Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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7. jeffrey is looking at a map of his town to help him get from his sch…
2.25 miles
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5. if 1 inch is equal to 150 miles, what is the scale factor? options: …
$\frac{1}{150}$ (the second option, i.e., the option with $\frac{1}{150}$)
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in which figure is ∠1 congruent to ∠2? (four figures with lines and ang…
The top-left figure (where ∠1 and ∠2 are vertical angles) is the one where ∠1 is congruent to ∠2.
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17. in each figure, for what values of x and y is the figure a parallel…
a. $x = -\frac{1}{2}$, $y = 5$ b. $x = 17$, $y = 26$
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16. is each quadrilateral a parallelogram? explain. see examples 1 and …
a. Yes, this quadrilateral is a parallelogram. Its opposite sides are congruent, which meets the criteria for a parallelogram. b. No, this quadrilateral is not a parallelogram. It…
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11. error analysis ahmed uses the following explanation to prove that a…
Ahmed's error is that he applied the theorem to different pairs of opposite sides: the congruent sides and parallel sides are not the same pair. The theorem requires that a single…
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imagine that you are the principal of a school and you just found out t…
Different versions occur due to: 1) Unique perspectives (varying viewpoints/angles), 2) Selective attention/memory (focusing on different details), 3) Subjective interpretation of…
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practice & problem solving understand 10. use appropriate tools if you …
To determine if the quadrilateral is a parallelogram, verify one of its defining properties: 1. Check if **both pairs of opposite sides are equal in length** (use a ruler to measu…
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write the equation of the line in fully simplified slope-intercept form…
$y = -\frac{1}{2}x - 1$
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use the diagram for exercises 8 and 9. 8. if \\(\\overline{ab} \\parall…
8. Yes, $ABCD$ is a parallelogram. One pair of sides ($\overline{AB}$ and $\overline{DC}$) are both parallel and congruent, which satisfies a sufficient condition for a quadrilate…
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what must each length be in order for quadrilateral jklm to be a parall…
6. $JK = 10$ 7. $JL = 14$
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3. you are helping to create a map of a town. a. use the coordinate pla…
Plotted points (on the coordinate grid): - Town Hall: $(0,0)$ - Fire Station: $(5,0)$ - Police Station: $(5,6)$ - School: $(-3,6)$ - Ice Cream Shop: $(-5,-2)$ - Museum: $(2,3)$ (e…
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do you know how? what must each angle measure be in order for quadrilat…
4. $m\angle D = 65^\circ$ 5. $m\angle E = 115^\circ$
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name use the arrays to help you fill in the blanks. 1. 2 × 8 2 groups o…
1. 2 groups of $\boldsymbol{2 \times 4}$; $2 \times (\boldsymbol{2 \times 4})$ 2. 4 groups of $\boldsymbol{2 \times 3}$; $4 \times (\boldsymbol{2 \times 3})$ 3. 4 groups of $\bold…
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2. draw a rectangle in the coordinate plane that satisfies each of the …
One valid set of vertices is $(-5, 3)$, $(-1, 3)$, $(-1, -3)$, $(-5, -3)$ (other valid sets exist, e.g., using positive x-values like $(2,4)$, $(8,4)$, $(8,-4)$, $(2,-4)$ also mee…
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the point of concurrency of the perpendicular bisectors of a triangle i…
circumcenter ### Second Blank:
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problem solving with the coordinate plane the figure factory 1. draw a …
One valid set of vertices is: - Quadrant 1: $(6, 5)$ - Quadrant 2: $(-3, 5)$ - Quadrant 3: $(-3, -5)$ - Quadrant 4: $(6, -5)$ (When plotted, these form a rectangle meeting all cri…
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determine if the properties define a ray or a line segment. cannot be m…
To solve this, we recall the definitions of a ray and a line segment: ### Ray: - A ray **cannot be measured** (it extends infinitely in one direction). - A ray **continues forever…
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find x, jk, and jm.
\( x = 12 \), \( JK = 17 \), \( JM = 17 \)
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graph the points (-8, 3) and (-6, 5) on the coordinate plane. click to …
The point $(-8, 3)$ is plotted at the intersection of the vertical line $x=-8$ and horizontal line $y=3$. The point $(-6, 8)$ is plotted at the intersection of the vertical line $…
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what are the coordinates of point l?
$(6, 2)$
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the two lines are parallel and the system has no solution. the two line…
The two lines are parallel and the system has no solution.
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triangle stu, shown in the coordinate plane below, is translated up 4 u…
(1,1)
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a triangle has these properties: - three sides of different lengths - t…
scalene, obtuse
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01/07 - rotations & dilation practice l possible points: 5.05 the pre -…
1. Image: \(\boldsymbol{(6, -2)}\), Scale Factor: \(\boldsymbol{2}\) 2. Image: \(\boldsymbol{(2, 0)}\), Rule: \((x, y)\to(\boldsymbol{\frac{1}{3}}x, \boldsymbol{\frac{1}{3}}y)\) 3…
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01/07 - rotations & dilation practice l rectangle abcd is similar to re…
2.5
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is $\\triangle pmr$ similar to $\\triangle smn$? if so, which postulate…
\( \triangle PMR \) is similar to \( \triangle SMN \) by the SAS Similarity Theorem. (Corresponding option: the one with SAS Similarity Theorem)
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rotations & dilation practice l directions—for each set of points below…
Rule \((x, y)\): \((-x, -y)\) \(A'(-2, -5)\) \(B'(-6, -7)\) \(C'(-9, -5)\) \(D'(-6, -2)\)
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find tan j and tan k. write each answer as a fraction and as a decimal …
\( \tan J=\frac{8}{15}\approx0.5333 \) \( \tan K=\frac{15}{8} = 1.875 \)
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90° counterclockwise rotation rule (x, y): (□, □) d (□, □) e (□, □) f (…
Rule \((x, y)\): \((-y, x)\) \(D'(-2, 5)\) \(E'(-4, 2)\) \(F'(-1, 0)\) \(G'(1, 3)\)
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90° clockwise rotation rule (x, y): (□, □) s(□, □) t(□, □) u(□, □) v(□,…
Rule: \((x, y) \to (y, -x)\) \(S'(3, -2)\) \(T'(0, 1)\) \(U'(-1, -4)\) \(V'(2, -5)\)
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find the tangents of the acute angles in the right triangle. write each…
\( \tan R = \frac{45}{28} \approx 1.6071 \) \( \tan S = \frac{28}{45} \approx 0.6222 \)
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180° rotation rule (x, y): ( p( q( r( s(
Rule \((x, y)\): \((-x, -y)\) \(P'(2, -4)\) \(Q'(-3, -4)\) \(R'(-1, -2)\) \(S'(4, -2)\)
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details no additional details were added for this assignment. which tri…
$\triangle ABC$ is similar to $\triangle GHI$ by AA Similarity Postulate.
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90° counterclockwise rotation rule (x, y): (□, □) c (□, □) d (□, □) e (…
- Rule (x, y): \((-y, x)\) - \(C(-2, 0)\) - \(D'(5, 0)\) - \(E'(0, 2)\) - \(F'(3, 0)\)
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calculator what is the value of x? enter your answer in the box. □ unit…
27
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90° clockwise rotation rule (x, y): (□, □) e(□, □) f(□, □) g(□, □) h(□,…
Rule \((x, y)\): \((y, -x)\) \( E'(1, 4) \) \( F'(1, 0) \) \( G'(-1, -1) \) \( H'(-1, 5) \)
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180⁰ rotation rule (x, y): (□, □) t (□, □) u (□, □) v (□, □) w (□, □)
Rule \((x,y)\to\boldsymbol{(-x,-y)}\) \(T\): \(\boldsymbol{(-1,4)}\) \(U\): \(\boldsymbol{(-4,4)}\) \(V\): \(\boldsymbol{(-4,1)}\) \(W\): \(\boldsymbol{(-1,1)}\)
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use the graph of the circle to answer the question. what is the equatio…
\(h = 2\) \(k = 4\) \(r = 4\)
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find sin d, sin e, cos d, and cos e. write each answer as a fraction in…
\(\sin D=\frac{35}{37}\approx0.9459\) \(\sin E=\frac{12}{37}\approx0.3243\) \(\cos D=\frac{12}{37}\approx0.3243\) \(\cos E=\frac{35}{37}\approx0.9459\)
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(\frac{1}{2}\).
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state the coordinates of each point. 3) a (-10, 2) f ( , ) b ( , ) g ( …
B (5, 10) C (-8, -4) D (-8, -9) E (1, -5) F (2, -4) G (-7, 7) H (2, 5) I (7, -1) J (-7, -6)
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11. what is the slope of a line perpendicular to $y = \\frac{3}{4}x + 5…
(Question 12): A. \(-\frac{1}{4}\)
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more practice with circumcenter & incenter directions: if w is the circ…
1. $RS=42$ 2. $TQ=21.5$ 3. $WS=19$ 4. $QV=43$ 5. $TW=2.5$ 6. $WV=19$ 7. $BC=54$ 8. $AP=19$ 9. $DP=36$ 10. $FC=14$
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△ dns ~△ arh. what is the value of x? enter your answer in the box. □ u…
68
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which is the equation of the line that passes through (6,2) and is perp…
C. \( y - 2 = 3(x - 6) \)
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3. m is the circumcenter of δghi. a) gi b) mh c) ik d) hi e) mg © gina …
a) $GI = 60$ b) $MH = 23$ c) $IK = 23$ d) $HI = 46$ e) $MG = 23$
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part 2: observation deck 1 square = 1 yard question 5 5 pts convert all…
3 yards = 9 feet 15 yards = 45 feet 18 yards = 54 feet $P = 216$ feet $A = 891$ square feet
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write an equation for the parabola that has the given vertex and passes…
For the first box (the coefficient of the square term's denominator) is \(3\), the second box (inside the \(x+\square\)) is \(-4\), and the third box (the constant term) is \(-3\)…
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let \\( \\mathbf{u} = \\langle 5, -12 \ angle \\) and \\( c = -3 \\). w…
39
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the magnitude and direction of two vectors are shown in the diagram. wh…
\(2\sqrt{5}\)
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robert made a design on his wall with the similar pentagon tiles shown.…
D. 6 cm
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score on last try: 0 of 1 pt. see details for more. you can retry this …
10
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what type of angle or shot looks through the photographers eyes? (think…
B. Point of view
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the boy and the whale by mordicai gerstein 1 every day, i loved to watc…
It shows how important the net is to Papa. ### Question 2 (Note: The second option text is cut off, but assuming a typical reading comprehension context, if we consider the visibl…
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first thing needed is to convert our measures into feet. 20 yards = 60 …
Perimeter = 252 feet Cost = $3906
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(\frac{2}{3}\)
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1. what is the area of the triangle? ______ (with a right triangle imag…
1. 14 square inches 2. $x=5$ 3. c. $\text{A}=\frac{1}{2}bh$ 4. True 5. b. $\text{C}=\pi d$ 6. $3.14$ (o $3.1416$) 7. $7$ 8. b. equilateral 9. c. scalene 10. a. isosceles BONUS: $x…
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if a circular railroad crossing sign has an area of 254.34 in.², what i…
18
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problem 10: spiral review figure abcd is the image of figure abcd after…
9
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4. which equation represents line t, shown in the accompanying diagram?…
B. $y = \frac{1}{2}x + 3$
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6.2 assignment possible points: 0.67 find the value of x. (figure with …
30
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6.2 assignment possible points: 0.67 find the value of x. (there is a d…
30
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these two lines are parallel. write an equation for each line. line a l…
Line a: \(y = \frac{4}{5}x\) (or \(y = 0.8x\)) Line b: \(y = \frac{4}{5}x - 3.2\) (or \(y=\frac{4}{5}x-\frac{16}{5}\))
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solve for x. round to the nearest tenth of a degree, if necessary. tria…
$53.1^\circ$
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look at this diagram; if (overleftrightarrow{qs}) and (overleftrightarr…
\(44\)
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vertical lines what is the equation of the line that passes through the…
undefined ### Sub - Question 2: Does a vertical line have a y - intercept?
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solve for x. round to the nearest tenth, if necessary. triangle image w…
$1.2$
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horizontal lines what is the equation of the line that passes through t…
s: 1. The slope \( m=\boldsymbol{0} \) 2. The y - intercept \( b=\boldsymbol{-4} \) 3. The equation of the line is \( \boldsymbol{y=-4} \)
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solve for ( x ). round to the nearest tenth, if necessary. right triang…
$x = 95.8$
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question 7 points 4 show that circle $c_1$ with center $(0, 2)$ of radi…
Translation rule: \((x, y) \to (x, y - 7)\); Scale factor: \(\frac{1}{4}\)
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find tan j and tan k. write each answer as a fraction in simplest form …
- \( \tan J=\frac{3}{4}=0.75 \) - \( \tan K=\frac{4}{3}\approx1.3333 \)
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find tan j and tan k. write each answer as a fraction in simplest form …
For \( \tan J \): - As a fraction: \( \frac{3}{4} \) - As a decimal: \( 0.75 \) For \( \tan K \): - As a fraction: \( \frac{4}{3} \) - As a decimal: \( \approx 1.3333 \)
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question 6 find the translation rule and the scale factor of the dilati…
Translation rule: \( (x, y) \to (x - 8, y - 5) \), Scale factor: \( \frac{1}{2} \) (Note: Depending on radius calculation, but the key steps are finding the center translation and…
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translation: (x, y) → (x + 10, y + 3) and scale factor (reduction ratio…
The correct option is: "Translation: \( (x, y) \to (x + 10, y + 3) \) and Scale factor (enlargement ratio): 2" (the second option in the list).
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solve for ( x ). round to the nearest tenth, if necessary. right triang…
$11.5$
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question 4 points 3 circle a: center (7, 0) and radius 5 circle b: cent…
Translation: 3 units left and scale factor: \(\frac{5}{2}\) (corresponding to the third option: "Translation: 3 units left and scale factor: \(\frac{5}{2}\)")
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95. where is the statue of liberty? a. boston harbor b. new york harbor…
95. b. New York Harbor 96. a. Because there were 13 original colonies 97. c. Because there are 50 states 98. c. The Star-Spangled Banner 99. b. July 4 100. b. Labor Day and Christ…
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error analysis describe the error in the statement of the tangent ratio…
The error is that the tangent ratio for \( \angle D \) was calculated using the hypotenuse (37) instead of the adjacent side (12) to \( \angle D \). The correct tangent ratio is \…
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translation: (x, y) → (x + 10, y + 6) and scale factor (enlargement rat…
Translation: \((x, y) \to (x + 10, y + 6)\) and Scale factor (enlargement ratio): 4 (the first option)
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which of the following best describes the translation rule and the scal…
The correct option is: Translation: 10 units to the left and 6 units down; Scale factor (reduction ratio): \( \frac{1}{4} \) (assuming this is one of the options, likely the third…
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if the image is larger than the original figure, then the dilation is a…
C. enlargement
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find sin d, sin e, cos d, and cos e. write each answer as a fraction in…
- \(\sin D=\frac{28}{53}\approx0.5283\) - \(\sin E=\frac{45}{53}\approx0.8491\) - \(\cos D=\frac{45}{53}\approx0.8491\) - \(\cos E=\frac{28}{53}\approx0.5283\)
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solve for x. round to the nearest tenth, if necessary. triangle image w…
21.9
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the equation $y = \\frac{4}{3}x$ represents a proportional relationship…
line
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solve for ( x ). round to the nearest tenth, if necessary. triangle ima…
$82.3$
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what is the surface area? image of a rectangular prism with length 5 m,…
280 square meters
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jordan is flying a kite, holding his hands a distance of 2.5 feet above…
45.20 feet (rounded to the nearest hundredth)
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coordinate into the equation for x and the y-coordinate into the equati…
\( m = 2 \) ### 2. Find the y - intercept of the line.
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12.) use multiple methods, factor the polynomial completely $27x^{2}z +…
\( 3z(3x + 2)^2 \) ### Problem 13: Factor \( 5x^5 - 80x \) completely
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solve for x. round to the nearest tenth, if necessary. triangle tuv wit…
$83.6$
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solve for x. round to the nearest tenth, if necessary. triangle image w…
$2.1$
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solve for x. round to the nearest tenth, if necessary. triangle lmn wit…
$8.6$
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solve for x. round to the nearest tenth, if necessary. triangle lmn wit…
$1.9$
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locate and name the point at the 11. (3, 15) 12. (20, 13) plot each poi…
s: 11. (3, 15) is point C. 12. (20, 13) is point K (approx, considering the grid). 15. Point N (6, 19) cannot be plotted on the given grid as y = 19 exceeds the y - axis limit (up…
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review of writing equations of lines given the slope a what is the equa…
$\frac{5}{3}$ ### 2. What is the y - intercept of the line?
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solve for x. round to the nearest tenth, if necessary. triangle mlk wit…
$9.5$
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solve for x. round to the nearest tenth, if necessary. triangle image w…
$9.9$
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solve for $x$. round to the nearest tenth, if necessary. image of a rig…
$83.0$
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which segment is the hypotenuse? (image of a right triangle with right …
$\overline{BT}$