几何
三角形、圆、解析几何与证明题。
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a _________ can help generate a list of similarities and differences. o…
C. venn - diagram ### Question 10 (second multiple - choice question)
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13. a solid is made up of a conical frustum and a hemispherical top as …
### Part (a) #### (i) Area of the circular base The formula for the area of a circle is \( A = \pi r^2 \), where \( r = 3.5 \, \text{cm} \). ## Step 1: Substitute \( r = 3.5 \) in…
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3. which ordered pair is in the solution set of \\( y \\leq \\frac{3}{5…
(5, -4) (assuming the first option is (5, -4))
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8. a line is graphed on a coordinate grid. which statement about the li…
The option: "The equation of the line is \( y = 2 \), and the slope is equal to zero." (the second option in the list)
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timeline analysis questions answer in complete sentences. 1. which pres…
1. Sam Houston served two terms as the president of the Republic of Texas. His first term was from 1836 to 1838, and his second term was from 1841 to 1844. 2. Texas existed as an …
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for problems 9 and 10, find the scale factor of the dilation centered a…
\(\frac{3}{4}\) ### Problem 10
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warm up #11 9/23 ① right triangle with horizontal leg 12, vertical leg …
For the first triangle: \( x = 24 \), \( y = 12\sqrt{3} \) For the second triangle: \( x = y = \frac{9\sqrt{2}}{2} \)
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warm up #10 can the following form a triangle? if so, is it a right, ob…
Yes, it can form a triangle, and it is an obtuse triangle.
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nessa proved that these triangles are congruent using asa. roberto prov…
The statement " \(\boldsymbol{\overline{AB} \cong \overline{QN}}\) because they are both opposite a right angle" is the one included in Roberto's proof but not Nessa's.
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which rigid transformation would map △abc to △abf? a reflection across …
a reflection across the line containing \( \overline{BA} \)
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in the diagram, dc is 10 units and bc is 6 units. what is the length of…
16 units
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which new angle is created by extending one side of a triangle? a compl…
an exterior angle
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what is the equation of the line in slope - intercept form that is perp…
The equation of the line is \( y = -\frac{4}{3}x-6 \) (the option with this equation, looking at the options, it's the left - most option: \( y = -\frac{4}{3}x-6 \))
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ethan drew a pre - image of a trapezoid using a dashed line. which show…
The Middle Graph (the second figure from the top)
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card 13 and equation: equation:
Equation for A: \( y = 4 \) Equation for B: \( y = 2 \)
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nolan drew a pre - image of a trapezoid using a dashed line. which show…
The Middle Graph (the second figure from the top)
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6. consider $\\triangle pqr$ in the coordinate plane. a. what are the c…
a. \( P'(-7.5, 3) \), \( Q'(-6, 6) \), \( R'(-3, 6) \) b. (Graphing: Plot \( P'(-7.5, 3) \), \( Q'(-6, 6) \), \( R'(-3, 6) \) and connect them to form \( \triangle P'Q'R' \))
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which diagram shows possible angle measures of a triangle? diagram 1: t…
The second diagram (with angles \(32^\circ\), \(115^\circ\), \(33^\circ\))
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which diagram shows lines that must be parallel lines cut by a transver…
The third diagram (the one with two \(91^{\circ}\) angles)
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which shows ∠poq?
(Assuming the correct figure is the third one from the top, but without full visibility, the key is the figure with vertex O and sides OP, OQ. If options are labeled as Top, Secon…
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which type of triangle will always have a perpendicular bisector that i…
equilateral
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semester 1 consider the triangle shown. triangle image with angles at p…
\(\overline{RQ}, \overline{PQ}, \overline{RP}\) (the option with this order)
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5. what are the coordinates of a point that maps back to itself under a…
The coordinates are \( (0, 0) \) (the origin), because a dilation centered at the origin with scale factor \( k \) maps \( (x, y) \) to \( (kx, ky) \); for \( (x, y) = (kx, ky) \)…
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consider the rotational symmetry of rhombus wxyz. what is the order of …
2
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3. plot the image of point z under a dilation centered at the origin wi…
The coordinates of the image of Z are \((0, - 6)\) ### Question 4
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could △abc be congruent to △adc by sss? explain. yes, but only if \\(\\…
Yes, but only if $\overline{BC}\cong\overline{DC}$ (the first option among the four given options)
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which best describes the accuracy of carls solution? carls work and ans…
Carl’s work and answer are incorrect. He chose a vertex, \( V \), that does not make a right triangle with \( MN \).
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solve for m. 40 ≥ 8 + m write the solution as an inequality (for exampl…
\( m \leq 32 \) For graphing: The endpoint is at 32 (closed circle because the inequality is "less than or equal to"), and the ray extends to the left (towards decreasing values o…
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solve for h. 24 < h - 3 write the solution as an inequality (for exampl…
\(h > 27\) For graphing: Plot an open circle at 27 (since the inequality is strict, \(h > 27\) not \(h \geq 27\)) and draw a ray to the right (towards increasing values of \(h\)) …
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carl is trying to determine the length of segment mn using the pythagor…
# Explanation: ## Step 1: Identify Coordinates of M and N From the graph, \( M(-3, 1) \) and \( N(4, 5) \)? Wait, no, looking at the grid, M is at (-3,1)? Wait, no, the x-axis: M …
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1) solve for g. 40 ≤ g - 8 2) write the solution as an inequality (for …
The inequality is \(g\geq48\). For the graph, plot a closed circle at 48 and draw a ray to the right.
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the graph shows point a. if point a is translated 2 units left and 4 un…
$(1, -1)$
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quinton tried to transform triangle fgh according to the rule ((x, y) \…
Correct. He transformed the triangle according to the rule \((x, y) \to (-y, x)\)
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card 4 the graph of a line goes through the points (-4, 10) and (-2, -6…
The slope of the line is -8. ### Part (b)
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read the proof. given: \\(\\overline{ab} \\parallel \\overline{de}\\) p…
AA similarity theorem
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what is m∠phj? 140° 160° 100° 120° (and the image of intersecting lines…
\(120^\circ\) (corresponding to the option with \(120^\circ\))
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triangle rst is rotated 180° about the origin, and then translated up 3…
\(\triangle RST \cong \triangle BAC\) (the option with \(\triangle RST \cong \triangle BAC\))
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card 5 refer to the graph. graph of line m passing through the origin w…
a) (Drawing: A line parallel to \( m \) shifted up or down, e.g., \( y=\frac{2}{3}x + 3 \) plotted with y - intercept 3 and same slope as \( m \)) b) Line \( m \): \( y=\frac{2}{3…
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which system of inequalities corresponds to the following graph: graph …
\( y < 2x + 1 \) \( y > \frac{1}{2}x - 2 \) (the second option in the list)
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what is the rule for the reflection? $t_{y\\text{-axis}} (x, y) \\to (-…
The correct option is the one labeled \( T_{x\text{-axis}}(x,y)\to(x, - y) \) (the second option among the four, with the rule \( (x,y)\to(x, - y) \) for reflection over x - axis).
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what is the rule for the reflection? t_y-axis (x, y) → (-x, y) t_x-axis…
The second option (from the left) labeled as \( T_{x\text{-axis}} (x, y) \to (x, -y) \) (or the option with text " \( T_{x\text{-axis}} (x, y) \to (x, -y) \) " depending on exact …
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(04.01 mc) two lines, a and b, are graphed: image of two lines a (blue)…
B. (2, 8), because the graph of the two equations intersects at this point
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planes s and r both intersect plane t. which statements are true based …
The three correct statements are: - The line containing points A and B lies entirely in plane T. - Planes R and T intersect at line y. - Line v intersects lines x and y at the sam…
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part a: write an addition inequality x + 17 > 23 -17 -17 ← solve using …
To solve the inequality \(x + 17>23\): 1. Identify the operation on the variable side (addition of 17). 2. Use the inverse operation (subtraction) and subtract 17 from both sides:…
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the equations $y = 2x + 4$ and $y = -3x - 1$ are shown in the graph. wh…
B. (-1, 2) (assuming the options are labeled as A. (-2,1), B. (-1,2), C. (2,-1), D. (1,-2))
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point a has an x coordinate of -2 and lies on a circle with a center at…
4.6
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which composition of transformations will create a pair of similar, not…
D. a rotation, then a dilation
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a composition of transformations maps $\\triangle klm$ to $\\triangle k…
a \( 90^\circ \) clockwise rotation about point \( P \) (the option: "a \( 90^\circ \) clockwise rotation about point \( P \)")
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angles 1 and 2 are complementary and congruent. what is the measure of …
\(45^\circ\)
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the equations $y = -2x - 4$ and $y = 3x + 1$ are shown in the graph. wh…
C. \((-1, -2)\) (assuming the options are labeled as A. \((-2, -1)\), B. \((-2, 1)\), C. \((-1, -2)\), D. \((1, -2)\))
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two parallel lines, e and f, are crossed by two transversals. what is t…
\( m\angle 15 = 83^\circ \) (the option with \( 83^\circ \))
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which transformations could have occurred to map △abc to △a\b\c\? ○ a r…
D. a translation and a dilation (Wait, no, the options are: first option "a rotation and a dilation", second "a rotation and a reflection", third "a reflection and a dilation", fo…
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two similar triangles are shown. δrst was __________, then dilated, to …
B. reflected
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which must be true in order for the relationship δzyx ~ δwvu to be corr…
D. $\angle Z \cong \angle W$ and $\angle X \cong \angle U$ (assuming D is the identifier for this option; if the options were labeled as per the order, the last option with $\angl…
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the radius of a circle is 3 kilometers. what is the circles circumferen…
\( 18.85 \)
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two similar triangles are shown. δmno was dilated, then _________, to c…
B. reflected
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find the distance from the line to the given point. y = \\frac{1}{6}x +…
$\frac{6}{\sqrt{37}}$ (or approximately $0.986$)
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which point is on the line that passes through point r and is perpendic…
# Explanation: ## Step1: Find slope of PQ Points \( P(4, -6) \) and \( Q(-4, 4) \). Slope \( m_{PQ} = \frac{4 - (-6)}{-4 - 4} = \frac{10}{-8} = -\frac{5}{4} \)? Wait, no, wait: Wa…
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which transformations could be performed to show that △abc is similar t…
a reflection over the x-axis, then a dilation by a scale factor of \(\frac{1}{3}\) (the second option)
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which statement must be true about the diagram? (options: point k is a …
Ray KM is an angle bisector of \(\angle NKL\)
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find the distance from the line to the given point. y = \\frac{1}{6}x +…
$\frac{6\sqrt{37}}{37}$
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find the distance between the pair of parallel lines with the given equ…
A) $\boldsymbol{\sqrt{10}}$ or about 3.16 units
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8. find the center (h, k) and radius r of the circle. graph the circle.…
Center: \((5, 1)\), Radius: \(3\)
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11) the observation deck of the skylon tower in niagara falls, ontario,…
The distance between the two planes is \(\boldsymbol{148.4 \, \text{km}}\) (to the nearest tenth of a kilometre).
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find the value of x so that ℓ || m. (3x + 10)° (4x − 10)° x =
20
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$\\angle 1\\cong \\angle 6$ a) $p \\parallel q$; converse of correspond…
D) \( g \parallel h \); Alternate Interior Angles Converse
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∠3 ≅ ∠7 a) a || b; converse of corresponding angles theorem b) ℓ || m; …
B) $\ell \parallel m$; Converse of Corresponding Angles Theorem
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which statements are true about trapezoid abcd and its translated image…
The correct answer is the option: "The rule for the translation can be written as \( (x, y) \to (x - 3, y + 1) \)" (the last option among the given options) and if we consider the…
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which is another way to name ∠ust? ∠usr ∠uts ∠tsu ∠tsr
$\angle TSU$
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select the graph of the line that passes through k (3, 7), perpendicula…
B)
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select whether the pair of lines is parallel, perpendicular, or neither…
(Assuming the lines are \( x = -2 \) (a vertical line) and \( y = 10 \) (a horizontal line)) Perpendicular
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which statement is true about the given information? ∠ced measures 45°.…
\( \angle AEC\) measures \(90^{\circ}\)
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select whether the pair of lines is parallel, perpendicular, or neither…
Parallel
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a regular decagon has 10 sides. how many reflectional symmetries does a…
The regular decagon has 10 reflectional symmetries, so the correct option (assuming the first option with 10 is the answer) is the one labeled "10" (e.g., if the options are A. 15…
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use a model lines a and b are parallel and are cut by transversal t to …
86
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which piece of additional information can be used to prove △cea ~ △cdb?…
\(\boldsymbol{\angle BDC}\) and \(\boldsymbol{\angle AED}\) are right angles (the first option)
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in the figure, m∠3 = 75° and m∠10 = 105°. find the measure of ∠15.
$75^\circ$
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find the value of the variables in the given figure. (8x - 10)° (7x)° (…
\( x = 10 \), \( y = 10 \)
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find the value of the variables in the given figure. x = y = (3y - 1)° …
\( x = 10 \), \( y = 13.67 \) (or \( y=\frac{41}{3} \))
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city engineering seventh avenue runs perpendicular to 1st and 2nd stree…
$65^\circ$
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given: m∠b = 46°; m∠c = 45°; m∠r = 46°; m∠t = 89° prove: △abc ~ △trs me…
The sum of the measures of the interior angles of a triangle is $180^{\circ}$.
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in the figure, m∠7 = 100°. find the measure of ∠2.
80
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use the figure. what type of angles are ∠3 and ∠10? select choice angles
Alternate Exterior Angles
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select the transversal connecting ∠7 and ∠15. then classify the relatio…
First blank: Line \( a \) (assuming the transversal is line \( a \), but need to check the angles. Wait, \( \angle 7 \) is on line \( d \) and another line, \( \angle 15 \) is on …
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identifying similarity transformations determine the similarity transfo…
dilation with center C (from the dropdown options: "dilation with center C")
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select the transversal connecting ∠5 and ∠15. then classify the relatio…
The transversal is the line that intersects both the lines containing ∠5 and ∠15. Looking at the diagram, ∠5 is on line \( d \) and ∠15 is on the lower slanted line (let's call it…
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select the transversal connecting ∠4 and ∠5. then classify the relation…
The transversal is line \(a\); the relationship is alternate interior angles.
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which statements regarding the diagram of △ebc are true? choose three c…
The three correct statements (to check the boxes for) are: - \(\angle DEC\) is an exterior angle. - \(\angle ABE\) and \(\angle EBC\) are supplementary angles. - \(\angle BEC\) is…
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how could you characterize the relationship between faces abcd and dcgh…
The relationship between faces ABCD and DCGH is that they are perpendicular. Face DCGH contains segment CG, which is perpendicular to segment DC (a side of face ABCD). So, the fir…
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is $\\triangle mnl \\cong \\triangle qnl$? why or why not? (options: ye…
Yes, they are congruent by either ASA or AAS.
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what additional information could be used to prove that △abc ~ △nml? ch…
$\angle B\cong\angle M$, $\triangle ABC$ was rotated and dilated by a scale factor between 0 and 1, $\angle C\cong\angle L$ (i.e., the options: $\boldsymbol{\angle B \cong \angle …
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identify a segment skew to \\( \\overline{ab} \\) using the figure show…
B. \(\overline{EH}\)
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triangle def is congruent to △ghj by the sss theorem. which rigid trans…
translation
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triangle xyz was reflected across m and then dilated to form a similar …
The Middle Graph (the triangle in the center with \( X' \), \( Y' \), \( Z' \) below \( m \) and matching angle arcs)
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is there a series of rigid transformations that could map △qrs to △abc?…
Yes, \(\triangle QRS\) can be translated so that \(R\) is mapped to \(B\) and then rotated so that \(S\) is mapped to \(C\).
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b) calculate the percent grade of the ramp to the nearest percent c) sh…
### Part b) # Explanation: ## Step 1: Find the height of the ramp (using Pythagoras) The ramp is the hypotenuse (\(c = 13\) m) and the horizontal distance is \(b = 12\) m. Let the…
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a regular pentagon is created using the bases of five congruent isoscel…
\(54^\circ\) (the option with \(54^\circ\))
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triangles and congruence a triangle abc has a 130° angle at vertex b, w…
The statement " \(m\angle A + m\angle C = 50^\circ\) " (the fourth option) must be true.
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triangle def is similar to triangle def. which similarity transformatio…
rotation and dilation
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triangles and congruence if triangle rst is an acute triangle, then m∠s…
less than \(90^\circ\)