Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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given: abcd is a parallelogram, ∠gec ≅ ∠hfa and \\(\\overline{ae} \\con…
The reason for \( \overline{EF} \cong \overline{EF} \) is the Reflexive Property of Congruence. And the proof of \( \triangle GEC \cong \triangle HFA \) can be done using the ASA …
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step | statement | reason 1 | abcd is a parallelogram e is the midpoint…
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
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statement reason abcd is a parallelogram e is the midpoint of \\(\\over…
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent (SAS)
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en: abcd is a parallelogram, e is the midpoint of \\(\\overline{ab}\\) …
Opposite angles of a parallelogram are congruent
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given: abcd is a parallelogram, e is the midpoint of \\(\\overline{ab}\…
For step 5, the reason is "When a midpoint divides a segment into two parts, each part is half the length of the whole segment". And the final proof shows \( \overline{DE}\cong\ov…
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given: abcd is a parallelogram, e is the midpoint of \\(\\overline{ab}\…
For step 4, the reason is "Definition of a midpoint (a midpoint divides a segment into two equal - length segments, so each segment is half the length of the original segment)". A…
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given: abcd is a parallelogram, e is the midpoint of \\(\\overline{ab}\…
Opposite sides of a parallelogram / rhombus / rectangle / square are congruent
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question given: abcd is a parallelogram, e is the midpoint of \\(\\over…
The reason for \(\overline{AD} \cong \overline{CB}\) is "Opposite sides of a parallelogram are congruent".
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prove: \\(\\overline{df}\\) bisects \\(\\overline{bc}\\). step | statem…
For step 6, the reason is "Corresponding Angles Postulate (If two parallel lines are cut by a transversal, corresponding angles are congruent)". And by proving \( \triangle DCE \c…
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question given: abcd is a parallelogram and b is the midpoint of \\(\\o…
The reason for \(\overline{DC}\parallel\overline{AB}\) is "Opposite sides of a parallelogram are parallel". And by proving \(\triangle DCE\cong\triangle FBE\) (using AAS with the …
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question given: (abcd) is a parallelogram and (b) is the midpoint of (o…
The reason for Step 4 ($\overline{BF} \cong \overline{DC}$) is the **Transitive Property of Congruence** (or "If two segments are congruent to the same segment, then they are cong…
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question given: abcd is a parallelogram and b is the midpoint of \\(\\o…
The reason for \(\overline{AB} \cong \overline{DC}\) is "Opposite sides of a parallelogram are congruent".
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question given: abcd is a parallelogram and b is the midpoint of \\(\\o…
The reason for \( \overline{AB} \cong \overline{BF} \) is "Definition of Midpoint" (A midpoint divides a segment into two congruent segments).
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prove: $\\angle a \\cong \\angle e$. step | statement | reason 1 | $abc…
The reason for \( \angle A \cong \angle E \) is the Transitive Property of Congruence (if \( \angle A \cong \angle CDE \) and \( \angle E \cong \angle CDE \), then \( \angle A \co…
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step | statement | reason 1 | abcd is a parallelogram \\(\\overline{ab}…
The reason for \( \angle A \cong \angle CDE \) is "Corresponding Angles Postulate (If two parallel lines are cut by a transversal, corresponding angles are congruent)" (or also ca…
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given: abcd is a parallelogram and \\(\\overline{ab} \\cong \\overline{…
The reason for step 5 (statement \(\overline{AB} \parallel \overline{CD}\)) is "Opposite sides of a parallelogram are parallel".
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given: abcd is a parallelogram and \\(\\overline{ab} \\cong \\overline{…
The reason for $\overline{CD} \cong \overline{CE}$ is the Transitive Property of Congruence (If two segments are congruent to the same segment, then they are congruent to each oth…
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given: abcd is a parallelogram and \\(\\overline{ab} \\cong \\overline{…
Opposite sides of a parallelogram are congruent
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the graph represents a function. which ordered pair can be plotted toge…
(-1, 2)
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following is shown as 62.8 m in the circle? rence 20m 314m² 10m 62.8m
The circumference of the circle (with diameter 20 m or radius 10 m) is 62.8 m, calculated using the formula \( C = \pi d \) (or \( C = 2\pi r \)) where \( d = 20 \) m (or \( r = 1…
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angle theorems - handout date 1. determine the measure of the missing a…
\( 75^\circ \) #### b)
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question 13 (1 point) saved determine the measure of n in the following…
\(n = 65^\circ\)
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a floor map of a house is drawn to scale. on this map, 1 inch represent…
The length of the real kitchen is 40 feet and the width is 17.5 feet.
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the great basin: a harsh environment - the great basin is geographicall…
A. environmental challenges
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ites parallèles b) $d_1:\\begin{cases}x = 1 + 3t\\\\ y = 2 - t \\\\ z =…
0 - 5)^2 = 41 eq 25 \). No intersection. #### Intersection with \( z \)-axis ( \( x = 0 \), \( y =
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Question was provided via image upload.
### Problem 5 - 17 (First Diagram: Lines \( r \) and \( s \) parallel, cut by transversals) We use properties of parallel lines (corresponding angles, vertical angles, linear pair…
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what are the coordinates of point p on the directed line segment from r…
\((-3.5, 2.3)\)
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what is the location of point f, which partitions the directed line seg…
\(\frac{1}{11}\) (corresponding to the option with \(\frac{1}{11}\))
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question find the length of the three missing sides in the rhombus belo…
\( x = 19 \), \( y = 19 \), \( z = 19 \)
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what are the coordinates of the center of dilation for the dilation sho…
# Explanation: ## Step1: Recall dilation center property The center of dilation is the point that remains fixed (or lies on the line through each corresponding point and its image…
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find the measure of the three missing angles in the rhombus below. (ima…
\(x = 122\), \(y = 122\), \(z = 58\)
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question 4 all work for this question must be shown on the cap #3 works…
The equation of the line in slope - intercept form is \( y=\frac{2}{5}x+\frac{27}{5} \)
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factoring polynomials worksheet 1. factor out the greatest common facto…
\(6x(x + 2)\) For question 1b (\(8x - 24\)):
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26. o is the centre of the circle. determine the value of f to the near…
b. 8 ### Question 27
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26. o is the centre of the circle. determine the value of f to the near…
c. \(94^{\circ}\)
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a. p b. s c. q d. r unit 8: circle geometry 25. o is the centre of this…
b. \( 53^\circ \)
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23. which figure shows the rotation image of pentagon a after a 216° cl…
a. Figure iii ### Question 24
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unit 7: similarity and transformations 20. a rectangle has length 6 cm …
b. 48 cm ### Question 21
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line m has a y - intercept of c and a slope of \\(\\frac{p}{q}\\), wher…
B. \( \frac{p}{q} \) (assuming the slope of line \( m \) is \( \frac{p}{q} \) and parallel lines have equal slopes)
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the coordinates of a, b, and c in the diagram are a(p, q), b(5, 1), and…
B. \(p + q = 7\)
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select the correct line. which line is perpendicular to \\( \\overleftr…
Line 2 (or the specific line labeled as having the steep negative slope that is the negative reciprocal of \(\overrightarrow{AB}\)'s slope)
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question 4 of 5 select the correct answer. a graphic designer is creati…
\( -6x + y=-29 \) (the second option, assuming the options are: 1. \( 2x + 8y = 12 \), 2. \( -6x + y=-29 \), 3. \( 2x + y = 14 \), 4. \( 4x - y=-29 \))
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in the figure below, m || n and p || q. find the values of x and y. x =…
\( x = 64 \) \( y = 34 \)
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the two triangles below are similar. also, m∠s = 15° and m∠t = 110° as …
\(m\angle D=\boldsymbol{110^\circ}\), \(m\angle E=\boldsymbol{55^\circ}\), \(m\angle F=\boldsymbol{15^\circ}\)
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use the given information to prove that f || g. given: ∠8 ≅ ∠1 prove: f…
To prove \( f \parallel g \): ### Step 1: State the Given Statement: \( \angle 8 \cong \angle 1 \) Reason: Given ### Step 2: Vertical Angles Theorem Statement: \( \angle 8 \cong \…
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the map of a farmers property is displayed on a coordinate plane. there…
(Part b): The blanks should be filled with \( 5 \) and \( 4 \) (order does not matter). So: \( \boldsymbol{5}^2 + \boldsymbol{4}^2 = x^2 \)
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calculate the distance between the points m=(-5, -6) and p=(2, 2) in th…
\(\sqrt{113}\)
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calculate the distance between the points p=(-9, 0) and h=(-3, 8) in th…
\( 10 \) (Wait, no, wait, \( \sqrt{100} \) is 10, so the exact distance is 10. But let me confirm once more. The distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). …
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calculate the distance between the points n = (3, -2) and h = (7, -9) i…
\(\sqrt{65}\)
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find the distance between the points a and b given below. (that is, fin…
5.39
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8 which of the following is the definition of tragedy? a type of fictio…
D. A serious drama that portrays the downfall of a noble, heroic individual (Note: The original options are presented with circles, and the correct one is the last option: "A seri…
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find the distance between the points a and b given below. (that is, fin…
7.07
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find the distance between the points a and b given below. (that is, fin…
\(8.49\)
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the pentagons abcde and jklmn are similar. find the length x of \\(\\ov…
\( x = 4.8 \)
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the quadrilaterals abcd and jklm are similar. find the length x of \\(\…
\( 9.8 \)
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for each triangle, check all that apply. | triangle a | triangle b | tr…
- Triangle A: Isosceles, Equilateral - Triangle B: Isosceles - Triangle C: Scalene - Triangle D: Scalene (To mark on the table: Triangle A: Check Isosceles, Check Equilateral; Unc…
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for each triangle, check all that apply. triangle a: sides 6, 6, 10; op…
To solve this, we analyze each triangle based on side lengths (for scalene/isosceles/equilateral) and angles: ### Triangle A - Sides: \( 6, 6, 10 \). Two sides are equal. - **Clas…
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try again your answer is incorrect. for each triangle, check all that a…
(Checkboxes): - **Triangle A**: \(\boxed{\text{Scalene}}\) - **Triangle B**: \(\boxed{\text{Isosceles}}\), \(\boxed{\text{Equilateral}}\) - **Triangle C**: \(\boxed{\text{Scalene}…
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type the correct answer in the box. use numerals instead of words. if t…
2.5
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which graph shows a function and its inverse? a. graph a b. graph b c. …
C. (The graph in option C shows a function and its inverse, as the two lines are symmetric about \( y = x \).)
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select all the statements that describe the graph of the equation x = -…
B. The slope of the line is undefined. C. The graph passes through the ordered pair \((-2, 3)\). D. The \( x \)-intercept of the line is \((-2, 0)\).
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finding unknown angle measures which shows the angle addition postulate…
\( \boldsymbol{\angle PQS + \angle SQR = \angle PQR} \) (the first option: \( \angle PQS + \angle SQR = \angle PQR \))
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select the reason why these triangles are similar. if they are not, sel…
SSS
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the triangles below are similar. image of two triangles: yellow triangl…
\( y = 15 \)
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select the reason why these triangles are similar. if they are not, sel…
AA
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select the reason why these triangles are similar. if they are not, sel…
Not similar
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select the reason why these triangles are similar. if they are not, sel…
AA
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these two polygons are similar. 4 2 3 9 6 15 w w = ?
\( \boxed{9} \)
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what is the equation of this line? ○ $y = -\\frac{3}{2}x$ ○ $y = \\frac…
\(y=\frac{2}{3}x\) (the option is \(y = \frac{2}{3}x\), which is the fourth option: \(y=\frac{2}{3}x\))
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the triangles formed on the line are similar. using the slope of the li…
$\square \frac{a}{2} = \frac{1}{10}; a = \frac{1}{5}$ $\square \frac{a}{10} = \frac{1}{2}; a = 5$ $\square \frac{1}{a} = \frac{2}{10}; a = 5$ $\square \frac{a}{10} = \frac{1}{2}; …
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the triangles formed on the line are similar. which statements explain …
□ $-\frac{4}{2}=-\frac{1}{2}$ (Note: Assuming the first option has a typo, likely $\frac{2}{4}=\frac{1}{2}$ but with correct slope sign; the correct relation is that the ratio of …
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the triangles formed on the line are similar. which statements explain …
- $\boxed{-\frac{4}{2}=-\frac{1}{2}}$ (Note: Assuming the first option has a typo, likely $\boxed{-\frac{2}{4}=-\frac{1}{2}}$ and $\boxed{-\frac{4}{2}=-2}$ is incorrect; the corre…
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the triangles formed on the line are similar. using the slope of the li…
A. \( \frac{3}{2}=\frac{x}{4};x = 6 \) D. \( \frac{x}{3}=\frac{4}{2};x = 6 \)
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5. ok, lets see, suppose that m∠f = (4x - 9)°, m∠g = (3x + 5)°, and m∠h…
\((4x - 9)+(3x + 5)+x = 180\) ### Part (b)
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in the triangle, suppose that ( mangle f = (4x - 9)^circ ), ( mangle g …
\((4x - 9)+(3x + 5)+x = 180\) ### Part (b)
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in the triangle below, with right angle ∠i, suppose that m∠j = (4x + 1)…
\(m\angle I = 90^\circ\), \(m\angle J = 29^\circ\), \(m\angle K = 61^\circ\)
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incorrect your answer is incorrect. find x. (there is a diagram with an…
\(x = 60\)
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in the figure below, ( l parallel m ). find ( x ). (there is a figure s…
\(x = 55\)
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problem 8 ali and sid graphed this system $y = -\frac{1}{4}x - 1$ $y = …
The solution to the system of equations is \((4,-2)\)
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all and sid graphed this system: $y = -\\frac{1}{4}x - 1$ $y = \\frac{1…
They marked the \( y \)-intercepts instead of the intersection, point of the two lines. (The second option in the given choices)
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1. let abc be a triangle with ab = 18, bc = 24, and ca = 20. d is place…
\(\frac{559}{27}\) (or if we consider decimal, approximately \(20.70\), but as a fraction, \(\frac{559}{27}\))
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select the correct answer. a parallelogram rotates about its center. at…
C. \(180^\circ\)
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type the correct answer in the box. write your answer to one decimal pl…
2.7
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the oatmeal box shown is shaped like a cylinder. use a net to find the …
The surface area is about \( 326.6 \) square inches. The number of square feet of cardboard needed is about \( 3402 \).
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11. a sphere is inscribed in a cone of radius 5 and height 12. find the…
$\frac{10}{3}$
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7. if a circle of radius 3 and a circle of radius 4 intersect with cent…
4.8
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9 (\frac{3}{4}x - 3) which graph correctly represents the equation? (th…
The graph with a positive slope (rising from left to right) and y - intercept at \(y = - 3\) (the second graph among the given options, assuming the second graph has these propert…
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question 1-7 two points are shown. (-8, 13) and (-6, 3) which of the fo…
The correct option is the first one: \( \boldsymbol{m=\frac{13 - 3}{-8-(-6)}=\frac{10}{-2}=-5} \) (the first circle option, with the calculation \( m=\frac{13 - 3}{-8-(-6)}=\frac{…
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12 compare/contrast. notice the variety used in fig. 11.2, pg. 288. com…
To compare/contrast the variety in the two artworks: ### Step 1: Analyze Variety in Fig. 11.2 (Left) - **Elements of Variety**: Geometric shapes (circles, patterned “figures,” sol…
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2. a cube made of 1,331 small cubes gets a painted surface. find the nu…
729
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dara is building a plant stand. she wants to stain all sides of both pi…
1044
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an equation is shown. $y = -\\frac{2}{3}x + 7$ use the line tool to gra…
To graph \(y =-\frac{2}{3}x + 7\), plot the points \((0,7)\) (y - intercept) and another point (e.g., \((3,5)\) or \((6,3)\) or \((-3,9)\)) and draw a line through them. For examp…
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find the slope of the line passing through the points (-2, 3) and (-6, …
\(-\frac{5}{4}\)
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find the slope of the line passing through the points (-9, -3) and (7, …
\(-\frac{1}{4}\)
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find the sum point(a, b)on the line 2x-3y +6= 0 2x-3y + 6 = 0 that is c…
Final Answer: 61/13 Wait but let me confirm once more: yes, all steps are correct. So answer is 61/13. Yes. So the answer is 61/13.
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the design for the palladium window shown includes a semicircular shape…
\( 5843 \)
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a₁, a₂, a₃, … aₙ is a geometric sequence follow a₂ = \\(\\frac{4}{25}\\…
$\frac{4}{5}$
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the parabola has the equation $y^2 - 6y + 24x - 111 = 0$ find the dista…
\( 10 \)
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the design for the palladium window shown includes a semicircular shape…
7595
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sal is tiling his entryway. the floor plan is drawn on a unit grid. eac…
\(\$66.00\) (Note: The answer may vary depending on the accurate area calculation from the grid. If the area is different, the cost will change. For example, if the area is 42 squ…