Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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find the measure of ∠x in the figure. the measure of ∠x is □°.
52
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find the surface area of this sphere. use 3.14 for π. image of sphere w…
To find the surface area of the sphere, we use the formula \( SA = 4\pi r^2 \), where \( r = 2 \) cm and \( \pi \approx 3.14 \). Substitute the values into the formula: \( SA = 4 …
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find the surface area of this sphere. use 3.14 for π. 4 cm (diagram of …
\( 200.96 \)
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find the measure of ∠x in the figure.
\( 43^\circ \)
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read this excerpt from \the world on turtles back.\ the birds of the se…
B. felt compassion for the woman because she was scared
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find the surface area of this sphere. use 3.14 for π. 6 cm surface area…
To find the surface area of the sphere, we use the formula \( SA = 4\pi r^2 \), where \( r = 6 \) cm and \( \pi = 3.14 \). First, substitute the values into the formula: \( SA = 4…
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find the surface area of this sphere use 3.14 for π. 9 cm surface area …
To find the surface area of the sphere, we use the formula \( SA = 4\pi r^2 \), where \( r = 9 \) cm and \( \pi = 3.14 \). First, calculate \( r^2 \): \( 9^2 = 81 \) Then, substit…
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12. construct the bisector of ∠a.
The angle bisector of \( \angle A \) is constructed by drawing a ray from \( A \) that splits \( \angle A \) into two equal angles (using compass - and - straightedge construction…
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use figure t to answer questions 1-6. 1. name a pair of perpendicular l…
\( GC \) and \( AC \) (or \( GH \) and \( CD \), etc. - any pair with the right angle at \( C \)) ### Question 2
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which sentence from the world on turtles back best illustrates why the …
The woman placed the dirt on Turtle’s back and performed a ritual to create the earth
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construct a segment congruent to \\(\\overline{kl}\\) on \\(\\overright…
The constructed segment is $\overline{MP}$ (where $P$ is the intersection point from the arc drawn with compass centered at $M$ with radius equal to $KL$ length) congruent to $\ov…
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which is the correct measurement for the location marked by the arrow? …
A) 17.76
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use figure j to answer questions 7-7. name a line segment. 8. name an a…
$\overline{LO}$ (or $\overline{LM}$, $\overline{MN}$, $\overline{NO}$) ### Question 8
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type which row is incorrect all of the statements are correct. 3 of the…
Incorrect row: 6 Corrected reason: Definition of Supplementary Angles (or Linear Pair Theorem)
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what is an angle that is adjacent to ∠cfe?
# Explanation: ## Step1: Recall adjacent angle definition Adjacent angles share a common side and vertex, and their non - common sides form a linear pair (or are adjacent rays). F…
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draw △lmn with vertices l(2, −2), m(5, −3), and n(4,2). find the coordi…
The coordinates after a 90° counterclockwise rotation about the origin are \(L'(2, 2)\), \(M'(3, 5)\), and \(N'(-2, 4)\). (If clockwise, they would be \(L'(-2, -2)\), \(M'(-3, -5)…
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this question is calculator active. the sides (in yards) of a triangle …
\(x = 3\) (so the option with 3, e.g., if options are A. -1, B. 3/2, C. 0, D. 3, then D. 3)
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statements 1. ( k parallel ell ) 2. ( angle 3 ) and ( angle 4 ) are sup…
The three incorrect reasons are: 1. Reason 1 (Parallel Line Postulate) 2. Reason 6 (Definition of Complementary Angles) 3. Reason 7 (Addition Property)
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find the value of x. diagram: point t with three rays: ts (vertical up)…
\( x = 6 \)
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what is the surface area of the box formed by the pattern below? a. $1,…
C. \( 772\space m^{2} \)
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margo needs to wrap a gift for her sister. the gift is in the box shown…
B. \( 2(18 \times 18) + 4(18 \times 36) \)
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17. what is the name of this figure?
Line (or Line BC, Line CB)
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margo needs to wrap a gift for her sister. the gift is in the box shown…
B. \(2(18\times 18)+4(18\times 36)\)
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use figure x to answer questions 1-6. 1. name an obtuse angle. 2. name …
∠IBA (or other valid obtuse angle from the figure, e.g., ∠ABI) ### Question 2: Name an acute angle.
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s is the midpoint of \\(\\overline{rt}\\). if \\(st = x + 4\\) and \\(r…
\( 10 \)
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for exercises 24–27, find the measure of each angle. see example 4 24. …
### 24. $\angle 1$ # Explanation: ## Step1: Recall triangle angle sum Triangle sum is $180^\circ$. In the triangle with angles $37^\circ$, $116^\circ$, and $\angle 1$? Wait, no, l…
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what is mariana’s invention supposed to do? wash and dry students’ bicy…
The blue - circled option: remove rust from bicycles
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what is the value of c?
\( 40.7^\circ \)
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13. which polynomial represents the area of a rectangle with sides $3x$…
a. \( 3x^3 + 6x^2 + 3x \)
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9.1 ... figure abc. draw the resulting figure after each transformation…
### Part (a): Translation of Figure \( ABC \) #### Step 1: Identify Coordinates of Vertices First, determine the coordinates of points \( A \), \( B \), and \( C \) from the grid.…
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after bisecting an angle, edwin has two new angles, each with a measure…
\( 180.8^\circ \)
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statements 1. ( k parallel ell ) 2. ( angle 3 ) and ( angle 4 ) are sup…
The three incorrect reasons are: - Reason 6: "Definition of Complementary Angles" (should be "Definition of Supplementary Angles"). - Reason 7: "Addition Property" (should be "Sub…
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5½ in 6 in. number sentence: 6 × 5½ = 8 area: 8
The correct number sentence is \( 6\times5\frac{1}{2}=33 \) and the area is \( 33 \) square inches.
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13 reflections preserve congruence. a true b false c sometimes 14 which…
A. True ### Question 14
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construct the bisector of ∠a.
The angle bisector of \( \angle A \) is constructed by drawing a ray from \( A \) through the intersection point of the two arcs (as per the steps above), dividing \( \angle A \) …
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6 cm 4\\(\\frac{1}{4}\\) cm number sentence: ________ area: ________
The area of the rectangle is \(\boldsymbol{25\frac{1}{2}}\) square centimeters (or \(\boldsymbol{\frac{51}{2}}\) \(cm^2\) or \(\boldsymbol{25.5}\) \(cm^2\)). The correct number se…
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11 pentagon abcde is rotated 180⁰ clockwise about the origin to form pe…
A. Pentagon \( ABCDE \) is congruent to pentagon \( A'B'C'D'E' \). ### Question 12
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which construction uses the compass for only one step in addition to dr…
a regular hexagon inscribed in a circle
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10 find the coordinates of the image of j (8, 7) after a reflection ove…
A. \((8, - 7)\)
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a square on a coordinate plane is translated 9 units down and 1 unit to…
$T_{1,-9}(x,y)$
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what is an angle that is adjacent to ∠dea?
$\angle DEB$ (or $\angle AEC$)
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7 in. 2½ in. number sentence: 7×2½=5½ area: 5½
The correct number sentence is \(7\times2\frac{1}{2}=17\frac{1}{2}\) and the area is \(17\frac{1}{2}\) square inches.
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9 find the coordinate of the image of b (4, 0) after a reflection over …
\((-4,0)\)
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the measure of an angle is 78.8°. what is the measure of its complement…
\(11.2\)
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(a) part a what is the coordinate rule for this? (over the y-axis:) a (…
B. \((x, y) \to (-x, y)\) ### Part B
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a regular decagon has 10 sides. how many reflectional symmetries does a…
10
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how can you explain to a classmate how a rotation keeps size and shape …
A rotation preserves size and shape because: 1. **Size**: Distances between points (side lengths) remain unchanged as rotation is a rigid transformation (uses circular arcs with c…
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what are the coordinates of the image of vertex r after a reflection ac…
(3, 4)
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what is the area of the shaded region? 67.6 in 39.7 in 39.7 in 67.6 in …
2993.67 square inches
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which composition of transformations maps figure rstuv to figure rstuv?…
A reflection across line \( n \) followed by a translation down and to the right.
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7\\(\\frac{1}{8}\\) m, 4 m. number sentence: \\(\\boldsymbol{7\\frac{1}…
Number Sentence: \( 7\frac{1}{8}\times4 = 28\frac{1}{2} \) Area: \( 28\frac{1}{2} \) square meters (or \( \frac{57}{2} \) square meters)
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the perimeter of a right triangle is 52 in. one leg of the triangle is …
120 m
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4 a circle is graphed on the coordinate plane with its center at (-4, 7…
B. \((x, y) \to (-4 + p, 7 - v)\) ### Question 5
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7. look at this angle: name this angle in three different ways: uv+ and…
\( \angle UVT \), \( \angle TVU \), \( \angle V \)
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3 rectangle mnpq is translated 4 units left and 3 units up. drag the co…
\((x,y)\to(x - 4,y + 3)\)
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2 choos the rule that represents a reflection across the y-axis. $(x, y…
C. \((-x, y)\)
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6. classify the angle. image of an angle with two blue arrows as rays a…
acute
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what is the value of r? 26.4° 76.3°
\(49.9^{\circ}\)
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1 which rule describes the transformation applied to quadrilateral tuvw…
C. \((x,y)\to(x + 6,y - 2)\)
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5. what is the value of p? diagram with angle markings (e.g., 70.3° and…
\(50^\circ\)
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what are the values of the variables in each figure? see examples 1–3 1…
\(x = 63\) ### Problem 17:
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15. use the figure on the right to find the following. a) find the area…
The area of the larger rectangle is \( 15x^2 - 35x \) square units. ### Part (b)
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i can solve equations, inequalities, set up equations for word problems…
All real numbers ### Problem 20: \( 7x-8>6x - 11 \)
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draw a line representing the ise\ and a line representing the un\ of th…
To determine the slope of the line, we first identify two points on the line. From the graph, we can see that the line passes through the origin \((0, 0)\) and another point, say …
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12. what rotation(s) about the origin would rotate the point (-7, 7) to…
The rotation is 180 degrees about the origin (assuming the rotated point is \((7, -7)\) due to a possible typo; if the rotated point is indeed \((-1, -7)\), there may be an error …
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3. scale factor = ____ (image shows two rectangles: top labeled \origin…
\( \frac{1}{4} \)
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2. what is the name of this figure?
Line segment \( AB \) (or segment \( AB \))
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unit 1:essentials of ge test 2 estimate the measure of this angle withi…
\(120^\circ\) (or a value between \(110^\circ\) and \(130^\circ\) is acceptable as per the \(10^\circ\) tolerance)
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4. scale factor = ____ (original hexagon with side 30 in, smaller hexag…
\(\frac{1}{5}\) (or \(0.2\))
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1 cm 4 cm 6 cm 6 cm 1 cm find the surface area of the prism using the n…
48
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find these (or similar) items in your house: a cereal bowl a drinking g…
a cereal bowl ### 2.
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4. scale factor = ____ two regular hexagons: left hexagon with side len…
$\frac{1}{5}$ (or 0.2)
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21) solve for x. circle your answer. diagram: three angles around a poi…
\( x = 105 \)
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(\boldsymbol{1}\).
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for exercise 11-13, answer the questions. 11. error analysis a classmat…
The classmate is incorrect. The rule for rotating a point \((x, y)\) \(180^{\circ}\) about the origin is \((x, y)\to(-x, -y)\), not \((-x, y)\). This is because a \(180^{\circ}\) …
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how many triangles are contained in the figure? diagram of a cat - shap…
11
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20) solve for x. circle your answer. (2x + 7)° 131° (diagram of a strai…
\(x = 21\)
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5. scale factor = ____ original 2 in 5 in
\( 2.5 \) (or \( \frac{5}{2} \))
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find the surface area of the prism using the net. what is the area of t…
48
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5. scale factor = ______ 2 in original 5 in
\( \frac{5}{2} \) (or \( 2.5 \))
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19) solve for x. circle your answer.
\(x = 15\)
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what is the area of the shaded region? 84.5 mm 46.4 mm 52.5 mm 95.7 mm …
2825.33
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3. scale factor = ______ 200 ft original 800 ft 50 ft 200 ft
$\frac{1}{4}$
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2. scale factor = ____ small triangle (original) with sides 3, 4, 5; la…
2
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(x, y) → (y, -x) (x, y) → (-x, -y) for exercises 9 and 10, use the grap…
(Problem 9 Coordinates): \( D'(1, 2) \), \( E'(3, 0) \), \( F'(5, -2) \), \( G'(-2, -3) \) (or adjusted per graph)
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use the triangle area formula ( a = \frac{1}{2}bh ) to fill in the char…
a) Base Column: \( b = \frac{2A}{h} \), Height Column: \( h = \frac{2A}{b} \) b) | \( A \) (cm²) | \( b \) (cm) | \( h \) (cm) | |--------------|-------------|-------------| | 25 …
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graph the compound inequality on the number line. ( x geq 4 ) or ( x < …
- For \( x \geq 4 \): Closed dot at \( 4 \), arrow right. - For \( x < -8 \): Open dot at \( -8 \), arrow left. (Graphically, on the given number line, place a closed circle at \(…
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calculate the measure of ∠b. circle your answer.
\(282^\circ\)
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calculate the measure of ∠b. circle your answer.
\( 282^\circ \)
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graph the compound inequality on the number line. ( x < 4 ) or ( x > 8 )
To graph \( x < 4 \) or \( x > 8 \) on the number line: 1. For \( x < 4 \): Place an open circle at \( 4 \) and draw a line with an arrow pointing to the left (covering all number…
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15) calculate the measure of ∠b. circle your answer.
$67^{\circ}$
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what is the area of the shaded region? 62.4 mi 62.4 mi 35.5 mi 35.5 mi …
2633.51
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graph the compound inequality on the number line. ( x > -4 ) and ( x le…
To graph \( x > -4 \) and \( x \leq 1 \): - At \( x = -4 \), draw an **open circle** (since \( x > -4 \), \( -4 \) is not included) and draw a line to the right from \( -4 \) (but…
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17) calculate the measure of ∠b. circle your answer.
\(67^{\circ}\)
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2) reflection across y-axis
To reflect the figure across the \( y \) - axis, we use the reflection rule \((x,y)\to(-x,y)\). For the given points (assuming \( U(-3,4) \), \( L(-3,1) \), \( X(0,4) \)): - \( U …
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11. scale factor = 1/7 35 ft 287 ft original
The scaled width is 5 ft and the scaled height is 41 ft.
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both circles have the same center. what is the area of the shaded regio…
7514.69
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calculate the measure of ∠b. circle your answer.
224°
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briyana wants to make a pyramid out of plaster for her social studies c…
176
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what is the area of the shaded region? 71 ft, 48 ft, 50 ft, 74 ft. writ…
1427 square feet