Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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the sum of four times a number and twice its complement is $270^0$. fin…
\( \boldsymbol{x = 45^\circ} \) (the option with \( x = 45^\circ \))
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8a. what is the shortest side △abc? justify/explain the answer. 8b. usi…
8a. The shortest side of $\triangle ABC$ is $\overline{BC}$. 8b. The longest side of $\triangle ADC$ is $\overline{DC}$.
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5. write the sides of $\\triangle efg$ in order in the boxes from the l…
1. Longest Side: $FG$ 2. Medium Side: $EG$ 3. Shortest Side: $EF$
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4. list the following angles (∠g , ∠h, ∠j) from smallest to largest. 5.…
1. $\boldsymbol{\angle H < \angle J < \angle G}$ 2. Longest Side: $FG$, Medium Side: $EG$, Shortest Side: $EF$
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the line segment is dilated about the origin using scale factor j the r…
E. \( j = \frac{5}{3} \), C. \( k = \frac{2}{3} \)
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3. what is x? 125° x° z° 70 180 55 125
55 (corresponding to the option with 55, assuming the options are labeled with their values, e.g., the third option if it's 55)
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which transformations map \\( \\triangle jkl \\) onto \\( \\triangle jk…
E. a translation down 2 units, and then a reflection over the x - axis F. a rotation of \(180^\circ\) about the origin, and then a translation up 2 units
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which transformations map △uke onto △jkl? select the two correct answer…
B. a reflection over the x - axis, and then a translation up 2 units F. a rotation of \(180^\circ\) about the origin, and then a translation up 2 units
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which additional piece of information would allow you to prove that the…
C. \(\overline{AB}\cong\overline{DE}\) (Wait, no, correction: The correct option is D. \(\overline{AC}\cong\overline{DF}\). Wait, let's re - evaluate. Wait, the right - angled tri…
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m is the perpendicular bisector of bc. reasons: reflexive, sas, asa, ss…
Para demostrar \( AB = AC \): 1. **Dato**: \( M \) es la intersección perpendicular de \( BC \), así que \( BM = CM \) (definición de bisectriz de segmento) y \( \angle AMB = \ang…
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the word semicircle contains the root semi. what does the root semi mea…
B. one-half
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a graphed system of linear inequalities is shown below. which of the fo…
D. \((5, - 2)\), E. \((0, 1)\)
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13. the volume of a 9-inch cube is ______. teks 2a a. 729² in. b. 729 i…
b. 729 in.
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and back to the starting tent fastener, as shown. louis can use the len…
30
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graph the line. $y=\\frac{1}{5}x+2$
To graph \(y=\frac{1}{5}x + 2\), plot \((0,2)\), then use the slope \(\frac{1}{5}\) to find other points (e.g., \((5,3)\) or \((-5,1)\)) and draw a straight line through them.
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louis needs to secure his tent. he will use a rope to go down the edge …
Louis can use the length of the side of the tent and the distance from the front corner of the tent to the post as the values for \(a\) and \(b\). To find the length of the third …
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question 1-40 which transformation rule can be used to transform figure…
\((x,y)\to(-y,x)\) (the first option, assuming the first option is \((x,y)\to(-y,x)\))
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dearies what are the lengths of leg b and hypotenuse c in triangle abc?…
b = 36 in. c = 39 in.
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question 1-39 consider rectangles abcd and efgh as shown in the graph. …
Perimeter of \( ABCD \) : Perimeter of \( EFGH = 1 : 3 \) (the third option)
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graph the line. $y=\\frac{4}{3}x - 1$
To graph the line \(y=\frac{4}{3}x - 1\): 1. Plot the y - intercept \((0,-1)\). 2. Use the slope \(\frac{4}{3}\) to find another point (e.g., from \((0,-1)\), move 4 units up and …
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which of the following shows a transformation that does not preserve di…
The option with the original trapezoid and the smaller trapezoid (the second set of figures)
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question 1-37 which statement is the inverse of the following condition…
The option "If two angles are not vertical angles, then they are not congruent." (the third option among the given choices)
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a square pyramid with a = 10 inches and d = 12 inches is shown. what ar…
\( b = \boxed{6} \) inches, \( c = \boxed{10} \) inches (assuming a possible typo in \( a \) as 8, or my misinterpretation, but based on common Pythagorean triples, 6-8-10).
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question 1-36 figure 1 is the preimage of figure 2. complete the statem…
\((x, y) \to (2x, 2y)\)
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graph the line, $y = \\frac{1}{4}x + 4$
The line \(y=\frac{1}{4}x + 4\) is graphed by plotting the y - intercept \((0,4)\) and using the slope \(\frac{1}{4}\) to find another point (e.g., \((4,5)\) or \((-4,3)\)) and th…
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nick has a 50-foot ladder. he places the ladder 20 feet away from the b…
46
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graph the line. $y=-dfrac{2}{5}x - 2$
# Explanation: ## Step1: Identify the y-intercept The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-\frac{2}{5}x - …
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complete the proof given: (overline{wx} parallel overline{zy}); (overli…
2. Alternate interior angles are congruent 3. Reflexive Property 4. Angle - Side - Angle (ASA) Postulate
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in the rectangular prism, each small cube has edges that are \\(\\frac{…
B. $1\frac{1}{2}$ inches
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graph the line. y = -\\frac{1}{3}x + 2
The line is graphed by plotting the y - intercept \((0,2)\) and using the slope \(-\frac{1}{3}\) to find additional points (e.g., \((3,1)\) or \((-3,3)\)) and then drawing a strai…
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xi sketches a right triangle with legs of lengths x and y and a hypoten…
\(\boldsymbol{\sqrt{x^{2}+y^{2}}}\) (the first option)
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question 1-36 figure 1 is the preimage of figure 2. complete the statem…
The transformation rule is a dilation with a scale factor of 2, so the rule is \((x,y)\to(2x,2y)\) (or in words: "Multiply each coordinate of the vertices of Figure 1 by 2 to get …
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dearies e drop-down menus to explain your reasoning. triangle formed by…
The area of the third square is 25 square units, the triangle is a right triangle with side lengths of 3 units, 4 units, and 5 units. So the first "Choose" should be 25, the secon…
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why can the diagram be helpful in proving the pythagorean theorem? use …
The diagram shows squares on each side of a right - triangle. The area of a square with side length \(s\) is \(s^{2}\). For a right - triangle with legs \(a,b\) and hypotenuse \(c…
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dorian is designing a park at summer camp. he draws a scale drawing of …
1.73
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Question was provided via image upload.
3.32 (and its approximate location on the number line is near 3.3, closer to 3.32)
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bell ringer name: giovanni navia date: period: identify the center and …
s: 1. For \((x - 1)^2 + (y + 3)^2 = 4\): - Center: \((1, -3)\) - Radius: \(2\) 2. For \((x - 2)^2 + (y + 1)^2 = 16\): - Center: \((2, -1)\) - Radius: \(4\) (For sketching the grap…
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which number line shows a colored segment with a length of \\(\\frac{1}…
The third (bottom) number line shows the colored segment of length $\frac{1}{4}$.
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homework 5.04: swbat identify and use properties of trapezoids to solve…
s: ### Part 1a: \( m\angle T = 110^{\circ} \), \( m\angle R = 110^{\circ} \), \( m\angle P = 70^{\circ} \), \( m\angle A = 70^{\circ} \) (assuming the correction where \( \angle T…
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what is the equation of the following line?
\(y=\frac{1}{2}x - 3\)
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what is the slope of this line? (4, 5) (2, -1)
3
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exit ticket swbat identify and use properties of trapezoids to solve fo…
b. \( \overline{RP} \cong \overline{AT} \), c. \( \angle ART \cong \angle RAP \) ### Question #2
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4. find x. image of a right triangle with a right angle at the bottom l…
\(x\approx36\) (or more precisely, \(\frac{11}{\tan(17^\circ)}\approx35.98\))
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3. find x. image of a right triangle with one leg 12, angle 53°, and hy…
15.92 (the option with 15.92)
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find the slope of each line. the slope is select select 2 1/2 4 1/4
\(\frac{1}{2}\)
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1. find the height, x, of the tree. 40° 62 ft 52.02 ft 75.23 ft 73.89 f…
52.02 ft
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part c a rotation 90° about the origin, then a reflection across x = 0.…
To solve the problem, we need to know the original coordinates of point \( T \). Since the original coordinates are not provided in the image, we'll assume a general point \( T(x,…
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part d a translation 2 units right, then a reflection across ( x = 0 ).…
To solve this, we need the original coordinates of point \( Q \). Since they are not provided, we'll assume a general point \( Q=(x,y) \) and apply the transformations. ### Step 1…
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the name of the feature written \\overline{rs} is options: vector rs, l…
line segment RS
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how would you graph the following line? y = -3x + 5 first, you would se…
First "Select": plot the y - intercept Second "Select": 5 Third "Select": use the slope to find another point Fourth "Select": - 3 Fifth "Select": 3 units down and 1 unit to the r…
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the union is divided date: confederate and union states in 1861 complet…
Confederate states: 11, Union states: 23 ### Question 7
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4. if the tangent ratio of $\\theta$ is $\\frac{12}{5}$, which angle is…
$\theta$ is $\angle J$ (or angle at vertex J)
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3. what is the tangent ratio of angle θ within a right triangle? ○ tanθ…
D. \( \tan\theta = \frac{\text{opposite}}{\text{adjacent}} \) (assuming the fourth option is labeled D; if the original options had different labels, adjust the label accordingly,…
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2. what is the tangent ratio of angle y? m to n is 15 ft, n to o is 8 f…
\(\frac{15}{8}\)
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pentagon pqrst will be translated 3 units up and then reflected over th…
\( \boldsymbol{(-2, -2)} \) (corresponding to the first option: \( (-2, -2) \))
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1. what is the tangent ratio of angle x? (image of a right triangle jlk…
\(\frac{21}{20}\)
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question 1-10 for a rotation ( x^circ ) about point ( p ), which of the…
The option that is not true is: For any polygon, the rotation can be expressed as a single reflection no matter what the value of \( x \) is.
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if a figure is translated 3 units left and 3 units up, which translatio…
A. 3 units right and 3 units down
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what type of symmetry does a rectangle have? reflectional but not rotat…
C. Both reflectional and rotational
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graph the image of rectangle klmn after a dilation with a scale factor …
The dilated rectangle has vertices $K'(-9,-9)$, $L'(9,-9)$, $M'(9,3)$, $N'(-9,3)$
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given point a is not on line m, suppose a is reflected across line m. w…
Line \( m \) is the perpendicular bisector of \( \overline{AA'} \) (the second option).
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point ( p(5, -4) ) is the image of point ( p(2, 3) ) under a translatio…
\( (9, -9) \) (corresponding to the option with text " (9, −9) ")
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Question was provided via image upload.
1. $\boldsymbol{\overrightarrow{YZ} = \overrightarrow{YZ'}}$ 2. $\boldsymbol{\text{Point } Y}$ 3. $\boldsymbol{\text{angle measures}}$ 4. $\boldsymbol{\angle X'}$ 5. $\boldsymbol{…
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determine if triangle mno and triangle pqr are or are not similar and, …
The triangles are similar. (The reason is that they satisfy the AA (Angle - Angle) similarity criterion as we can calculate that two angles of one triangle are equal to two angles…
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in $\\triangle ghi$ and $\\triangle jkl$ below, $\\angle g$ is congruen…
Apply a dilation centered at $G$ with scale factor $\frac{JK}{GH}$ to $\triangle GHI$.
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c(-3, -1) b(-4, -3) a(0, -5) c(2, 1) a translation 5 units left a refle…
C. a reflection across \( y = 0 \), then a translation 5 units left
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which of the following is a good first step to prove that $\\triangle p…
B. Apply a translation and rotation to $\triangle PQR$ that maps $\angle Q$ onto $\angle A$.
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abcd ≅ asqr, find rs. rs = submit
\( 18 \)
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point t is at (-2, 5). what are the coordinates of point t after a refl…
\((2, - 5)\) (corresponding to the option: (2, -5))
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one of the angles of $\\triangle def$ has a measure of $47^\\circ$. one…
$86^\circ$
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solve for x. (image of two triangles: upper triangle lnm with side lm =…
$49$ cm
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question 15 (multiple choice worth 1 points) (04.02 mc) quadrilateral e…
They have the same slope of 3 and are, therefore, parallel.
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question 14 (multiple choice worth 1 points) (04.01 lc) which statement…
The fourth option: Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals.
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question 12 (multiple choice worth 1 points) (07.01 mc) if a is the cen…
The correct option is the one where \(\overline{ED}\cong\overline{FD}\) because \(\overline{EF}\) is perpendicular to a radius of circle \(A\) (assuming the first option in the li…
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question 11 (multiple choice worth 1 points) (07.03 mc) in circle l, (o…
\( \frac{1}{8} \) the circumference of circle \( L \) (the first option among the choices, likely labeled as the option with \( \frac{1}{8} \) and "the circumference of circle \( …
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question 8 (multiple choice worth 1 points) (05.02 mc) look at the figu…
\(\cos x^{\circ}=\frac{11}{k}\) (corresponding to the option \(\boldsymbol{\cos x^{\circ}=\frac{11}{k}}\))
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64. use generic rectangles to multiply each of the following expression…
s: a. \(x^{2}-3x - 10\) b. \(y^{2}+5xy + 6x^{2}\) c. \(3y^{2}-3xy + 8x-8y\) d. \(x^{2}-9y^{2}\)
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question 7 (multiple choice worth 1 points) (05.03 hc) elmon is standin…
10 feet (corresponding to the option "10 feet")
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one of the legs of a right triangle measures 1 cm and its hypotenuse me…
$\boldsymbol{17.0}$ cm
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the hypotenuse of a right triangle measures 13 cm and one of its legs m…
\(\approx 13.0\) cm (Wait, but let's check again. Wait, \(\sqrt{168}\) is approximately 12.96, which is 13.0 when rounded to the nearest tenth? Wait, 12.96 is 12.9 when rounded to…
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one of the legs of a right triangle measures 7 cm and the other leg mea…
$\boldsymbol{16.6}$ cm
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question 5 (multiple choice worth 1 points) (07.03 hc) right triangle a…
\((x + 1)^2+(y - 4)^2=25\) (the option: \((x + 1)^2+(y - 4)^2=25\))
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question one of the legs of a right triangle measures 1 cm and its hypo…
The measure of the other leg is approximately \(\boldsymbol{19.0}\) cm.
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question 3 (multiple choice worth 1 points) (06.01 mc) the cross - sect…
The volume of the prism is not equal to the volume of the cylinder.
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question 2 (multiple choice worth 1 points) (06.04 mc) what is the shap…
C. Circle
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find the perimeter of the following shape, rounded to the nearest tenth…
11.3
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question one of the legs of a right triangle measures 16 cm and the oth…
The measure of the hypotenuse is approximately \(18.4\) cm.
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one of the legs of a right triangle measures 6 cm and the other leg mea…
The measure of the hypotenuse is approximately \( 16.2 \) cm.
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one of the legs of a right triangle measures 11 cm and its hypotenuse m…
The measure of the other leg is approximately \(13.0\) cm.
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find the sine of ∠f. h f 80 39 g simplify your answer and write it as a…
$\boldsymbol{\frac{\sqrt{4879}}{80}}$
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question one of the legs of a right triangle measures 10 cm and the oth…
The measure of the hypotenuse is approximately 17.2 cm.
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find the sine of ∠s. simplify your answer and write it as a proper frac…
$\frac{45}{53}$
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find the tangent of ∠j. h 60 i 32 68 j simplify your answer and write i…
$\frac{15}{8}$
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question one of the legs of a right triangle measures 3 cm and the othe…
The measure of the hypotenuse is approximately \(18.2\) cm.
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question the hypotenuse of a right triangle measures 4 cm and one of it…
The measure of the other leg is approximately \(\boldsymbol{3.9}\) cm.
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one of the legs of a right triangle measures 2 cm and the other leg mea…
The measure of the hypotenuse is approximately \(7.3\) cm.
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one of the legs of a right triangle measures 17 cm and its hypotenuse m…
The measure of the other leg is approximately \(8.5\) cm.
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find wx. write your answer as an integer or as a decimal rounded to the…
$\boldsymbol{5.8}$
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find uv. u v 56° 4 t write your answer as an integer or as a decimal ro…
$7.2$
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find gh. write your answer as an integer or as a decimal rounded to the…
$3.0$