Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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a triangle on a coordinate plane is translated according to the rule $t…
\((x,y)\to(x-3,y + 5)\) (the first option)
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find x in each. 11. 12. 13. 14. 15. 16. 17. * 18. draw a straight angle.
\(x = 50\)
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finding coordinates of a pre-image triangle abc is translated to image …
\(B(-2,3)\)
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consider the diagram and proof by contradiction. given: △abc with ∠b ≅ …
A. converse of the isosceles triangle theorem
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1. calculate the length of side using the cosine law. show your work. 3…
\(\angle B\approx73^\circ\), \(\angle C = 55^\circ\), \(a\approx17.31\) (exact values may vary slightly with rounding)
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triangle qst is isosceles, and \\(\\overline{rt}\\) bisects \\(\\angle …
B. \(m\angle QRT = m\angle SRT\), D. \(m\angle QRT = 2*m\angle RTQ\)
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triangle sqt is isosceles. the measure of angle stq is 48°. what is the…
A. 24°
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in the figure, m∠1 = (5x)° and m∠2 = (x + 6)°. (a) write an equation to…
(a) Equation: \(5x+(x + 6)=90\) (b) \(m\angle1 = 70^{\circ}\), \(m\angle2=20^{\circ}\)
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triangle abc is isosceles. what is true about the measure of angle b? i…
D. It is equal to the measure of angle C.
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triangle abc is an isosceles right triangle. what is the measure of one…
B. 45°
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triangle abc is shown below. what is the length of line segment ac? 7 9…
14
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explaining how to translate a figure you are given the coordinates of a…
First, find the translation vector by subtracting the coordinates of the original vertex from the coordinates of its image. Then, apply this vector to all vertices of the original…
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right triangle abc is isosceles and point m is the midpoint of the hypo…
It is an isosceles right triangle.
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in the figure, ( mangle 1 = (x + 72)^circ ) and ( mangle 2 = (3x)^circ …
(a) Equation: \(x + 72+3x=180\) (or \(4x+72 = 180\)) (b) \(m\angle1 = 99^{\circ}\), \(m\angle2 = 81^{\circ}\)
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5. do the following proof using the t-table provided. given: ( r ) is t…
| Statement | Reason | |--|--| | \( R \) es el punto medio de \( \overline{QS} \) | Dato | | \( QR = SR \) | Definición de punto medio | | \( \overline{QT}\cong\overline{ST} \) | …
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in the figure, ( mangle 1 = (8x)^circ ) and ( mangle 2 = (x - 18)^circ …
(a) Equation: \(8x+(x - 18)=180\) (b) \(m\angle1 = 176^{\circ}\), \(m\angle2 = 4^{\circ}\)
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randy draws triangle abc on the coordinate plane with vertices a(7, -4)…
\(T_{-2,5}(x,y)\)
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triangle knm is isosceles, where angle n is the vertex. what is the mea…
D. 65°
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the cosine law: $c^{2}=a^{2}+b^{2}-2ab(\\cos c)$ or $\\cos c = \\frac{a…
For the first problem (length of \( x \)): \( x\approx6.87 \) (if sides are 6.5 and 5 with included angle \( 72^{\circ} \)); For the second problem (measure of angle \( X \)): \( …
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consider the diagram and proof by contradiction. given: △abc with \\(\\…
B. ∠B ≅ ∠C
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what is the sum of the areas of circle c and circle d? 7 cm o d 7π unit…
D. \(98\pi\) units²
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a regular octagon has an apothem measuring 10 in. and a perimeter of 66…
C. \(332\ \text{in.}^2\)
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analyzing a translation li transformed rectangle abcd. the image is sho…
Yes, the image represents a translation.
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find the value of c.
\(c = 44\)
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a square is inscribed in a circle of diameter 12√2 millimeters. what is…
A. \((72\pi - 144)\text{ mm}^2\)
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identifying a translation a graphic designer wants to translate rectang…
The image of rectangle \(DEFG\) has vertices \(D'(-2,5)\), \(E'(3,5)\), \(F'(3,3)\), \(G'(-2,3)\)
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triangle qrs has vertices q(8, -6), r(10, 5), and s(-3, 3). what are th…
\(Q'=(0.4,-1.7)\), \(R'=(2.4,9.3)\), \(S'=(-10.6,7.3)\)
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find eg. f 7 h 6w+5 e 5 i 4w+8 g © algebra einstein, 2023
\(EG = 75\)
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writing a rule for a translation which rule describes the translation? …
\((x,y)\to(x + 8,y - 3)\) (the third option)
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find ac. (image of a triangle with points b, d, e. segment bc = 8, cd =…
\(15\)
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identifying a translation assume each figure shown has the same orienta…
Square \(4\)
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on occasion, one of the pairs of sides that are congruent will simply b…
| Statement | Reason | |--|--| | \( \overline{QTS} \) | Given | | \( \overline{QR}\cong\overline{SR} \) | Given | | \( \overline{RT} \) is the median from \( R \) to \( \overline{…
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find the value of y. 6y 2 4y+5 3 © algebra einstein, 2023
\(y = 1\)
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a triangle is drawn on the coordinate plane. it is translated 4 units r…
\((x,y)\to(x + 4,y-3)\) (the third option)
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in triangle abc, ( mangle abc = (4x - 12)^circ ) and ( mangle acb = (2x…
No, Yin is not correct. When x=19, the angles are 64°, 64°, and 52°, so the triangle is isosceles but not equilateral.
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the measure of central angle rst is π radians. what is the area of the …
B. \(8\pi\) units\(^{2}\)
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find the value of y. 6y 2 4y+8 3 © angelina instein, 2023
\(y = 1.6\)
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find the perimeter of δqrs. q 3t - 1 4 o → p 8t - 1 12 r → 18 s © algeb…
\(54\)
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a regular hexagon has a radius of 20 in. what is the approximate area o…
1,038 in.²
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triangle wxy is isosceles. ∠ywx and ∠yxw are the base angles. \\overlin…
D. 150°
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the base of the right triangle drawn in the regular octagon measures 0.…
11.2 cm
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identifying an angle measure what is the measure of ∠nlm? m∠nlm = (6x +…
65°
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in circle v, r = 14ft. what is the area of circle v? 14π ft² 28π ft² 49…
\(196\pi\) \(ft^{2}\) (the fourth option)
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the vertex angle of an isosceles triangle measures 42°. a base angle in…
$x = 33$ Each base angle measures $69^\circ$
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the area of the regular pentagon is 6.9 cm². what is the perimeter? 2 c…
\(10\space cm\)
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identifying a leg length what is the length of \\(\\overline{pr}\\)? \\…
40
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reasoning 4. fill in the missing reasons for each given statement. give…
# Explanation: ## Paso 1: Dato Se da que \(I\) es el punto medio de \(\overline{EF}\). ## Paso 2: Definición de punto medio Si \(I\) es el punto medio de \(\overline{EF}\), entonc…
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cd bisects ∠acb. which statements must be true? check all that apply. a…
m∠ACD = m∠BCD
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which fact helps you prove the isosceles triangle theorem, which states…
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
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3. in the diagram shown, f lies on \\(\\overline{eg}\\) and \\(\\overli…
(4) \(\overline{HF}\) bisects \(\angle EHG\)
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identifying an unknown value what is the value of x? 40 70 140 160
B. 70
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2. in the diagram shown, it is given that \\( \\overline{qn} \\) bisect…
(1) \( \triangle MQN \) and \( \triangle QPN \)
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5.1 assignment possible points: 0.45 algebra find the value of x. (ther…
\(x = 4\)
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which properties belong to all isosceles triangles? check all that appl…
The base angles are congruent., The two sides opposite the base angles are congruent., The bisector of the vertex angle is the perpendicular bisector of the base.
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fluency 1. in the diagram shown below, \\(\\overline{wx} \\cong \\overl…
(3) a reflection across $\overline{WY}$
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5.1 assignment possible points: 0.45 algebra find the value of x. diagr…
\(5\)
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question 7 points 4 the vertices of a polygon abcd is a (1, 2), b (1, 4…
The coordinates of the dilated polygon are \(A'(3, 6)\), \(B'(3, 12)\), \(C'(6, 18)\), and \(D'(15, 12)\).
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what is the area of the shaded region? (25π − 48) cm² (25π − 30) cm² (2…
\((25\pi - 24)\space cm^{2}\)
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what is the area of the sector that is not shaded? 12π units² 24π units…
\(120\pi\) units\(^{2}\) (the third option)
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determining translations on the coordinate plane what is the y-coordina…
\(1\)
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triangle △abc is the image of △abc under a dilation with a scale factor…
4 (assuming \( A'C' \) length is 8; adjust if grid count differs, but standard scale factor inverse gives \( AC = \frac{A'C'}{2} \))
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a regular pentagon is shown. what is the measure of the radius, c, roun…
\(17.01\) cm
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find k. (there is a triangle with vertices h, i, j. point k is on hi, p…
\(k = 36\)
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amaury draws an acute triangle on the coordinate grid. he finds the are…
\(11\) square units
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quadrilateral abcd is the image of quadrilateral abcd under a dilation …
8
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5.1 assignment 9 of 22 possible points: 0.45 perpendicular bisectors us…
\( 50 \)
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question 6 points 4 the rectangle is rotated by 360° about the origin. …
Vertices of rotated figure: \( A(-4, 3) \), \( B(4, 3) \), \( C(4, -3) \), \( D(-4, -3) \)
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the measure of central angle abc is \\(\frac{pi}{2}\\) radians. what is…
\(9\pi\) units\(^{2}\) (the second option)
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a worker lays the floor of a 4-meter square shed. what is the floor’s a…
A. 16 m²
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5.1 assignment 8 of 22 possible points: 0.45 perpendicular bisectors us…
\( 43 \)
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what is the area of the composite figure? 262 cm² 264 cm² 266 cm² 268 c…
\(264\ cm^2\)
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how is the square footage of any building area determined? add length t…
multiply length by width
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question 5 points 3 the endpoints of the line segment pq are (10, 1) an…
\(P'(-10,1)\) and \(Q'(-7,1)\) (the second option)
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5.1 assignment 7 of 22 possible points: 0.45 perpendicular bisectors us…
\( 50 \)
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the polygon abcd is rotated by 270° anticlockwise about the origin. fin…
A' (1, -2), B' (1, -8), C'(6, -8), D' (6, -2) (the third option)
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what type of angle measures 36°? ○ acute ○ obtuse ○ opposite ○ adjacent
acute
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find b. © algebra einstein, 2023
\(b = 20\)
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point g is the center of the small circle. point x is the center of the…
\(676\pi\mathrm{cm}^{2}\)
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transformations on the coordinate plane what is the image of triangle a…
The image of point \(E(6,0)\) after the transformation is \(E'(1,4)\)
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what is the area of the composite figure if \\(\\overline{ab} \\cong \\…
\((2\pi + 28)\) \(mm^{2}\)
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5.1 assignment 3 of 22 possible points: 0.45 algebra find the length of…
\(55\)
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to find the distance across a river, a surveyor choose points a and b, …
distance \(= 249.12\space m\) height \(= 247.25\space m\)
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nccer 00102 - introduction to construction math 47min what is the circu…
the distance around the outside of the circle
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an equilateral triangle has an apothem measuring 2.16 cm and a perimete…
\(24.2\space cm^{2}\) (rounded to the nearest tenth)
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5.1 assignment 2 of 22 possible points: 0.45 algebra find the length of…
\(30\)
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the coordinates of the kite abcd is a (1, 1), b (2, 0), c (3, 1), d (2,…
A' (5, 3), B' (6, 2), C' (7, 3), and D' (6, 5)
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question 2 points 2 the image of (3, -5) after a dilation with respect …
B. 5
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tell me what you want to do options: translation, reflection, rotation,…
Rotation (the option "Rotation" among the choices: Translation, Reflection, Rotation, Dilation)
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nathan draws a triangle on the coordinate grid. he marks his points at …
The perimeter of the triangle is \(26.2\) units.
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note: the picture is not drawn to scale. ancient alien theorists mannin…
distance from \(A = 281.87\) km \(h = 281.33\) km
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calculator the coordinates of the vertices of a rectangle are (-4, 3), …
21.6
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what is the area of the triangle whose vertices are x(-5, -1), y(-5, -1…
18
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△ qrs is mapped to △ qrs using the rules (x, y) → (-x, y) followed by (…
△QRS is congruent to △Q'R'S' because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
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zx bisects ∠wzy. if the measure of ∠yxz is (6m − 12) °, what is the val…
B. 17
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no additional details were added for this assignment. what are the step…
1. Use the compass to construct a circle. 2. Draw a point anywhere on the circle. 3. Place the point of the compass on the new point and draw an arc that intersects the circle, us…
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one cubic meter represents a cube - shaped space measuring 1 meter in a…
C. 100
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find the length of the missing side of the right triangle. round to thr…
1. \(10\) 2. \(12\) 3. \(20\) m 4. Approximately \(47.8\) m
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question 6 points 4 find the arc length of the circle whose radius is 1…
The arc length is approximately \( 20.93 \) cm.
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question 5 points 1 lines are composed of an infinite set of ______. po…
A. points in a row
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quadrilateral qrst has vertices at q (-1,5), r (2,8), s (4,4), and t (1…
Quadrilateral \(QRST\) is a parallelogram and \(x = 18\)