Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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question 10 (5 points) listen kaylee found the surface area, in square …
158
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14. if m∠1 = 11x + 5 and m∠2 = 8x − 15, find m∠2. options: 75, 115, 10,…
65
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5. a rectangle has length 8 × 10⁴ millimeters and width 6 × 10⁴ millime…
$\frac{4}{3}$ (or approximately $1.33$)
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coach hernández made a scale drawing of the school gym. the scale of th…
10
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13. \\(\\overline{sq}\\) is an angle bisector. \\(m \\angle qst = 2x\\)…
40
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12. if m ∠rst = 70, m ∠qst = 2x, and m ∠qsr = 3x − 10, what is the m ∠q…
38
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7. points j, k, and l are collinear. point k lies between j and l. find…
12
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11. which property justifies the following statement? if ∠a ≅ ∠b and ∠b…
B. Transitive Property of Congruence
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find the value of x so that the area of the rectangle is equal to the a…
\( 6 \)
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5. points x, y, and z are collinear. point y bisects xz. find xz if xy …
\( \boxed{-40} \) (Note: The negative sign might indicate a direction or a mistake in the problem setup, but mathematically, this is the result.)
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a) the actual lengths of the garden are shown in the table. choose an e…
1 in. to 4 ft
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1. points a, b, and c are collinear. point b is between c and a. find b…
\( 5 \)
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congruence transformations find the composition of transformations that…
The translation is \((x + 3,y+0)\), so the values are 3 and 0.
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find the value of x so that the area of the rectangle is equal to the a…
\( 8 \)
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find cd b •———•———• d 2 2x - 6 c blue arrow labeled x + 2 cd= box 16
\( 6 \)
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which model represents the ratio of 4 triangles to 8 circles?
The right - hand model (the second column of figures) represents the ratio of 4 triangles to 8 circles.
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applying the law of cosines to surveying dan is standing 25 feet from a…
\(41\) (or approximately \(41\) degrees, if we round \(41.41\) to the nearest degree)
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if ( mangle lmn = 164^circ ), ( mangle fmn = (18x - 6)^circ ), and ( ma…
\( 98^\circ \)
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which model represents the ratio of 9 triangles to 2 squares?
The model with 9 orange triangles and 2 blue squares (the right - hand model in the image)
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which model represents the ratio of 7 circles to 5 triangles?
The right - hand model (the one with 7 blue circles and 5 green triangles)
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the actual lengths of the garden are shown in the table. choose an equi…
The equivalent ratio is \( 1:4 \) (or for the first row, \( 6:24 = 1:4 \), \( 8:32 = 1:4 \), \( 10:40 = 1:4 \)). The simplified equivalent ratio is \( \boldsymbol{1:4} \) (scale d…
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if m∠efv = 50°, m∠vfg = (63x − 1)°, and m∠efg = (88x − 1)°, find m∠vfg.
\(125^\circ\)
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use a scale to solve problems. (image shows a rectangle with ( l = 4 ) …
If for length: 12 ft, width: 6 ft; if for area: 72 square feet (depending on the actual problem, but since the problem says "use a scale to solve problems" and gives length, width…
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if m∠tuv = 176° and m∠tul = 21°, find m∠luv.
\( 155^\circ \)
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points r, s, and t are collinear, point s lies between r and t. find rt…
\( 8 \)
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6. points l, m, and n are collinear. point m bisects ln. find ln if lm …
160
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to make cream ice pops, nina uses conical molds that each have a height…
B. \( 20\pi \) cubic centimeters
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select the correct answer. which equation represents circle n? image: c…
C. \((x + 7)^2 + (y - 6)^2 = 50\)
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what is the missing length in the scaled copy? units 45 90 original ? 3…
15
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4. solve for x. h •———4———•g———x-3———•f ←———-9 + 2x———→ x=□
\( x = 10 \)
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what is the missing length in the scaled copy? units original rectangle…
80
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type the correct answer in the box. use numerals instead of words. if n…
The length of the longest side is \(\boldsymbol{5}\) inches. The other two sides will each be \(\boldsymbol{4}\) inches in length.
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2. points j, k and l are collinear. point k bisects jl. find jl if jk =…
\( 24 \)
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select the correct answer from each drop-down menu. how can the surface…
38.5
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checkup for questions 1 and 2, state whether each statement is true or …
False. Because real numbers consist of both rational and irrational numbers, not all real numbers are irrational (e.g., integers like 3 are rational and real). ### Question 2:
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7. points j, k, and l are collinear. point k lies between j and l. find…
\( 6 \)
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the scale factor is the number you multiply each length in the original…
10
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select the correct answer from each drop-down menu. how can the surface…
The surface area of the onion can best be modeled by a sphere. Based on the model, the approximate surface area of the onion is approximately 39.6 (or similar value depending on r…
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5. points x, y, and z are collinear. point y bisects xz. find xz if xy …
\( 56 \)
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original scaled copy 5 ? 3 6 4 8 what number can you multiply each orig…
2
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select the correct answer. circle o has radius of 24 units. arc xy loca…
B. \( 120\pi \)
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select the correct answer. what is the value of x in the triangle? imag…
B. 3
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find the missing side length, in units, in the scaled copy. | original …
30
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1. points a, b, and c are collinear. point b is between c and a. find b…
8
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4. is there a mathematical relationship between a scale factor from fig…
Yes, there is a mathematical relationship. The scale factor from figure A to figure B and the reverse scale factor from figure B to figure A are reciprocals (their product is 1). …
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shapes (cylinder: 5,027 ft²; cone; prism: 38,455 ft²; pyramid: 29,027 f…
\(130336\)
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16. w(-12, -7), t(-8, -4)
The distance between \( W(-12,-7) \) and \( T(-8,-4) \) is \( 5 \).
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what is true about the angles in the original figure and the scaled cop…
equal (or the same)
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1. if m∠2 = 7x + 7, m∠3 = 4y, and m∠4 = 112, find the values of x and y…
x = 15, y = 17 (Option: x=15, y=17)
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2. draw the image of quadrilateral abcd when translated by the directed…
To solve, translate each vertex of \( ABCD \) by the vector \( v \) (e.g., if \( v \) is 3 units right, shift \( A, B, C, D \) 3 units right to get \( A', B', C', D' \), then conn…
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which figure has the same shape as figure a? figure c 1 × 2 = 2 4 × 2 =…
Figure C has the same shape as Figure A (since their length - to - height ratios are equal, indicating similar rectangles).
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10. find ( mangle abc ). diagram: points ( d ), ( b ), ( c ) on a strai…
\( 130^\circ \) (corresponding to the option "130°")
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lesson 10 practice problems 1. here are 4 triangles that have each been…
D
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9. find the value of x. diagram: horizontal line, vertical line (right …
20
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8. the graph of line a is shown. use the similar slope triangles to com…
The slopes of segments \(GI\) and \(IK\) are equal. ### Problem 9:
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of semester test: florida geometry, semester b an image of a castle is …
The shapes are a cylinder (tower) and a rectangular prism (building). The approximate surface area is \( \boldsymbol{31,427 \, \text{ft}^2} \).
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6. ∠1 and ∠2 are supplementary and ∠1 ≅ ∠2. which one of these statemen…
\(\angle1\) and \(\angle2\) are right angles
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applying the law of cosines with sas which equation correctly uses the …
\(s^{2}=9^{2}+10^{2}-2(9)(10)\cos(100^{\circ})\) (the third equation)
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1. grid with figure a and b 2. grid with figure a and b 3. grid with fi…
The scale factor from \( A \) to \( B \) and from \( B \) to \( A \) are reciprocals (multiplicative inverses). To find this, pick a side length from \( A \) and \( B \) (using gr…
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5. find m∠abc? diagram: straight line boc with point a forming angles (…
\(48^\circ\)
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1. is there a mathematical relationship between a scale factor from fig…
The scale factor from figure A to figure B and the scale factor from figure B to figure A are reciprocals (their product is 1). To find this, pick a measurement (like side length)…
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find the composition of transformations that map abcd to ehgf. reflect …
# Explanation: ## Step1: Analyze reflection over x - axis Let's take a point from ABCD, say point A. From the graph, the coordinates of A seem to be \((-5, 2)\). When we reflect a…
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6. find the value of x. (4x - 101)° (2x + 3)° options: 46, 31, 107, 52
52
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select the correct answer from each drop-down menu. a composite figure …
The surface area of the pyramid is \(\boldsymbol{60}\) square feet. The surface area of the square prism is \(\boldsymbol{480}\) square feet. The surface area of the cube is \(\bo…
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reverse it! figure b is a scaled copy of figure a. for each set of figu…
The scale factor from \( A \) to \( B \) and from \( B \) to \( A \) are reciprocals (their product is 1). For example, if \( A \) to \( B \) is \( \frac{1}{3} \), \( B \) to \( A…
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what is the value of x in the figure below? (figure shows two parallel …
\(55\)
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diagram with intersecting lines at point b, angles (3x + 8)° and (5x - …
\(80^\circ\) (corresponding to the option with \(80^\circ\))
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what is the value of x in the figure below?
\(x = 17.3\) (or if there was a typo, but based on the given problem, \(x=\frac{173}{10}=17.3\))
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4. find ( mangle abc ). diagram: horizontal line ( ebd ) with ( b ) as …
\( 53^\circ \)
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for each value of y, determine whether it is a solution to \\(\\frac{y}…
- For \( y = 50 \): No - For \( y=-20 \): Yes - For \( y = 30 \): No - For \( y = 0 \): No
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select the correct answer. in the given figure, what is the measure of …
# Explanation: ## Step1: Recognize vertical angles in a circle In a circle, vertical angles formed by intersecting chords are equal. So, the arc \( (2x + 28)^\circ \) and arc \( (…
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3. find m∠abc. diagram: lines ac and de intersect at point b. ∠abc is l…
\(58^\circ\) (corresponding to the option with 58°)
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if the given figure is sliced through points j, k, and l, which best de…
A. triangle
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2. find the value of x. (3x + 12)° (5x)° options: 30, 21, 9, 6
6
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select the correct answer. the circle is rotated around the horizontal …
A. sphere
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1. find m∠abc. (6x - 7)° (4x + 23)° options: 90°, 15°, 83°, 41°
\( 83^\circ \)
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8. enter your answer. 289 in² instructions what is the side length of t…
17
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3. are the two triangles congruent? how do you know? if m∠r=71.6° and o…
# Explanation: ## Step1: Identify Coordinates First, find coordinates of vertices for both triangles. For \(\triangle PLC\): \(P(4, -1)\), \(L(4, -6)\), \(C(7, -2)\). For \(\trian…
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which diagram shows lines that must be parallel lines cut by a transver…
The diagram with the two horizontal lines (parallel candidates) cut by a vertical transversal, where the corresponding angles (or alternate interior angles, or consecutive interio…
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tell whether each triangle with the given side lengths is a right trian…
To determine if a triangle with given side lengths is a right triangle, we use the Pythagorean theorem, which states that for a right triangle with side lengths \(a\), \(b\) (the …
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the law of cosines follow these steps to derive the law of cosines. 5. …
rearranging
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given the information in the diagram, which theorem best justifies why …
D. converse of the same side interior angles theorem (Note: The sum of 72° and 108° is 180°, so they are supplementary same - side interior angles. The converse of the same - side…
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figure b is a scaled copy of figure a. for each set of figures, calcula…
From A to B: $\frac{1}{3}$; From B to A: $3$ ### Problem 2
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the law of cosines follow these steps to derive the law of cosines. ...…
\( c \cos(A) \) (or the option labeled with \( c \cos(A) \) in the original problem's choices)
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follow these steps to derive the law of cosines. 3. the equation ( a^2 …
c
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tell whether each triangle with the given side lengths is a right trian…
A. 10 ft, 24 ft, 26 ft
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look at the colored part of each shape. which shape shows three-fourths?
The third shape (the square divided into 4 equal small squares with 3 of them colored)
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in the diagram, dc is 10 units and bc is 6 units. what is the length of…
12 units
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choose two of these three figures. figure m scale factor: $\frac{1}{2}$…
- For Figure N (scale factor \(1\)): Draw the same figure as Figure N (no change in dimensions). - For Figure M (scale factor \(\frac{1}{2}\)): Redraw Figure M with each segment l…
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gr 8 | guided notes: creating and interpreting transformati... a ____ i…
A. rotation involves turning a shape around a fixed point. ### Second Blank (flips a shape over a line, creating a mirror image)
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follow these steps to derive the law of cosines. 1. the relationship be…
substitution
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follow these steps to derive the law of cosines. 1. the relationship be…
expanded
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two parallel lines are crossed by a transversal. what is the value of g…
\(g = 75\) (corresponding to the option \(g = 75\))
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(-3, -7) and (-7, -1) click twice to draw a line. click a segment to er…
Leg 1: 4, Leg 2: 6, Hypotenuse: $2\sqrt{13}$
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lesson 2: corresponding parts and scale factors cool down: comparing po…
The scale factor from polygon \( ABCD \) to polygon \( PQRS \) is \( 2 \).
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they lie in different planes but will intersect if a plane is drawn to …
They lie in different planes and will be parallel if a plane is drawn to contain both lines.
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a football field is 120 yards by 53.333 yards. what is the area of the …
\boxed{1.32} (or \boxed{1.3} if 120 is considered two sig figs, but likely 1.32)
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graph a right triangle with the two points forming the hypotenuse. usin…
\(2\sqrt{13}\)
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follow these steps to derive the law of cosines. 1. the relationship be…
Pythagorean theorem
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in the diagram, the length of segment tr can be represented by 5x −4. w…
15 units