幾何
三角形、円、座標幾何、証明問題。
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performing multiple transformations shaded pre - image to the dashed im…
To transform the pre - image to the image, a vertical translation down by 4 units (vertical translation \(y=-4\)) or the specific transformation (depending on the exact coordinate…
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progress x = w = (image of a right - angled isosceles triangle with hyp…
For $x$: If we consider the isosceles right - triangle with legs equal and the given leg length 6, then $x = 6$. For $w$: $w = 6$. But if we consider 6 as the hypotenuse, $x = 3\s…
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which theorem correctly justifies why the lines m and n are parallel wh…
A. converse of the corresponding angles theorem
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question 2 of 10 the triangles shown below may not be congruent. a. tru…
A. True
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look at this graph: graph of a parabola with vertex, axes labeled x and…
(-2, -5)
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spiral review figure qrst is graphed on a coordinate plane. determine t…
- \(Q'\): \((-3, -15)\) - \(R'\): \((6, 12)\) - \(S'\): \((0, 9)\) - \(T'\): \((4, -3)\)
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if $\\triangle def \\cong \\triangle uvw$, what are the corresponding p…
A. $\overline{DE} \cong \overline{UV}$ (correct), B. $\overline{DF} \cong \overline{UW}$ (correct), C. $\angle D \cong \angle U$ (correct), D. $\overline{FE} \cong \overline{WV}$ …
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calculator △ abc ~△ efg given m∠c = 52° and m∠e = 61°, what is m∠b? ent…
\( 67 \)
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look at this graph: graph of a parabola what is the equation of the axi…
\(x = 0\)
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layla tried to define a rotation. - for the center point c, the image c…
C. The lengths of \(\overline{CP}\) and \(\overline{CP'}\) must be equal.
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look at this graph: graph of a parabola with vertex at (0,0), y-axis fr…
0
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question which equation represents a line which is parallel to the line…
\( 5x + 7y=-42 \) (the second option among the given choices)
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tony tried to define a translation. - point a maps to point a. - every …
B. \(\overline{PP'}\) must have the same length as \(\overline{AA'}\).
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rectangle defg is similar to rectangle lmnp. what is the scale factor o…
2.5
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what are the coordinates of a point in quadrant i which is 5 units away…
\((1, 1)\)
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look at this graph: graph of a parabola opening downward with vertex at…
0
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a certain mapping in the xy-plane has the following properties: - every…
B. A reflection
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question 1 of 10 what else would need to be congruent to show that △abc…
D. $\overline{AC}\cong\overline{DF}$
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a certain mapping in the xy-plane has the following properties: - for t…
C. A rotation
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question which equation represents a line which is parallel to the line…
\(y=\frac{1}{7}x + 5\) (the first option)
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question 10 of 10 is △uvw ≅ △xyz? if so, name the postulate that applie…
A. Might not be congruent
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a sequence of transformations is described below. - a dilation about a …
A. Angle measures only
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look at this graph: graph of a parabola what are the coordinates of the…
(3, -1)
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graph the image of kite rstu after a reflection over the line y = -x.
The reflected kite has vertices at \( R'(10, 0) \), \( S'(8, -4) \), \( T'(6, -1) \), and \( U'(8, 0) \). (To graph, plot these points and connect them in order.)
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a sequence of transformations is described below. - a translation - a d…
A. Angle measures only
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question 9 of 10 is △pqr ≅ △stu? if so, name the congruence postulate t…
A. Congruent - ASA
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by substitution, \\(\\frac{ba + cb}{cb} = \\frac{de + cd}{cd}\\). by aa…
The correct order of the steps for the proof is: 1. We are given \(\overline{BD} \parallel \overline{AE}\), so \(\angle 4 \cong \angle 1\) and \(\angle 3 \cong \angle 2\) because …
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a sequence of transformations is described below. - a translation - a r…
A. Angle measures only
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proof create a paragraph proof of the triangle proportionality theorem …
To prove the Triangle Proportionality Theorem (Thales' theorem) for \( \overline{BD}\parallel\overline{AE} \) in \( \triangle CAE \): 1. **Identify Similar Triangles**: Since \( \…
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look at this graph: graph of a parabola opening downward with vertex at…
\(x = 0\)
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what is the value of x for which m || n? ○ x=40 ○ x=5 ○ x=105 ○ x=30 (3…
\( x = 40 \) (corresponding to the option "x = 40")
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problem 3 in the diagram shown, x represents the weight of each triangl…
- \(x + 9 = 3x + 3\) - \(6 = 2x\) - \(2x + 12 = 4x + 6\)
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△ abc is similar to △ xyz. also, side ab measures 6 cm, side bc measure…
36
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carpentry jake is fixing an a - frame. he wants to add a horizontal sup…
12
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the rectangle bcde is a dilation of the rectangle bcde. what is the sca…
\(\frac{3}{4}\)
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question 8 of 10 is △xyz ≅ △abc? if so, name the postulate that applies…
C. Congruent - SAS
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calculator △ abc is similar to △ pqr. also, angle a measures 35° and an…
\(95\)
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a sequence of transformations is described below. - a dilation about a …
A. Angle measures only
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look at this graph: graph of a parabola what is the y-intercept?
\(0\)
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in △abc, \\(\\overline{de}\\) is parallel to \\(\\overline{ac}\\) and \…
\( 20 \)
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the triangle mno is a dilation of the triangle mno. what is the scale f…
\(\frac{3}{2}\)
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question 7 of 10 what else would need to be congruent to show that $\\t…
C. \(\angle B\cong\angle Y\)
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segment \\(\\overline{ab}\\) is the result of rotating \\(\\overline{ab…
C. \( \overline{AB} \) and \( \overline{A'B'} \) have the same lengths.
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jh is a midsegment of △klm. find the value of x.
\(x = 8\)
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jh is a midsegment of △klm. find the value of x.
\( x = 18 \)
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question 6 of 10 is △lmn ≅ △opq? if so, name the congruence postulate t…
D. Congruent - SSS
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quadrilateral abcd is reflected across line m to create quadrilateral a…
41
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solve for x and graph the solution. (x + 3)(x - 5) > 0 plot the endpoin…
The solution for \(x\) is \(x < -3\) or \(x > 5\). To graph it, plot open circles at \(x = -3\) and \(x = 5\), then draw rays to the left of \(-3\) and to the right of \(5\) on th…
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problems 1–2 in this balanced hanger diagram, x represents the weight o…
Equation: $3x = 2y$ (or $x + 3y = 4x + y$), Value of $y$: $9$
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triangle $\\triangle abc$ is the result of dilating $\\triangle abc$ ab…
The lengths of $\overline{AB}$ and $\overline{A'B'}$ are equal: False The areas of $\triangle ABC$ and $\triangle A'B'C'$ are the same: False
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jh is a midsegment of △klm. find the value of x.
\( \boldsymbol{15} \)
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question 5 of 10 what else would need to be congruent to show that $\\t…
D. $\overline{EG}\cong\overline{HJ}$
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find the values of x and y. (image of a triangle with a midline segment…
\( x = 2 \), \( y = 4 \)
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triangle $\\triangle abc$ is the result of translating $\\triangle abc$…
A. \( \angle A \) and \( \angle A' \) have the same measures. C. The areas of \( \triangle ABC \) and \( \triangle A'B'C' \) are the same.
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the rectangle lmno is a dilation of the rectangle lmno. what is the sca…
\(\frac{2}{5}\)
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question 4 of 10 the sss postulate states that if the sides of one tria…
A. True
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find the values of x and y. (image of parallel lines cut by transversal…
\( x = 6 \), \( y=\frac{13}{2} \) (or \( 6.5 \))
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5. determine the exact perimeter of this shape made from parts of circl…
The exact perimeter is \( \boldsymbol{6\pi} \) units.
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quadrilaterals efgh and abcd are congruent. which of the following sequ…
Only sequence A (the option with "Only sequence A" text, likely the first option among the choices presented as a radio button with that label)
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solve for x and graph the solution. (x - 1)(x - 2) ≥ 0 plot the endpoin…
The solution to the inequality \((x - 1)(x - 2)\geq0\) is \(x\leq1\) or \(x\geq2\). To graph this, we plot closed circles at \(x = 1\) and \(x = 2\), draw a ray to the left of \(x…
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n7.2, n7.3, & n7.4 7 use a number line to order each set of numbers fro…
a) $\frac{3}{8}$, $\frac{5}{8}$, $\frac{7}{8}$, $\frac{10}{8}$ b) $\frac{4}{10}$, $\frac{9}{10}$, $\frac{12}{10}$, $1\frac{4}{10}$
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solve for x and graph the solution. (x - 3)(x + 5) ≤ 0 plot the endpoin…
The solution is \( -5 \leq x \leq 3 \). To graph: Plot closed circles at \( x = -5 \) and \( x = 3 \), then shade the segment between them on the number line.
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solve for x and graph the solution. (x + 2)(x + 6) ≤ 0 plot the endpoin…
The solution is \(-6 \leq x \leq -2\). To graph it, plot closed circles at \(-6\) and \(-2\), then draw a line segment connecting them.
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question 3 of 10 what else would need to be congruent to show that $\\t…
D. $\angle C\cong\angle Z$
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find another ordered pair(coordinate) that falls on the line that passe…
One possible ordered pair is \((4, - 4)\) (or other pairs like \((7, -6)\), \((-2,0)\) etc. can also be correct as long as they satisfy the line equation \( y=-\frac{2}{3}x-\frac{…
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4. a soup can with a diameter of 3 inches has a wrapper that wraps exac…
The approximate length of the wrapper is \( 9.42 \) inches (or using \( \pi\approx\frac{22}{7} \), the length would be \( \frac{22}{7}\times3\approx9.43 \) inches).
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question 2 of 10 in △jkl and △pqr, if ∠j ≅ ∠p, ∠k ≅ ∠q, and ∠l ≅ ∠r, th…
B. False
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given: m || n, ∠1 ≅ ∠3 prove: p || q complete the two - column proof. s…
2. \( \angle 1 \cong \angle 2 \) 4. transitive property (or substitution) 5. converse of alternate interior angles theorem
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n7 2, n7 3, & n7 4 7. use a number line to order each set of numbers fr…
a) \(\frac{3}{8}\), \(\frac{5}{8}\), \(\frac{7}{8}\), \(\frac{10}{8}\) b) \(\frac{4}{10}\), \(\frac{9}{10}\), \(\frac{12}{10}\), \(1\frac{4}{10}\)
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4. find the scale factor between the figures below. quadrilateral a has…
$\frac{3}{8}$
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6. triangle xyz with vertices x(-8, 3), y(-6, 5), and z(-5, -2): in the…
\(X'(0, 3)\), \(Y'(-2, 5)\), \(Z'(-3, -2)\)
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playscapes prassad is building a two - story playscape using the plans …
13 ft 4 in
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problems 1–2: here is a quarter-circle. it was created using a circle w…
s: 1. The two straight sides (radii) of the quarter - circle are labeled as 6 inches, and the curved part is a quarter - arc of a circle with radius 6 inches. 2. The perimeter of …
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triangle △abc is the result of dilating △abc about point p by a scale f…
For "\( \overline{BC} \) and \( \overline{B'C'} \) are on the same line": True For "\( \overline{AB} \) and \( \overline{A'B'} \) are both parallel to the \( x \)-axis": True
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question 10 of 10 you can find the ______ parts of two congruent triang…
D. corresponding
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triangle $\\triangle abc$ is the result of dilating $\\triangle abc$ ab…
The measures of $\angle C$ and $\angle C'$ are equal: True The areas of $\triangle ABC$ and $\triangle A'B'C'$ are the same: False
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problems 7–9: determine whether each measurement represents the radius,…
### Problem 7: - Radius: \( 7 \) feet - Diameter: \( 14 \) feet - Circumference: \( 43.96 \) feet ### Problem 8: - Radius: \( 12.10 \) feet - Diameter: \( 24.20 \) feet - Circumfe…
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question 9 of 10 if $\\triangle abc \\cong \\triangle def$ and $\\trian…
B. False
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problems 7–9: determine whether each measurement represents the radius,…
### Problem 7: - Radius: \( 7 \) feet - Diameter: \( 14 \) feet (given as tire height) - Circumference: \( 14\pi\approx 43.96 \) feet ### Problem 8: - Radius: \( \frac{38}{\pi}\ap…
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quadrilateral abcd is the result of dilating quadrilateral abcd about p…
The first claim "The lengths of $\overline{AB}$ and $\overline{A'B'}$ are equal" is False. The second claim "$\overline{AB}$ and $\overline{A'B'}$ are on distinct parallel lines" …
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question 8 of 10 assume △abc≅△def. if ab=12, bc=15, and ac=17, what is …
D. 15
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problems 7–9: determine whether each measurement represents the radius,…
- Radius: 7 feet - Diameter: 14 feet - Circumference: \( 14\pi \) feet
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question 7 of 10 which statement is an example of the symmetric propert…
D. If \( \triangle KLM \cong \triangle PQR \), then \( \triangle PQR \cong \triangle KLM \)
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the ratio of the measures of the angles in a triangle is 8:3:4. find th…
Smallest angle = \(36^{\circ}\) Middle angle = \(48^{\circ}\) Largest Angle = \(96^{\circ}\)
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solve the following system of equations graphically on the set of axes …
The solution to the system of equations is \(x=-2\), \(y = 5\) (or the point \((-2,5)\)).
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what is the measure of ∠spq in this rhombus? m∠spr = (4x + 11)° m∠qpr =…
\( 142 \)
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a triangle has interior angle measures of 3x, 45°, and 2x. what is the …
\(27\)
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problems 7–9: determine whether each measurement represents the radius,…
- Radius: 7 feet - Diameter: 14 feet - Circumference: \( 14\pi \) feet (or approximately 43.98 feet) ### Problem 8
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quadrilateral abcd is a square and the length of \\(\\overline{be}\\) i…
12
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question find the distance between the two points in simplest radical f…
\( 10 \)
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which statement describes a parallelogram that must be a square? a para…
D. A parallelogram with a right angle and diagonals that bisect the angles.
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find the distance between the two points in simplest radical form.
\(\boxed{13}\)
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question 5 of 10 which property is illustrated by the statement given b…
A. Reflexive
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find the perimeter of $\\triangle mnp$ answer attempt 3 out of 99 $mp =…
\( MP = 44 \) \( NP = 50 \) \( x = 14 \) \( MN = 36 \) \( \text{Perimeter} = 130 \)
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from unit 1, lesson 2 which is a scaled copy of polygon a? identify a p…
Polygon B is a scaled copy of Polygon A. A pair of corresponding sides: the left - vertical side of Polygon A and the left - vertical side of Polygon B (both have the same length …
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point p was rotated by 135° (the center of rotation is indicated). d c …
C. \( C \)
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question find the length of the third side. if necessary, round to the …
\(8.2\)
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5. help your classmate a. john claims the triangles are congruent by ss…
Jack is correct because SSA is not a valid triangle congruence criterion, so there is not enough information to conclude the triangles are congruent. ### Part b
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point q was rotated about the origin (0,0) by 180°. which point is the …
B. B
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how can this quadrilateral be classified? select each correct answer. t…
trapezoid, parallelogram, rhombus, square