Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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what leg is considered the hypotenuse? the side opposite the smallest a…
the side opposite the right angle
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what is the acronym to help you remember the ratios to use in trigonome…
SOHCAHTOA
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3. in this diagram, line segment cd is the perpendicular bisector of li…
a. \(AM = BM\)
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1/10 what must be true for two lines to be considered parallel? they mu…
1. They must be on the same plane. 2. They must have the same slope.
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2. a, b, and c are the centers of the 3 circles. how many equilateral t…
There are \(8\) equilateral triangles in the diagram.
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a pentagon is transformed according to the rule ( r_{0,180} ). which is…
\((x,y)\to(-x,-y)\) (the first option)
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9. renee has walked in a straight line, 25° west of north, for 1200 met…
1088 m south, 508 m east (the third option)
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8. an airplane is taking off from a runway. the airplane climbs from th…
2160 m
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7 nikolas is in a mineshaft that descends into the ground at an angle o…
308 m
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question 7 (multiple choice worth 2 points) (polygon angle sums lc) fin…
\(540^{\circ}\) (the option \(540^{\circ}\) is correct)
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determine the value of x. x = 120 x = 9 x = 28.5 x = 21
\(x = 21\)
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6. a helicopter takes off, and travels forward at an angle of 65.1° abo…
471 m
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determine the degree measure of one angle of a 30 - sided regular polyg…
\(168^{\circ}\)
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quadrilateral abcd is transformed according to the rule (x, y) → (y, -x…
\(R_{0,270^{\circ}}\)
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quadrilateral abcd has the following angle measures: $m\\angle a=?^{\\c…
\(126^{\circ}\)
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(polygon angle sums mc) a 20 - sided regular polygon has an angle measu…
\(g = 54\) (the fourth option)
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determine the measure of one of its angles. 144° 162° 1,440° 1,800°
144°
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question 1 (multiple choice worth 2 points) (polygon angle sums mc) tri…
\(43^{\circ}\)
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5 a surveyor is drawing property lines. he draws one line that is 25.0 …
23.5 m
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3. cory is looking for a good campsite. from where he parked, he walks …
Walk 145 meters north, then go 126 meters west.
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question 2/13 given: \\( \\triangle a b c \\) on \\( \\overline{a d} \\…
B. Triangle Sum Theorem; Transitive Property
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given: line ( d ) is parallel to ( overline{ab} ). prove: ( mangle1 + m…
C. Alternate Interior Angle Theorem
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graph the solution to the following inequ $x^{2}-6x<-8$ note that you c…
The solution of the inequality \(x^{2}-6x < - 8\) is \(2<x<4\). So on the number - line, we draw an open circle at \(x = 2\) and \(x = 4\) and shade the region between them.
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a rectangle on a coordinate plane is translated 5 units up and 3 units …
\((x,y)\to(x - 3,y + 5)\) (the third option)
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3. triangle hef is the image of triangle fgh after a 180 - degree rotat…
D. Angle \(GHK\) is congruent to angle \(KHE\), E. Segment \(EH\) is congruent to segment \(FG\)
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graph the solution to the following inequality on the num $x^{2}-6x\\le…
The solution is $2\leqslant x\leqslant4$. On the number - line, we draw a solid circle at $x = 2$ and $x = 4$ (because the inequality includes equality) and shade the region betwe…
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geometry dilations homework name state whether a dilation with the give…
10. \(k = 5\) 11. \(k=\frac{2}{3}\)
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if a translation of $(x,y)\\to(x + 6,y - 10)$ is applied to figure abcd…
\((1,-2)\) It seems there is a mistake in the provided options. If we assume the coordinate of \(D\) is \((-5, - 2)\) (maybe a mis - read of the graph): ## Step1: Apply the transl…
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triangle abc is translated according to the rule (x, y) → (x + 2, y - 8…
\((6,-13)\) (corresponding to the fourth option)
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rectangle efgh is translated according to the rule ( t_{-5,9}(x,y) ). i…
\((-7,6)\)
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11x + 9 3x + 21 write an equation to solve for x : what is the value of…
Equation: \(11x + 9=3x + 21\) Value of \(x\): \(\frac{3}{2}\) Length of the left - side: \(\frac{51}{2}\)
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a triangle on a coordinate plane is translated according to the rule $t…
\((x,y)\to(x - 8,y + 4)\) (the third option)
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find the measure of the \?\ or \x\.
\(49^{\circ}\)
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5 jonah is walking along a trail the trail heads east for 1350 meters, …
1670 m, \(36.3^{\circ}\) east of north (the third option)
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find the measure of the \?\ or \x\. 23° ? =
\(78.5^{\circ}\)
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4 ariane is riding her motorcycle heading directly south. she drives so…
\(11^{\circ}\text{ west of south}\)
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square abcd was translated using the rule $(x,y)\to(x - 4,y + 15)$ to f…
None of the given options \((13,-23),(5,7),(18,1),(-6,-1)\) are correct. If we assume there is a typo in the problem (maybe the translation rule is \((x,y)\to(x + 4,y-15)\)): Let …
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assume \\( \\angle \\alpha \\) is opposite side \\( a, \\angle \\beta \…
\(\cos\beta\approx0.6558\), \(\cos\gamma\approx - 0.0388\)
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the rule as a mapping for the translation of a rectangle is $(x,y)\\to(…
a translation of 2 units to the left and 7 units up
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10 find the measure of the “?” or “x”. ? =
# Explanation: ## Step1: Find the base angle of the triangle Since the triangle is isosceles (two sides are equal), the base angles are equal. The base - angle adjacent to \(58^{\…
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9 find the measure of the \?\ or \x\. ?=
\(70^{\circ}\)
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which statements are true about triangle abc and its translated image, …
B. The rule for the translation can be written as \(T_{3,-5}(x,y)\) E. Triangle \(ABC\) has been translated 3 units to the right and 5 units down.
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irina wants to tile her floor using the translation shown below. which …
\(T_{2,-3}(x,y)\)
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8 find the measure of the \?\ or \x\. 76° 55° ? =
\(131\)
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quadrilateral mnop was transformed to create quadrilateral efgh. determ…
B. Quadrilateral \(MNOP\) is similar to quadrilateral \(EFGH\) because a dilation centered at the origin by a scale factor of \(3\) maps quadrilateral \(MNOP\) to quadrilateral \(…
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2) what is the statement and reason for a? given:abcd is a rectangle pr…
Statement: \(\angle A=\angle B=\angle C=\angle D = 90^{\circ}\); Reason: Definition of a rectangle (a rectangle has four right angles)
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use a transformation matrix to find the image of ( r(9,4) ) after a tra…
The image of the point \(R(9,4)\) is \((-1,3)\)
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use a transformation matrix to find the image of ( w(-8,0) ) after a di…
\((-2,0)\)
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graph the solution to the following inequality on the number lin $(x - …
The solution of the inequality \((x - 5)(x + 3)\leq0\) is \([-3,5]\). On the number line, we draw a solid circle at \(x=-3\) and \(x = 5\) (because the inequality includes equalit…
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prove that abc and def are similar by giving a sequence of transformati…
rotate \(90^{\circ}\) counterclockwise about the origin → dilate by a factor of 2 from the origin → translate up 2 units
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directions: select all the correct answers. consider the figures graphe…
Polygon \(KLMN\)
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what is the correct order of the following proof? given: abcd is a para…
The correct order is \(6,1,2,3,5,4\). But looking at the options, we note that in a proof: - We start with the given (statement 6). - Then use the definition of a parallelogram (s…
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figure efghij was changed to create figure klmnpq. determine if figure …
D. Figure \(EFGHIJ\) is similar to figure \(KLMNPQ\) because dilation \((x,y)\) to \((2x,2y)\) maps figure \(EFGHIJ\) to figure \(KLMNPQ\)
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the width of a rectangle measures $(9s + 6)$ centimeters, and its lengt…
\(14 + 20s\)
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practice 1. find the area. answer to the nearest tenth. a) b) 2. the fi…
1a) \(706.9\space cm^{2}\) 1b) \(28.3\space ft^{2}\) 2a) \(7\space in\) 2b) \(153.9\space in^{2}\) 3) \(7090.0\space ft^{2}\)
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figure pqrst was changed to create figure uvwxy. determine if figure pq…
B. Figure \(PQRST\) is similar to figure \(UVWXY\) because dilation \((x,y)\) to \((0.5x,0.5y)\) maps figure \(PQRST\) to figure \(UVWXY\).
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8. evaluate the formula $v = \\frac{bh}{3}$ for $b = 9\\text{ in}^2$ an…
\(96\space in.^{3}\) (the fourth option)
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practice 1. find the area. answer to the nearest tenth. a) b) 2. the fi…
1. a) \(706.5\space cm^{2}\); b) \(28.3\space ft^{2}\) 2. a) \(7\space in\); b) \(153.9\space in^{2}\) 3. \(7084.6\space ft^{2}\)
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triangle efg and triangle efg are given on the coordinate plane below. …
B. Triangle EFG was dilated with a center of dilation at vertex G, reflected about side EG, and translated two units down and four units to the right to create triangle E'F'G'.
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the width of a rectangle measures $(8u - 4)$ centimeters, and its lengt…
-12 + 32u
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determine if polygon vwxyz is similar to polygon mnpqr. if the polygons…
D. No, the polygons are not similar. The corresponding sides are not proportional.
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try it! 2. describe a series of transformations that shows (\triangle j…
First, rotate \(\triangle JKL\) to align the sides with the same tick - mark ( \(KL\) and \(NO\)). Then, translate and possibly reflect \(\triangle JKL\) so that the corresponding…
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look at the diagram. which equation can be used to solve for x? 5 + x =…
The equation is \(5x + 65=180\) and \(x = 23\)
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look at the diagram.which equation can be used to solve for x?5 + x = 6…
\(5x + 65 = 180\)
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look at the diagram. which equation can be used to solve for x? 13x - 1…
The equation is \(13x - 14 = 90\) and \(x = 8\)
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remember, even if you enter an answer rounded to a set number of decima…
$\sin B\approx0.90909$; $B_1 = 65.3^{\circ}$, $B_2 = 114.7^{\circ}$; $C_1 = 73.4^{\circ}$, $c_1\approx263.9$; $C_2 = 24.0^{\circ}$, $c_2\approx111.9$
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look at the diagram. which equation can be used to solve for x? 13x - 1…
\(13x - 14=90\)
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triangle abc was transformed to create triangle pqr. determine if trian…
# Explanation: ## Step1: Find the lengths of sides of triangle ABC Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or counting units on the grid. For \(AB\):…
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look at the diagram. which equation can be used to solve for x? 8x + 10…
The equation is \(8x + 10 = 90\) and \(x = 10\)
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1. what is the relationship between bx and cy? what conclusion can you …
\(BX = CY\) and \(\triangle AXB\cong\triangle CDY\) (by AAS congruence criterion as \(\angle A=\angle D\), \(\angle B=\angle C\) and \(AB = CD\))
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quadrilateral hijk was changed to create quadrilateral lmnp determine i…
D. Quadrilateral \(HIJK\) is similar to quadrilateral \(LMNP\) because dilation \((x,y)\) to \((0.5x,0.5y)\) maps quadrilateral \(HIJK\) to quadrilateral \(LMNP\).
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look at the diagram. which equation can be used to solve for x? 2x + 3x…
\(x = 7\)
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look at the diagram. which equation can be used to solve for x? 39x = 9…
The equation is \(3x + 36 = 90\) and \(x = 18\)
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triangle pqr was changed to create triangle stu determine if triangle p…
C. Triangle PQR is similar to triangle STU because dilation \((x,y)\) to \((0.25x,0.25y)\) maps triangle PQR to triangle STU.
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the scale is 1 in = 2 ft. area of triangle = \\( \\frac { 1 } { 2 } b h…
\(60\)
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given: \\( \\triangle pqr \\) is a dilation of \\( \\triangle pqr \\) b…
\(\overline{PR}\parallel\overline{P'R'}\), \(\angle QPR\cong\angle Q'P'R'\), Dilated segments are parallel, \(\angle PQR\) & \(\angle P'Q'R'\) are both right angles, \(\overline{Q…
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the scale is 1 in. : 2 ft area of triangle = \\( \\frac { 1 } { 2 } b h…
Actual base \( = 10\) ft, Actual height \(=12\) ft
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determine if polygon j k l m is similar to polygon p q r s. if the poly…
B. Yes, the polygons are similar. The similarity ratio is \(\frac{1}{2}\)
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points a and b are separated by a lake. to find the distance between th…
\(382.17\)
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what is the value of d?
\(32.7\)
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area of triangle = \\( \\frac { 1 } { 2 } b h \\) find the actual base …
Actual base \(=\frac{5}{12}\) ft, Actual height \(=\frac{1}{2}\) ft
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the graph shows triangle pqr with vertices p(0,2), q(6,4), and r(4,0) a…
B. \((16,12)\)
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if the polygons are similar, identify the similarity ratio. *note: figu…
B. No, the polygons are not similar. The corresponding sides are not proportional.
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the lengths of the legs of a right triangle are 5 and 6. the length of …
A. \(5^{2}+6^{2}\)
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what is the value of n?
\(102.5\)
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5. what does the circle of fifths illustrate in music theory? a. the rh…
C. The relationships among the 12 tones of the chromatic scale
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what is the value of m?
\(30\)
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an angle measures 20° less than the measure of its supplementary angle.…
\(80\) and \(100\)
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5. a polygon has a perimeter of 12 units. it is dilated with a scale fa…
C. 16 units
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what is the value of z?
\(51\)
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what is the value of u?
\(58.1\)
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what is the value of y? 100.6°
\(79.4\)
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what is the value of q?
\(44.1\)
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plane geometry hw: lesson 3 - 3 due fri 10/31 *not accepted after the u…
The scale factor of the dilation is \(\frac{5}{3}\)
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what is the value of c? 31° submit
\(121\)
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what is the value of t? 34° t
\(34\)
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what does the circle of fifths illustrate in music theory? a. the tempo…
C. The relationships among the 12 tones of the chromatic scale
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what is the value of z?
\(72\)
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3.) polygon p is dilated to get polygon q. a.) what is the value of y? …
a. \(y = 4.5\) b. The scale factor is \(\frac{3}{4}\)
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what does the formula note position = (7×steps) mod 12 determine? a. th…
C. The position of a note in the Circle of Fifths