Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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an architect is designing a ramp with a height of 2 meters and a horizo…
For the first question: c. 6.32 For the second question: a. The longest diagonal inside a 3D shape
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how is triangle abc being translated to triangle abc? down 9, right 4 u…
down 9, right 4
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the sides of a triangle are 30, 24, and 18. use the pythagorean theorem…
The triangle is right because the square of the largest side equals the sum of the squares of the other two sides.
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what is the pythagorean theorem used for in three - dimensional space? …
1. b. Calculating straight - line distances between points 2. d. 21.21 m
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consider the angles formed by the garden gate. what can be concluded fr…
a. Conclusion: \(\angle1\cong\angle2\), Theorem: Definition of congruent - angle measures b. D. It can be concluded that \(\angle3\cong\angle4\) since vertical angles are congruen…
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the sides of a triangle are 96, 44, and 82. use the pythagorean theorem…
The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.
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why is the pythagorean theorem important in real - world applications? …
1. b. It provides a method for calculating distances accurately 2. c. $\sqrt{l^{2}+w^{2}+h^{2}}$
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if you place a 32 - foot ladder against the top of a 23 - foot building…
$22.2$ feet
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consider the angles formed by the garden gate. what can be concluded fr…
A. It can be concluded that \(\angle1\cong\angle2\) since all right angles are congruent.
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if you place a 39 - foot ladder against the top of a 23 - foot building…
$31.5$
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determine the distance a player travels from (0, 0, 0) to (28, 15, 10).…
First question: c. 33.30 Second question: d. Measuring the circumference of a circle
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2. which best describes the transformation from figure a to figure b? t…
translation 8 units right and 6 units down
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the area of a rectangle is 105 square units. its width measures 7 units…
$16.6$
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a box has dimensions 3 ft by 4 ft by 12 ft. what is the length of its s…
1. d. 13 ft 2. b. 9.43
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if a point is at (-10,6), and it gets translated horizontally -6 units …
(-16,11)
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question the sides of a triangle are 24, 26, and 10. use the pythagorea…
The triangle is right because the square of the largest side equals the sum of the squares of the other two sides.
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the flag is an isosceles triangle. the bottom side of the flag measures…
The perimeter is approximately \(15.0\) ft.
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5. sp≅sq △spm≅△sqm any point on a bisector of a line segment is equidis…
Jamie made his first mistake in Step 3. He cannot conclude that $\overline{MP}$ is congruent to $\overline{MQ}$ based on the fact that line $MS$ is a bisector of $\overline{PQ}$.
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the flag is an isosceles triangle. the bottom side of the flag measures…
15.0 feet
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the sides of a triangle are 79, 40, and 64. use the pythagorean theorem…
The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.
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part a: multiple choice (circle the best answer) 1. what is the main go…
1. c) To reclaim items that were confiscated from them 2. No answer can be determined without more context 3. b) Handheld camera and quick cuts 4. c) Grime, drill, and hip - hop 5…
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the sides of a triangle are 30, 64, and 90. use the pythagorean theorem…
The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.
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the flag is an isosceles triangle. the bottom side of the flag measures…
The value of $x$ is approximately $3.1$ feet and the perimeter is $11.2$ feet.
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now look at triangles b and c. which type of transformation takes trian…
Rotation
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the flag is an isosceles triangle. the bottom side of the flag measures…
$22.0$
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line x is parallel to line y. line z intersects lines x and y. determin…
- \(m\angle1 + m\angle4 = 180^{\circ}\): Always True - \(m\angle5−m\angle7 = 0^{\circ}\): Always True - \(\angle2\cong\angle8\): Always True - \(m\angle2−m\angle3=m\angle1 - m\ang…
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a point is translated 3 units left and 4 units up. what is the correct …
$T(x,y)\to(x - 3,y + 4)$
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the flag is an isosceles triangle. the bottom side of the flag measures…
$11.2$
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what transformation is happening? (x, y)---->(x + 2,y - 3) slide right …
slide right 2, down 3
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jessie draws triangle abc on a coordinate grid. the slope of line - seg…
Rotation of 180° around the origin: Supports Jessie's Claim Reflection across the line y = 2: Supports Jessie's Claim Translation up 1.25 units: Supports Jessie's Claim Reflection…
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write the ratios for sin m, cos m, and tan m. give the exact value and …
$\sin M=\frac{52}{173}\approx0.3006$, $\cos M=\frac{165}{173}\approx0.9538$, $\tan M=\frac{52}{165}\approx0.3152$
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use the inverse trigonometric keys on a calculator to find the measure …
\(55\)
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determine how to translate triangle abc to triangle abc. (x + 2, y - 5)…
We need to know the coordinates of corresponding points of $\triangle A'B'C'$ and $\triangle ABC$ to determine the exact translation. But based on the given options, we would chec…
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use the inverse trigonometric keys on a calculator to find the measure …
\(55\)
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2. m∠abc = 61°. find m∠abd and m∠dbc. 3. ∠abc = 115°. find m∠abd and m∠…
$m\angle ABD = 37^{\circ}$, $m\angle DBC=24^{\circ}$
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find the length x to the nearest whole number. (round to the nearest wh…
$729$
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find the measure of side c. a = 35 m c = m (round the answer to the nea…
\(53\)
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determine how to translate triangle abc to triangle abc. (x+2, y-9) (x+…
We need to know the coordinates of the vertices of \(\triangle A'B'C'\) and \(\triangle ABC\) to precisely determine the translation. But in general, if we assume the correct tran…
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solve for x. x = (round to the nearest hundredth.)
$28.33$
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write the ratio for tan a. tan a = (type an integer or a simplified fra…
$\frac{8}{15}$
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you start driving west for 3 miles, turn right, and drive north for ano…
$11.4$ miles
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q. which rule correctly describes this translation?
\((x,y)\to(x - 4,y - 5)\)
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based on the given angles below, are the lines y and z parallel? why or…
Yes, the lines Y and Z are parallel because the corresponding angles are equal.
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find the value of x. (round to the nearest tenth as needed.)
$23.1$
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in △pqr, the obtuse - angle is 105°, and the shorter sides measure 4 an…
13.5
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based on the given angles below, are the lines c and d parallel? why or…
No, the lines \(C\) and \(D\) are not parallel because corresponding angles (if the lines were parallel) would be equal, and the given non - corresponding angles are not equal, wh…
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view this video because we live in an environment with streets and wall…
C. cognitive
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based on the given angles below, are the lines a and b parallel? why or…
No, the lines $A$ and $B$ are not parallel because the given angles do not satisfy the angle - relationships (equality or supplementary) required for parallel lines.
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an altitude is drawn from the vertex of an isosceles triangle, forming …
$73.9$ inches
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choose all of the following statements that prove that a and b are para…
$\angle3\cong\angle7$, $m\angle4 + m\angle6 = 180^{\circ}$, $\angle2\cong\angle6$
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choose all of the following statements that prove that e and f are para…
\(\angle4\cong\angle8\)
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choose all of the following statements that prove that a and b are para…
$\angle3\cong\angle6$
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if you place a 29 - foot ladder against the top of a building and the b…
23.6 feet
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choose all of the following statements that prove that e and f are para…
\(m\angle4 + m\angle6 = 180^{\circ}\), \(\angle3\cong\angle6\)
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you start driving east for 18 miles, turn right, and drive south for an…
$18.7$ miles
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find the coordinates of the missing endpoint. #7 midpoint of uv is m(4,…
#7: V(1,-3) #8: Y(2,13)
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the area of a rectangle is 380 square units. its length measures 20 uni…
$27.6$
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a certain television is advertised as a 59 - inch tv (the diagonal leng…
$32.9$ inches
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the altitude of the triangle abc, segment da, has been drawn. derive a …
$\sin(B)=\frac{h}{c}$, $h = c\sin(B)$, Area $=\frac{1}{2}ac\sin(B)$
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follow these steps to derive the trigonometric area formula. 1. for △ab…
substitute for
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a 35 foot ladder is set against the side of a house so that it reaches …
$24.5$ feet
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follow these steps to derive the trigonometric area formula. 1. for △ab…
$\frac{1}{2}bc\sin(A)$
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follow these steps to derive the trigonometric area formula. 1. for △ab…
$c\sin(A)$
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you start driving west for 3 miles, turn right, and drive north for ano…
3.6 miles
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follow these steps to derive the trigonometric area formula. 1. for △ab…
$\frac{h}{c}$
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an altitude is drawn from the vertex of an isosceles triangle, forming …
54.0 inches
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night ulrich had banded together his foresters to watch the dark forest…
Ulrich von Gradwitz wishes to hunt down Georg Znaeym and meet him face to face in order to kill him.
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the length and width of rectangles are given. use the formula a = l × w…
6. 50 in.$^{2}$ 7. 6 m$^{2}$ 8. 500 mi$^{2}$ 9. 210 ft$^{2}$ 10. 100 m$^{2}$ 11. 100 in.$^{2}$ 12. 74 13. 96 14. 85 15. 86 16. 59 17. 39.2 18. 40 19. 50 20. 20 21. $w = 6$ gives a…
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the graph shows percentages of sales made by various divisions of a com…
| Division | Measure of Angle Formed by Segment for Division | |--|--| | A | 97.2 | | B | 82.8 | | C | 68.4 | | D | 64.8 | | F | 46.8 | The percentage for Division C is 19.
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an altitude is drawn from the vertex of an isosceles triangle, forming …
$12.2$ inches
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q1 - accelerated mathematics gr 8 | guided notes: modeling and solving …
1. Hypotenuse 2. Diagonal 3. 90
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what is the length of the side opposite ∠d? units sin(d) =
The length of the side opposite $\angle D$ is $5$ units. $\sin(D)=\frac{5}{13}$
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determine the type of triangle that is drawn below.
Obtuse - isosceles triangle
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for the purpose of purchasing new baseboard and carpet, complete parts …
a. The area of the room is sq ft and the perimeter is ft b. Baseboard is related to perimeter. Carpet is related to area.
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the pythagorean theorem applies specifically to triangles. in the formu…
1. right - angled 2. hypotenuse 3. legs 4. legs 5. hypotenuse
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write a two - column proof for the following. given: m∠2 = 30, m∠1 = 2m…
90
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write a two - column proof for the following. given: m∠2 = 30 m∠1 = 2m∠…
| Statements | Reasons | |--|--| | 1) \(m\angle2 = 30\) | 1) Given | | 2) \(m\angle1 = 2m\angle2\) | 2) Given | | 3) \(m\angle1=2\times30\) | 3) Substitution | | 4) \(m\angle1 = 6…
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determine the type of triangle that is drawn below.
Equilateral triangle
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write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. st…
$12$
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solve the problem. 8) a rectangle with width 2x + 1 inches has an area …
$x^{3}+4x^{2}-11x - 30$ inches ### 9.
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write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. st…
7. \(11x = 132\) (after adding 1 to both sides of \(11x-1 = 131\)); \(x = 12\) (after dividing both sides of \(11x=132\) by 11) and we have proven \(m\angle EFI = 36^{\circ}\) as …
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the sign outside a companys headquarters has a width of 85 feet and an …
B. area = length $\cdot$ width
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a parallelogram has side lengths of 13 and 17 and an angle that measure…
16
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write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. st…
$11x - 1$ (for the blank in the two - column proof) and $m\angle EFI = 36^{\circ}$
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in a right triangle, if one leg is 24 units and the hypotenuse is 25 un…
c. 7 units b. 111.8 yards
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on which triangle can the law of cosines be used to find the length of …
The second triangle (the one with side - lengths 7 and 12 and included angle \(57^{\circ}\))
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triangle jkl was dilated using the rule $d_{m,\frac{1}{3}}$. the image,…
5 units
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if the legs of a right triangle are both 1 unit long, what is the lengt…
1. A. \(\sqrt{2}\) 2. A. Determining the hypotenuse in right triangles
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on a softball field, home plate is 43 feet from the pitchers mound. a b…
This problem belongs to Mathematics - Geometry. To solve, we can use the Law of Cosines. Let \(a = 43\), \(b=162\), and \(\theta = 27^{\circ}\). The Law of Cosines formula for the…
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the pythagorean theorem can be used to: a. solve quadratic equations b.…
First Question: c. Determine the distance between two points on a coordinate plane Second Question: a. A triangle with angles $60^{\circ},60^{\circ}$, and $60^{\circ}$
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which graph could represent a constant balance in a bank account over t…
The second graph (the one with the horizontal line) could represent a constant balance in a bank account over time.
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in a right triangle, if a = 7 and c = 25, what is b? a. 20 b. 24 c. 18 …
1. b. 24 2. b. The hypotenuse
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graph the following function on the axes provided. f(x)=\begin{cases}-4…
Graph a horizontal line \(y = - 4\) with an open - circle at \((-5,-4)\) extending to the left and a line \(y = 4x-15\) with an open - circle at \((3,-3)\) and slope \(4\) extendi…
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a ferry transports passengers to three different ports. from port a, th…
7.7
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a pilot flies 720 miles from dallas, texas, to his first destination. a…
Using the Law of Cosines \(c^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a = 720\), \(b = 290\), and \(C=125^{\circ}\). \(c=\sqrt{720^{2}+290^{2}-2\times720\times290\times\cos(125^{\circ…
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if a right triangle has a hypotenuse of 13 units and one leg of 5 units…
a. 12 units d. 13 feet
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write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. st…
The reason for step 5 is "Substitution Property (using step 4 for the angle - measure expressions in step 3)" and the proof is complete as we have shown that $m\angle EFI = 36^{\c…
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write a two - column proof. given: m∠gfi = 131°. prove: m∠efi = 36°. st…
$131$
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△def is an isosceles triangle with base angles e and f. what is the ang…
(1) 14 (2) 83
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5. if m∠def = 159°, then m∠cef = ____ (9x + 4)° (5x + 15)° d e f
$65^{\circ}$