Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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question 5 of 50 given: the figure at the right prove: ∠j ≅ ∠m statemen…
the vertical angles theorem
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question 4 of 50 the congruency theorem side - angle - side (sas) prove…
True
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question 2 of 50 the value of x is: two triangles with angle and side m…
\(66^{\circ}\)
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if $\\triangle art \\cong \\triangle xmi$ and the perimeter of $\\trian…
13.
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quiz 3 the triangles are similar by: ○ the sss similarity theorem ○ the…
the SAS similarity theorem
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write the equation of the line in slope-intercept form, $y = mx + b$.
\(y=\frac{3}{2}x + 3\)
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is $\\triangle gyk$ similar to $\\triangle bak$? yes no
Yes (the "Yes" option should be selected, as the triangles have proportional sides and equal included angles, satisfying SAS similarity criterion.)
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write the equation of the line in slope-intercept form, $y = mx + b$.
\(y=\frac{2}{3}x - 3\)
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the triangles are similar by: the sss similarity theorem. the sas simil…
the SAS similarity theorem.
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△rst ≅ △rqu. complete the proof that △qtu ≅ △sut. (image of a geometric…
\(\triangle QTU \cong \triangle SUT\) (by SSS Congruence Postulate)
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the perimeter of \\( \\triangle mnl \\) is: there are two triangles, on…
21
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quiz 2: similar polygons if $\\triangle abc \\sim \\triangle xyz$, the …
\(\frac{1}{4}\)
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write the equation of the line in slope - intercept form, $y = mx + b$.…
\(b = - 2\)
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the scale factor for δabc to δmnl is: images of two triangles and multi…
2
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write the equation of the line in slope - intercept form, y = mx + b. f…
\(b = - 1\)
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△uvx ≅ △wtx. complete the proof that △vwx ≅ △tux. (image of a quadrilat…
1. Reason: Given 2. Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) 3. Reason: CPCTC 4. Reason: Vertical angles are congruent 5. Reason: SAS (Side - Angle…
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which of the following statements is true? - if two polygons are simila…
The second option (the one stating "If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent")
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quiz 1: ratios and proportions the lengths of the sides of a triangle a…
20 feet (corresponding to the option with "20 feet")
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a square has a perimeter of 96 units. create a scale drawing of the squ…
The scale - drawn square has vertices at \((0,0)\), \((6,0)\), \((6,6)\), \((0,6)\) (and back to \((0,0)\)) with a side length of 6 units.
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write the equation of the line in slope - intercept form, $y = mx + b$.…
\(3\)
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the geometric mean of 5 and 4 is: $2\\sqrt{5}$ 10. 20. none of the choi…
\(2\sqrt{5}\) (the first option, with the dotted - boxed circle next to it)
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corey is doing renovations to his living room. the length of the room i…
148
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in the figure above, ab : bc is 3 : 1 and ac = 48. the length of ab is:…
36 (corresponding to the option with 36)
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figure abcdef is shown below. draw the figure using a scale factor of 0…
The scaled figure has vertices at \( (0,0) \), \( (0,5) \), \( (3,5) \), \( (3,3) \), \( (5,3) \), \( (5,0) \), and back to \( (0,0) \). Plot these points in order to draw the sca…
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write the equation of the line in slope - intercept form, $y = mx + b$.
\(y = 3x-2\)
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a picture is enlarged to poster size using a scale factor of 3. the dim…
The poster’s rectangle has vertices at \((0,0)\), \((12,0)\), \((12,18)\), \((0,18)\), and back to \((0,0)\) when plotted on the grid.
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use the slope and y-intercept to write the equation of the line. first,…
\(\frac{1}{4}\)
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a right triangle has legs with side lengths 12 and 9 create a scale dra…
The vertices of the scaled triangle are $(0, 0)$, $(3, 0)$, $(0, 4)$, and back to $(0, 0)$. To plot: start at $(0, 0)$, then plot $(3, 0)$, then $(0, 4)$, then back to $(0, 0)$ us…
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current skill graph: -10y + 3x = 60 line skill code: 312001
Plot the points \((20,0)\) and \((0,-6)\) and draw a line through them.
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compare the proof with the diagram. (diagram: a geometric figure with p…
s: - Step 9 Reason: Additive Property of Length - Step 11 Reason: Substitution - Step 13 Reason: SSS Congruence Postulate
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figure abcdef is shown below. draw the figure using a scale factor of 0…
Plot vertices at \((0,0)\), \((6,0)\), \((6,4)\), \((4,4)\), \((4,6)\), \((0,6)\), and back to \((0,0)\) to draw the scaled figure.
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a picture is enlarged to poster size using a scale factor of 2. the dim…
The scaled rectangle has vertices at (0,0), (12,0), (12,14), (0,14), and back to (0,0). When plotted on the grid, these points form the enlarged poster (a blue rectangle with widt…
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the radius of a circle is 5 miles. what is the length of a 45° arc? giv…
\( \frac{5\pi}{4} \)
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the diameter of a circle is 8 inches. what is the length of a 45° arc? …
\(\pi\)
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the diameter of a circle is 6 miles. what is the length of a 135° arc? …
\(\frac{9}{4}\pi\) (or \( \frac{9\pi}{4} \))
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a movie poster was shrunk using a scale factor of 0.25 so it can be use…
The new poster has a length of 12 grid units (24 inches) and a width of 5 grid units (10 inches). The vertices to plot are (0, 0), (12, 0), (12, 5), (0, 5), and back to (0, 0).
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draw a plan for a rectangular living room using the information below. …
To draw the rectangular living room: 1. Start at (0,0). 2. Move to (25,0) (10 feet length in units: \(10\times2.5 = 25\)). 3. Move to (25,20) (8 feet width in units: \(8\times2.5 …
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∠efj ≅ ∠gih, ∠ejf ≅ ∠hgi, and \\(\\overline{ij} ≅ \\overline{fg}\\). co…
Statement: $\triangle EFJ \cong \triangle HIG$; Reason: AAS (Angle - Angle - Side) Congruence Theorem
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figures abcd and efgh are similar. the scale factor of figure abcd to f…
\(224\)
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nora is doing renovations to her living room. the length of the room is…
148
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figure abcdef is shown below draw the figure using a scale factor of 0.…
The scaled - down figure has vertices at \( (0,0) \), \( (4,0) \), \( (4,1) \), \( (1,1) \), \( (1,4) \), \( (0,4) \) and back to \( (0,0) \) when plotted with the scale factor of…
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a picture is enlarged to poster size using a scale factor of 4. the dim…
Plot vertices at \((0,0)\), \((12,0)\), \((12,20)\), \((0,20)\), and back to \((0,0)\) on the grid. The rectangle will have width 12 units and height 20 units (matching the scaled…
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what is the value of v? f v e 43° g d 40° v = ° submit
\(97\)
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△bcd is dilated by a scale factor of \\(\\frac{1}{3}\\) with the center…
\((2, 2)\)
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a right triangle has legs with side lengths 21 and 15. create a scale d…
The vertices of the scaled right triangle are at $(0, 0)$, $(5, 0)$, and $(0, 7)$. When plotting with the polygon tool, plot these points in order and then connect back to the fir…
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tu ≅ tv. complete the proof that δtuv ≅ δtvu. triangle with vertices v,…
1. Reason: Given 2. Reason: Reflexive Property of Congruence 3. Reason: SAS (Side - Angle - Side) Congruence Postulate
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→ tw bisects ∠uwy and ∠vtx. complete the proof that △tvw ≅ △txw. statem…
For Statement 4, the reason is "Definition of angle bisector". For Statement 7, the reason is "Additive Property of Angle Measure".
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11 tell which quadrilateral(s) have the given property. a) diagonals bi…
Parallelograms (including Rectangle, Rhombus, Square)
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9 find the length of ef in the trapezoid shown below. ef=
34
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find the value of x and y in the isosceles trapezoid shown below. (6x -…
\( x = 11 \), \( y = 117 \)
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figures abcd and efgh are similar. the scale factor of figure abcd to f…
378
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Question was provided via image upload.
For step 3, the reason is "Vertical Angles are congruent" (or "Vertical Angles Congruence Theorem"). For step 7, the reason is "Substitution Property" (using \( \angle WVX \cong \…
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10 find the values of x and y in the kite shown below. x= y=
\( x = 90 \), \( y = 56 \)
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7 for the rhombus, find the value of x. (7x - 17)° (5x + 9)° x=______ 1…
13
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pqrs is a rectangle. find the value of x and the length of each diagona…
\( x = 3 \), \( PR = SQ = 26 \)
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the diameter of a circle is 18 inches. what is the length of a 90° arc?…
\( \frac{9}{2}\pi \)
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4 find the value of each variable in the rhombus below. (image of a rho…
\( x = 28 \), \( y = 90 \), \( z = 90 \)
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6) find the most precise name for the quadrilateral shown below. use pa…
Square
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find the value of the variables in the rectangle shown below. 6x - 6 4y…
\( x = 9 \), \( y = 15 \)
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find the value of the variables in the parallelogram shown below. 3x° (…
\( x = 25 \), \( y = 105 \)
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1 find the missing angle measures of the parallelogram. m∠b=_________ m…
\( m\angle B = 82^\circ \), \( m\angle C = 98^\circ \), \( m\angle D = 82^\circ \)
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the diameter of a circle is 18 inches. what is the length of a 90° arc?…
\(\frac{9}{2}\pi\)
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the diameter of a circle is 18 feet. what is the length of a 90° arc? d…
\( \frac{9}{2}\pi \)
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dilate △qrs by a scale factor of 3 with the center of dilation at the o…
Point \(R'\): \((-3, 0)\) Point \(S'\): \((-9, 6)\)
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a right triangle has legs with side lengths 12 and 9 create a scale dra…
The vertices of the scaled right triangle are plotted as follows: Start at $(0, 0)$, then plot $(3, 0)$, then plot $(0, 4)$, and finally plot $(0, 0)$ to close the triangle. The s…
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sal is tiling his entryway. the floor plan is drawn on a unit grid. eac…
50.00
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find the radius and the diameter to the nearest hundredth when $c = 3\\…
The radius is \( \boldsymbol{1.50} \) yards. The diameter is \( \boldsymbol{3.00} \) yards.
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use the drop-down menus to describe the transformations used to map △ab…
1) \( 90^\circ \) 2) \( \frac{1}{3} \) The triangles are similar. (Note: The exact coordinates might need rechecking, but the standard approach for such problems: rotation by \( 9…
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find the circumference of the circle. use 3.14 for π. round to the near…
47.1
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find the circumference of the circle. use 3.14 for π. 7 in. the circumf…
21.98
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suppose that you know that $\\angle t$ and $\\angle s$ are supplementar…
First blank: \(180\); Second blank: multiplying by 3 (or substituting into \(3x\))
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use the figure. find the measures of ∠a and ∠b. the measure of ∠a is th…
The measure of \(\angle A\) is \(60^\circ\). The measure of \(\angle B\) is \(80^\circ\).
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△abc undergoes three transformations: - it is translated 4 units left a…
The final image has the same orientation, is in a different position, and is larger in size as the pre - image. It is similar but also not congruent to the pre - image. (For the d…
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use the figure. complete the description. the pair of angles ∠agb and ∠…
The pair of angles ∠AGB and ∠DGE are vertical angles, so m∠DGE is 28°.
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9. the diameter of a circle is 8 centimeters. what is the area of the c…
A) \( 50.24\ \text{cm}^2 \)
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use the figure to complete the description. the sum of the measures of …
complementary
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write the point-slope form of the lines equation satisfying the given c…
- Point - slope form: \( y - 3=0(x + 6) \) (or \( y - 3=0(x - 5) \)) - Slope - intercept form: \( y = 3 \)
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15 cm 6 cm the scale in the drawing is 3 cm:5 m. what are the length an…
The length is \(25\) meters, the width is \(10\) meters, and the area is \(250\) square meters.
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select the correct answer from each drop - down menu. wxyz is a quadril…
- Length of \(\overline{WX}\): \(\sqrt{18}\approx4.24\) - Length of \(\overline{XY}\): \(\sqrt{45}\approx6.71\) - Length of \(\overline{YZ}\): \(\sqrt{45}\approx6.71\) - Length of…
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drag the tiles to the boxes to form correct pairs. match each set of ve…
- \(A(2,4), B(4,5), C(3,6)\) → acute isosceles - \(A(3,5), B(3,4), C(5,4)\) → right scalene - \(A(3,5), B(5,6), C(3,0)\) → obtuse scalene - \(A(2,4), B(3,5), C(2,6)\) → right isos…
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the scale of a room in a blueprint is 3 in. : 5 ft. a wall in the same …
s: - Table (Actual length for each blueprint length): 10, 15, 20, 25, 30 (for 6,9,12,15,18 in respectively) - Actual wall length: 30 feet - Blueprint window width: 1.5 inches
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select the correct answer. the points a(-3, 4), b(3, 2), c(1, -4), and …
B. The product of the slopes of the diagonals is -1
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the coordinates of the vertices of △abc are shown in the table below, a…
First \( \triangle ABC \) was \(\boldsymbol{\text{dilated}}\) (by scale factor 2), then \( \triangle A'B'C' \) was \(\boldsymbol{\text{translated}}\) (8 units left).
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describe how to use ratios to determine whether two shapes are similar.…
First select: equal (or congruent) Second select: proportional (or have equal ratios)
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are the shapes similar? complete the explanation. the shapes are simila…
The shapes are similar. All of the angles are right angles and the ratio of the corresponding sides is \(3:5\).
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△abc undergoes three transformations: - it is translated 4 units left a…
For the last drop - down (the one with "congruent" and "not congruent" options), the answer is "not congruent". The other filled - in options are correct as: orientation - the sam…
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the vertices of a quadrilateral are a(-3,-1), b(1,5), c(5,5), and d(5,-…
# Explanation: ## Step1: Calculate slopes of sides To determine the type of quadrilateral, we calculate the slopes of \(AB\), \(BC\), \(CD\), and \(DA\) using the slope formula \(…
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are the shapes similar? complete the explanation. the shapes are simila…
The shapes are similar. All of the angles are congruent angles and the ratio of the corresponding sides is \(3:5\).
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△abc undergoes three transformations: - it is translated 4 units left a…
The final image has the same orientation, is in a different position, and is not the same size as the pre - image. It is similar to the pre - image. (For the drop - down with the …
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are the shapes similar? complete the explanation. the shapes (select) s…
The shapes \(\boldsymbol{\text{are}}\) similar. All of the angles are \(\boldsymbol{\text{congruent}}\) angles and the ratio of the corresponding sides is \(3:\boldsymbol{5}\).
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△abc undergoes three transformations: - it is translated 4 units left a…
For the size dropdown: not the same size
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a rectangle made of square tiles measures 9 tiles long and 2 tiles wide…
18
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which of these four - sided shapes are similar? select is similar to qr…
ABCD (the rectangle with length 12 cm and width 4 cm) is similar to QRST.
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△abc undergoes three transformations: - it is translated 4 units left a…
- The final image has \(\boldsymbol{\text{the same}}\) orientation, it is in \(\boldsymbol{\text{a different}}\) position, and is \(\boldsymbol{\text{larger than}}\) the pre - ima…
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use the drop-down menus to select the correct type of transformation fo…
First transformation: dilated; Second transformation: rotated; Third transformation: reflected; Final image relationship: similar, not congruent
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use the drop - down menus to describe the transformations used to map $…
1) A dilation centered at the origin with a scale factor of \( 2 \) 2) A reflection across the \( x \)-axis The triangles are similar
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use the drop - down menus to describe the transformations used to map $…
2) A dilation centered at the origin with a scale factor of \( \frac{1}{2} \). The triangles are similar.
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use the drop-down menus to describe the transformations used to map △ab…
1) A rotation of \( 180^\circ \) counterclockwise about the origin. 2) A dilation centered at the origin with a scale factor of \( \frac{1}{2} \).
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type the correct answer in the box. use numerals instead of words. if n…
0.6
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graph each equation. 9) $\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1$
The graph is an ellipse with vertices at \((0,3)\), \((0, - 3)\) and co - vertices at \((2,0)\), \((- 2,0)\), sketched on the given coordinate grid by connecting these points smoo…