of the vertices from the graph. Let's assume the coordinates (by analyzing the grid): - \( X(-1, -2) \), \( V(5, 4) \), \( U(-3, 5…
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the vertices of rhombus defg are d(1, 4), e(4, 0), f(1, -4), and g(-2, …
20
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which steps will verify that a parallelogram is a rectangle? check all …
- Calculate the lengths of the diagonals, and show that they are equal. - Calculate the slopes of every side, and show that adjacent sides are perpendicular.
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esson practice 10 name: emily phong date: 9/9 period: problems 1–4: ali…
### Part 1: Writing two possible scales for Ali's map First, we know the actual width of the field (let's assume the missing number before "00 feet" is 100, as it's a common field…
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mary thinks the triangle is equilateral. how would you support or dispu…
C. Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
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problem 5 here is a polygon on a grid. a. draw a scaled copy of the pol…
Para dibujar la copia escalada (etiquetada como \( A \)): 1. Identifica cada segmento del polígono original (rectángulo + triángulo). 2. Multiplica la longitud de cada segmento po…
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triangles are considered similar if their corresponding angles are ____…
congruent (or equal) ### 2. Similar triangles have corresponding sides that are ______.
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if triangle abc is similar to triangle def and the length of ab is 5 un…
a. 2
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graph the image of parallelogram qrst after a translation 3 units right…
The translated parallelogram \( Q'R'S'T' \) has vertices \( Q'(-5,-6) \), \( R'(3,-6) \), \( S'(3,1) \), \( T'(-4,1) \). (To graph, plot these points and connect them in order.)
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a building casts a shadow 40 feet long, and a nearby 8-foot pole casts …
b. 160 feet ### Second Question (Sum of Interior Angles of a Triangle)
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what is the volume of this cone? use π ≈ 3.14 and round your answer to …
\( 2.09 \)
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graph the image of δbcd after a translation 5 units right.
The image of \( \triangle BCD \) after a translation 5 units right has vertices \( B'(0,-6) \), \( C'(0,3) \), and \( D'(1,-5) \). (To graph, plot these points and connect them.)
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40. this figure represents a step in a compass-and-straightedge constru…
a perpendicular bisector
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section a: what are ratios? problem 3 a. a square is 3 inches by 3 inch…
El área del cuadrado es 9 pulgadas cuadradas. ### Parte b
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what is the volume of this rectangular pyramid? diagram of a rectangula…
96
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in circle b, ( moverarc{dc} = 109^circ ). solve for ( x ) if ( mangle d…
\( x\approx9.4 \)
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a scale model of a roof has a base of 10 ft and a height of 8 ft. the a…
d. 20 ft ### Second Question (Ramps)
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section a: what are ratio problem 3 a. a square is 3 inches by 3 inches…
The area of the square is 9 square inches. ### Part b
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38. which construction will determine a midpoint? ○ a perpendicular bis…
A. a perpendicular bisector
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a 9-foot pole casts a 3-foot shadow. how tall is another pole that cast…
c. 18 feet ### Second Question:
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problem 3 the pentagons are scaled copies of one another. a) determine …
(a): Scale Factor: \( \frac{5}{4} \) (or 1.25) ### Part (b) - Use the Scale Factor to Find \( x \)
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37. name the intersection of plane bpq and plane cpq. the planes do not…
\( \overline{PQ} \) (the option corresponding to \( \overline{PQ} \))
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what is the surface area of this rectangular prism? 10 cm, 3 cm, 7 cm s…
242
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25. write an expression for ( mangle rst ). (overrightarrow{sq}) bisect…
\( 6x - 18 \) (corresponding to the option "6x - 18")
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34. find the circumference of a circle with radius of 18 in. leave your…
36π in (corresponding to the option "36π in.")
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33. if m∠xab = 32, what is m∠bac? 64 16 32 58
64
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finding area find the area of the figure. 29. image of a circle on a co…
The area of the circle is \( 4\pi \) (or approximately \( 12.56 \)) square units.
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32 name the segments that are skew to (overline{ab}). (overline{eg}, ov…
\(\boldsymbol{\overline{EG},\overline{DH},\overline{CG},\overline{FH}}\) (the first option: \(\overline{EG},\overline{DH},\overline{CG},\overline{FH}\))
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what is the volume? 5 mm 2 mm 2 mm cubic millimeters submit
20
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what inequality does the number line show? number line with ticks at 5,…
\(x < 6\)
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a#16: textbook 1-123 to 1-127 123. if no sides of a triangle have the s…
a. $\triangle ABC$ is isosceles. b. $\triangle ABC$ is scalene. c. $\triangle ABC$ is isosceles.
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31. how many cubes are needed to build the base of this structure? 5 3 …
4 (corresponding to the option with 4)
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angle diagrams labeled a to j (each with angle expressions: a: (17x+21)…
To solve these angle - related problems, we will use the properties of angles such as supplementary angles (sum to \(180^{\circ}\)), vertical angles (equal), and complementary ang…
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30. name the labeled segments that are parallel to $overline{ef}$. opti…
B. $\overline{AC}$, $\overline{CD}$, $\overline{GH}$ (assuming the second option is labeled as B, if the options are labeled A, B, C, D with the second option being B)
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4. wxyz is a kite. angle wxy has a measure of 133° and ∠zwx has a measu…
\( 17^\circ \) ### Problem 5:
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27. find the perimeter of the figure. not drawn to scale image of a tra…
35 in (assuming the last option is 35 in, as per the options shown: 34 in, 70 in, 84 in, 35 in)
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9) 15×12 area = dashed circle (right triangle with legs 12 yd and 15 yd…
90 square yards
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coordinate grid with a red dot, and options: (-1,3), 3, (3,-1)
\(\boldsymbol{(-1,3)}\) (the checkbox next to \((-1,3)\) should be selected)
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lesson 2 | session 2 3 figure jkl mn is reflected across the x-axis to …
True #### b.
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jack measured his house and made a scale drawing. he used the scale 8 c…
16
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the relationship between two figures where corresponding side lengths a…
similarity ### Second Question:
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what is the area of this figure? 3 cm, 8 cm, 4 cm, 6 cm, 8 cm, 6 cm, 6 …
72
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lesson 2 | session 2 3 figure jklmn is reflected across the x-axis to f…
False #### Part b: \( M' \) is located 1 unit below the \( x \)-axis - **Step 1: Find original coordinates of \( M \)** From the graph, \( M \) is at \( (4, 1) \). - **Step 2: Ref…
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what is the value of b? diagram of a triangle with angles labeled (2b -…
\(b=\frac{67}{3}\) (or approximately \(22.33\)) Wait, no, maybe I misread the angle labels. Let me check the problem again. The diagram shows a triangle with angles: left angle \(…
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math 7 unit 1 cfu a version 2 name:___________________________ date:___…
### Problem 1a To determine scaled copies, we check if the side - length ratios and angle measures (for parallelograms, angles should be preserved) are consistent with a scale fac…
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a transformation that resizes a figure by applying a scale factor is ca…
dilation ### 2. Second Question
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24. what can you conclude about (overline{ce})? (overline{ce}) bisects …
\(\boldsymbol{\overline{CE}}\) bisects \(\boldsymbol{\angle ACB}\) (the first option).
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these two shapes are similar. find b. 5 in. 20 in. b 8 in.
\( b = 2 \) inches
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22. if kc = 31, what is kn? 43 62 82 74 (diagram: points k, c, n on a l…
74