Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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problem 6.3: write an equation for this line: y = _ x + _
$y = 0x + 4$ (or simplified as $y = 4$)
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problem 6.2: write an equation for this line: y = ______ x + _______ (-…
\( y=-2x + 4 \)
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problem 6.1: write an equation for this line: y = ______ x + ______ (5,…
$y = \boldsymbol{1}x + \boldsymbol{(-1)}$ (or $y = x - 1$)
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24 the dashed figure is the image of the solid figure. what is the alge…
a) \((-5, 3)\) ### Problem 24 (Translation 9 units right and 3 units down)
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19 if angle p measures 50 degrees, what is the measure of angle q? a) 4…
c) 130° ### Problem 20 (Parallel Lines and Angle)
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in the diagram below, \\(\\overline{bd} \\parallel \\overline{ae}\\), \…
56
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in the diagram below, \\(\\overline{bd} \\parallel \\overline{ae}\\), \…
# Explanation: ## Step1: Find ∠ABF Since ∠BFE is 116°, its supplementary angle ∠BFA is \(180^\circ - 116^\circ = 64^\circ\). In triangle ABC, ∠C = 84°, and since BD || AE, ∠ABD = …
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4 the coordinate plane shows point j a. describe how to move from the o…
Move 3 units to the left (and 0 units up/down) from the origin. ### Part 4b
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find the equation of the line specified. the line passes through the po…
A. \( y = 2x - 8 \)
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complete problems 3–5. 3 a map is shown in the coordinate plane, with c…
a. right, down; b. The point for the movie theater is plotted at \((-4,4)\) on the coordinate plane (4 units left (along the negative x - axis) and 4 units up (along the positive …
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find the equation of the line that cuts through (0, 5) and (1, 2)? a. $…
A. \( y = -3x + 5 \)
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find the measures of the interior angles of the triangle. ∠a = 45 ° ∠b …
\(\angle A = 49^\circ\), \(\angle B = 41^\circ\), \(\angle C = 90^\circ\)
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3. $\\frac{-6}{7} \\leq \\frac{3}{7}f$
\(f \geq -2\) (On the number line, this would be a closed circle at -2 and an arrow pointing to the right.)
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find the value of ( x ), ( y ), and ( z ), in the rhombus below. (image…
\( x = -7 \), \( y = -43 \), \( z = 42 \)
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find the value of x, y, and z in the rhombus below. (2z+9)° (x+8)° 107°…
\(x = 65\), \(y = -63\), \(z = 49\)
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4 a. what does the sign of the x-coordinate of a point tell you about t…
The sign of the \(x\) - coordinate tells us whether the point is to the left (negative \(x\) - coordinate), to the right (positive \(x\) - coordinate) of the \(y\) - axis, or on t…
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find the value of x, y, and z, in the rhombus below. (image of a rhombu…
\(x = 1\), \(y = -5\), \(z = 1\)
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question find the value of x, y, and z in the parallelogram below. (5z+…
\(x = -13\), \(y = 8\), \(z = 22\)
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calculate the distance between the points k=(0, -9) and m=(5, -4) in th…
7.07
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calculate the distance between the points h = (-3, -2) and p = (1, -9) …
8.06
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choose all answers that describe the quadrilateral efgh if \\(\\overlin…
A. Parallelogram, B. Rectangle, E. Trapezoid
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choose all answers that describe the quadrilateral below. answer attemp…
A. Parallelogram, B. Rectangle
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choose all answers that describe the quadrilateral opqr if \\(\\overlin…
Parallelogram, Rectangle
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what does the video conclude about evaluating online information? weve …
A. We've always struggled with it (assuming the red - colored option with the triangle symbol is labeled A, the yellow with circle B, blue with diamond C, green with square D. If …
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model it complete the problems about ordered pairs with negative coordi…
Move 4 units to the right from the origin, then move 3 units down. ### Part (b)
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why are statistics and infographics not always reliable? ▲ they can be …
The correct option is the one with "They can be manipulated" (the pink - colored option with the triangle symbol).
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model it complete the problems about ordered pairs with negative coordi…
s: 3a. Move 2 units right and then 3 units down (or 3 units down and then 2 units right) from the origin. 3b. The ordered pair is \(\boldsymbol{(2,-3)}\) (using the movement to ge…
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what is the sum of the measures of the exterior angles of a regular tri…
\(360^\circ\)
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the measures of the exterior angles of a pentagon are $x^circ$, $3x^cir…
\(126^\circ\)
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2 to show locations west and south of spyglass rock, the axes in the co…
For part (a), the first blank is "left" and the second blank is "up". ### Part (b)
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the measures of the exterior angles of a quadrilateral are $2x^{circ}$,…
The measure of the largest exterior angle is \(150^\circ\)
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what is the sum of 2 of the interior angles of a regular pentagon? answ…
$216^\circ$
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how many sides does a polygon have if the sum of the interior angles is…
The polygon has 23 sides.
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how many sides does a polygon have if the sum of the interior angles is…
The polygon has 9 sides.
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why is design not a good measure of credibility? design is irrelevant t…
A. Design is irrelevant to truth (assuming the red option with the triangle is labeled A, but based on content, the option "Design is irrelevant to truth" is correct)
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what is the measure of each interior angle of the regular polygon pictu…
\( 108 \)
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what does the wise old fish joke illustrate? our ignorance of our envir…
The option with "Our ignorance of our environment" (the red - colored option with the triangle icon)
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what is the sum of the interior angles of the polygon pictured below? a…
\( 3780 \)
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what is the measure of each interior angle of the regular polygon pictu…
\( 150 \)
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question translate the figure 6 units left and 4 units up. plot all of …
(The translated figure is formed by plotting the points obtained by subtracting 6 from the x - coordinates and adding 4 to the y - coordinates of the original figure's vertices an…
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name that t can you describe the transformations that would tr figure (…
To transform the pink figure (pre - image) to the yellow figure, we can perform two transformations: 1. **Reflection over the y - axis**: This flips the pink figure across the ver…
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explore the four-quadrant coordinate plane understand: what do negative…
west; north
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in $\\triangle efg$, $\\overline{eg}$ is extended through point g to po…
$24$
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in δnop, \\(\\overline{np}\\) is extended through point p to point q, \…
$26$
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the transformation or series of that would transform the pink e) to the…
The transformation from the pink figure to the yellow figure is a 90 - degree clockwise (or counter - clockwise) rotation followed by a translation (the specific translation can b…
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the ratios of corresponding sides in the two triangles are equal. what …
\(\boldsymbol{\angle I \cong \angle F}\) (the option: \(\boldsymbol{\angle I \cong \angle F}\))
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△rst ~ △ryx by the sss similarity theorem. which ratio is also equal to…
\( \boldsymbol{\frac{ST}{YX}} \) (the last option: \( \frac{ST}{YX} \))
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in the diagram, \\(\\frac{sq}{om} = \\frac{sr}{on} = 4\\). to prove tha…
B. \(\overline{MN}\) and \(\overline{QR}\)
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what value of x will make the triangles similar by the sss similarity t…
30
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48. two circles have radii ( r_1 = 7 ) and ( r_2 = 21 ). what is the sc…
a. 3
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consider the two triangles. how can the triangles be proven similar by …
Show that the ratios \(\frac{UV}{XY}\), \(\frac{WU}{ZX}\), and \(\frac{WV}{ZY}\) are equivalent.
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46. what is the area of a sector with a radius of 10 meters and a centr…
d. \(\frac{25\pi}{2}\) square meters
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what value of x will make the triangles similar by the sss similarity t…
\(77\) (corresponding to the option "77")
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given: δwxy is isosceles with legs \\(\\overline{wx}\\) and \\(\\overli…
- Step 4 Statement: $WX = WY; WV = WZ$ - Step 6 Reason: Substitution Property - Step 9 Reason: SAS (Side - Angle - Side) Similarity Theorem
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43. in $\\triangle ghi$, $gh = 12$, $hi = 16$, and $\\angle g = 60^\\ci…
a. Yes, by the SAS Criterion
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which pairs of triangles are similar? check all that apply. □ △abc ~ △d…
$\triangle DEF \sim \triangle GHI$, $\triangle JKL \sim \triangle ABC$ (i.e., the options: $\triangle DEF \sim \triangle GHI$, $\triangle JKL \sim \triangle ABC$)
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what value of x will make the triangles similar by the sss similarity t…
\(28\)
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38. two triangles have corresponding sides with ratios of \\(\\frac{3}{…
d. They are similar.
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what additional information is needed to prove that the triangles are s…
MN = 6 and XZ = 17.5
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37. ∠1 and ∠2 are alternate interior angles formed by a transversal cut…
a. 8
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part a does he need the same number of square inches of glass for each …
Primera ecuación: $7 \times \boldsymbol{6} = \boldsymbol{42}$ square inches Segunda ecuación: $6 \times \boldsymbol{7} = \boldsymbol{42}$ square inches
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35. a triangle with vertices a(1, 2), b(2, 4), and c(3, 6) is dilated t…
a. 2
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test prep what is the area of the shaded part of the rectangle? 6 in. 7…
29
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34. according to the perpendicular bisector conjecture, in triangle $\\…
b. \( BD = 10 \) units, \( CD = 10 \) units
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problem 5: select expressions that could represent the slope of this li…
The expressions that represent the slope are \( \boldsymbol{\frac{1}{4}} \), \( \boldsymbol{\frac{4}{16}} \), and \( \boldsymbol{\frac{2}{8}} \) (assuming the checkboxes correspon…
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complete the statements to verify that the triangles are similar.\\(\fr…
For \(\frac{PQ}{ST}=\frac{\sqrt{52}}{\sqrt{13}}=\boxed{2}\) The triangle \(\triangle PQR\) (assuming the first triangle is \(\triangle PQR\) with vertices \(P,Q,R\)) \(\sim\triang…
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for each triangle, check all that apply. | triangle a (sides 12, 12, 12…
- Triangle A: $\boxed{\text{Isosceles}}$, $\boxed{\text{Equilateral}}$ (but since equilateral is a type of isosceles, and the options are checkboxes, we check Isosceles and Equila…
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in δklm, m∠k = 21° and m∠l = 36°. which list has the sides of δklm in o…
KL, MK, LM
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verifying that triangles are similar r(-2, 4) p(4, 4) q(-2, 0) t(-1, -2…
\(\frac{QR}{TU} = 2\), \(\frac{PR}{SU} = 2\), \(\frac{PQ}{ST} = 2\), and \(\triangle PQR \sim \triangle STU\) by the SSS (Side - Side - Side) similarity theorem.
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in $\\delta hij$, $m\\angle h = 92^\\circ$ and $m\\angle i = 20^\\circ$…
IJ > HI > JH (the option with "IJ > HI > JH")
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part a does he need the same number of square inches of glass for each …
Para la primera ecuación: \( 7 \times 9 = 63 \) Para la segunda ecuación: \( 9 \times 7 = 63 \) Entonces, los espacios serían: \( 7 \times \boldsymbol{9} = \boldsymbol{63} \) squa…
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a rectangular envelope has a clear window for the address to show. the …
24
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10 mm 4 mm 4 mm 10 mm 2 mm 2 mm enter the correct answer in the box. sh…
80
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which statement best describes triangles uvw and xyz? ○ they are simila…
They are similar, but not congruent.
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can the triangles be proven similar using the sss or sas similarity the…
Yes, $\triangle EFG \sim \triangle KLM$ by SSS or SAS. (Corresponding option: "Yes, $\triangle EFG \sim \triangle KLM$ by SSS or SAS.")
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find the area of the shaded part of the rectangle. (there is an image o…
54 square feet
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there is a rectangular - shaped pond with a path around it, as shown. w…
84
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27. in parallelogram pqrs, if diagonal pr is bisected at point o and po…
b. 3
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given: 3ab = 7ad and 3ac = 7ae prove: δabc ~ δade complete the steps of…
For the first blank (step 4 reason): division property For the second blank (step 8 reason, if we consider the similarity criterion): SAS similarity criterion (but based on the gi…
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a robot travels from position a to b to c to d. what composition of rig…
The composition is \(T_{(1,2)} \circ T_{(4,0)} \circ T_{(2,2)}\) (assuming the translation vectors are (2,2) for A→B, (4,0) for B→C, and (1,2) for C→D). So the boxes should be fil…
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select the correct answer from each drop - down menu. given: ∠aob ≅ ∠bo…
The key steps are: By vertical angles theorem, $\angle AOB \cong \angle DOE$; given $\angle AOB \cong \angle BOC$; by transitive property, $\angle BOC \cong \angle DOE$, contradic…
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write the equation of a line in slope intercept form given the points (…
$y = 3x - 11$
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write an equation of a line in point slope form given a slope of 3 and …
\( y + 4 = 3(x - 9) \)
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point e is added to the given figure so that point e lies on segment bd…
D. \( \angle ABD \cong \angle ABE \)
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plot the following points on the number line without measuring. i. \\(\…
i. $\frac{7}{12} > \frac{1}{2}$ ii. $\frac{7}{12} < \frac{5}{6}$ $\frac{1}{4} < \frac{3}{8}$ (example for second part a)
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enter segments in the blanks provided that would result in a true equat…
\( \frac{PR}{PQ} \) (or other correct corresponding side ratio based on similar triangle correspondence, but assuming the intended answer is \( \frac{PR}{PQ} \))
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given that \\(\\frac{ab}{de} = \\frac{bc}{ef} = \\frac{1}{2}\\), comple…
B and E
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type the correct answer in the box. use numerals instead of words. if n…
8
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which greek mathematician is known as the father of geometry? a. pythag…
C. Euclid
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given that \\(\\frac{ab}{de} = \\frac{bc}{ef} = \\frac{1}{2}\\), comple…
First dropdown: \( \angle ABC \) and \( \angle DEF \) (but from the options' context, the first blank's line: "Horizontal and vertical lines are \(\boldsymbol{\text{perpendicular}…
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name 1. a. plot the following points on the number line without measuri…
1. b. i. $\frac{7}{12} > \frac{1}{2}$; ii. $\frac{7}{12} < \frac{5}{6}$ 2. b. Example: $\frac{1}{4} < \frac{3}{8}$
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write equations for the vertical and horizontal lines passing through t…
vertical line: \( x=-1 \) horizontal line: \( y = 3 \)
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15. a window is shaped like a rectangle with a semicircle on each end. …
The total area of the window is \( 160 + 25\pi \) (or approximately 238.5) square inches.
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write equations for the horizontal and vertical lines passing through t…
horizontal line: \( y=-6 \) vertical line: \( x=-9 \)
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m∠1 = 110°, m∠2 = 70°, ∠1 is supplementary to ∠3, ∠2 is supplementary t…
To prove \( \angle1 \cong \angle2 \): 1. **Given/Definition**: \( \angle1 \) is supplementary to \( \angle3 \) (\( m\angle1 + m\angle3 = 180^\circ \)), \( \angle2 \) is supplement…
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22. the length of a rectangle is represented by ( x^2 + 3x + 2 ), and t…
Perimeter: \( \boldsymbol{2x^2 + 14x + 4} \) Area: \( \boldsymbol{4x^3 + 12x^2 + 8x} \)
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select the correct answer from each drop - down menu. given: ( cd = ef …
Statement: \( CE = DF \); Reason: Substitution Property of Equality
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what is the relationship between \\(\\angle 1\\) and \\(\\angle 2\\)? m…
The "alternate exterior angles" should be matched with the bottom - left figure (the figure in the second row, first column).
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find the x-intercept and y-intercept of the line. 7x - 8y = -12 x -inte…
x-intercept: \(\boldsymbol{-\frac{12}{7}}\) y-intercept: \(\boldsymbol{\frac{3}{2}}\)
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ab and pq are parallel lines. cr and ds intersect the two lines as show…
C. \(CR = DS\)