Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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9. what is the result of a 90 - degree clockwise rotation followed by a…
Rotation and reflection
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18. competency check replace each unknown box, ■, with algebra tiles to…
The unknown box should have \(-x^{2}+x + 3\) (one negative large square, one positive rectangle, and three positive small squares). The reasoning is based on equating the coeffici…
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8. if a triangles vertices are reflected across the x - axis, which tra…
\((x,-y)\)
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7. what is the result of rotating a point (x, y) 90 degrees countercloc…
\((-y,x)\)
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identify the angle shown below as acute, right, obtuse, straight, or re…
Obtuse
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carpentry mr. lewis is building a rustic dining table. instead of havin…
\(41^{\circ}\)
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6. if a point (3, 4) is translated by (2, -1), where is it? (3, 5) (1, …
\((5,3)\) (the third option)
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5. what is the result of reflecting a point $(x,y)$ across the $y$-axis…
\((-x,y)\)
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4. select all that apply: a rigid motion.. the position changes the ori…
The position changes, The orientation changes, The shape does NOT change, The size does NOT change
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∠uzv ≅ ∠xwy, ∠vuz ≅ ∠wxy, and \\overline{yz} ≅ \\overline{vw}. complete…
\(\triangle UZV\cong\triangle XWY\) (AAS); Corresponding parts of congruent triangles are congruent. So, \(\overline{UV}\cong\overline{XY}\)
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a composition of two reflections across parallel lines is... nothing, w…
a translation
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2. when a composition of transformations of \\( \\triangle a b c \\) is…
\(\triangle A''B''C''\)
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question 1 1. an example of a composition of transformations is a trans…
D. A translation then a reflection
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28. what is the effect of a 270 - degree clockwise rotation about the p…
\((-4,-6)\)
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27. what is the effect of a 270 - degree clockwise rotation about the o…
\((2,-2)\)
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design camila is designing a new image for her cell phone case. if ( ma…
\(116\)
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18. competency check replace each unknown box, ■, with algebra tiles to…
The unknown box should be replaced with one red large square (representing \(-x^{2}\)), one green rectangle (representing \(x\)), and three green small squares (representing \(+3\…
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26. what is the result after rotating a right triangle 90 degrees count…
The triangle preserves its shape but changes its orientation.
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25. a point (3,5) is rotated 90 degrees counter - clockwise about the o…
A. \((-5,3)\)
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24. what will be the rotation of a point on origin (0,0) when rotated 1…
The point remains the same
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23. a point is at (3, -4) in the coordinate plane. what coordinates wil…
\((3,14)\) (the third option)
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22. a point is at (3, -4) in the coordinate plane. what coordinates wil…
\((-3,4)\)
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find the value of x. round to the nearest degree. 14 9
\(33\)
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21. considering rotational transformation on a coordinate plane, how ma…
180 degrees
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show that the polygons are congruent by identifying all the congruent c…
$\angle X\cong\angle A$; $\angle Y\cong\angle B$; $\angle Z\cong\angle C$; segment $XY\cong$ segment $AB$; segment $XZ\cong$ segment $AC$; segment $YZ\cong$ segment $BC$; $\triang…
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20. a square is rotated about its center. what is the smallest degree o…
90 degrees
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writing a two - column proof given: \\( \\angle abc \\cong \\angle def …
| Statements | Reasons | | --- | --- | | \(m\angle ABC=m\angle DEF\) | Definition of congruent angles (\(\angle ABC\cong\angle DEF\)) | | \(m\angle GHI = m\angle DEF\) | Definitio…
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find the value of x. round to the nearest tenth.
\(33.9\)
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19. in rotational symmetry, an object is rotated about a fixed point ca…
Center of rotation
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18. a point a (2, 0) on a coordinate plane is rotated 90 degrees counte…
\((0,2)\)
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17. what is the degree of rotation that completes 1 full cycle on a coo…
360 degrees
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find the missing angle. round answer to the nearest degree
\(37^{\circ}\)
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concept rotations a rotation ( r_{(x, p)} ) is a transformation that ro…
15. True 16. False
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concept rotations a rotation ( r_{(x^{circ}, p)} ) is a transformation …
Is a ccw rotation, where the center of rotation is at the origin.
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concept rotations a rotation ( r_{(x^{circ}, p)} ) is a transformation …
Is a cw rotation, where the center of rotation is at \((2,1)\)
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find the value of x. round all answers to the nearest hundredth.
\(11.03\)
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12. resequence the events that the video showed to find the new image o…
1. Determine the coordinates of each vertex in the image that is to be rotated. 2. Subtract the center of rotation from each of the points, to make the center of rotation at the o…
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fill in the blank 1 point complete the proof. copy the diagram to your …
2. \(VY = WY\) (Common side, reflexive property of congruence). 3. \(SAS\) (Side - Angle - Side congruence criterion)
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11. why do we need to add 2 to the x and add 1 to the y? the video said…
B. The center of rotation is supposed to be at the point \((2,1)\) C. We altered the original point by subtracting \(2\) and subtracting \(1\). Then add \(2\) and add \(1\) cancel…
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what trig function are you using to solve this problem. cosine sine tan…
Sine
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what is the tan (s) t 90 r 56 106 s 28/45 45/28 28/53 45/53
$45/28$
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10. select all that apply: subtracting 2 units from the x and 1 unit fr…
B. Shifts the graph, 2 units to the left and 1 unit down. C. Moves the center of rotation 2 units left and 1 unit down. D. The center of rotation \((2,1)\) becomes \((0,0)\)
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learning goal: by the end of class, students will know about the rotati…
The center of rotation is any other point but the origin.
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what is the cos (s) 28/53 45/28 45/53 28/45
28/53
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what is the sin (s) 28/45 45/28 45/53 28/53
\(\frac{45}{53}\) (corresponding to the option \(45/53\))
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fill in the blank 1 point complete the proof. copy the diagram to your …
3. \( \overline{QS}\cong\overline{SU}\) 4. \(SSS\) (Side - Side - Side) Congruence Criterion
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which side is adjacent to \\( \\angle b \\)?
\(BC\)
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7. a rotation is a circular turn around a fixed point (usually the orig…
A circular turn around a fixed point (usually the origin), A change in orientation, Can be a change in Location
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which side is opposite to <b? ac bc ab
AC
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given: bd bisects ∠abc, ∠bad ≅ ∠bcd prove: △abd ≅ △cbd 1. bd bisects ∠a…
1. REASONS Line 2 - Definition of Angle Bisector 2. REASONS Line 3 - Given 3. REASONS Line 4 - Reflexive Property 4. REASONS Line 5 - AAS
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a 12 - foot long ladder leans against the side of a house. if the ladde…
A. \(6\sqrt{3}\)
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what is the value of y 18 30° √3 9 9√3 18
\(9\sqrt{3}\)
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question 8 what is the value of x 18 30° y
\(x = 9\)
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what is the value of x
\(13\)
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is this a right triangle? 18 30 24 screenshot 2025 - 09 - 22 133525.png…
yes
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is a triangle with these sides a right triangle? 8, 15, 17 yes no
yes
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is a triangle with these sides a right triangle? 18, 24, 32 no yes
no
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find the value of x. 5 12 x
\(13\)
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in the diagram, line a is the perpendicular bisector of \\( \\overline …
80 units
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what is sin α? (-√13,6) r α sin α =
\(\frac{6}{7}\)
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consider the incomplete paragraph proof. given: p is a point on the per…
point \(M\)
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what is \\( \\tan \\beta \\)? \\( \\tan \\beta = \\frac { \\sqrt { ? } …
\(11\)
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consider the diagram. lines a and d are non - coplanar. parallel. perpe…
skew.
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for the right triangle below, find the measure of the angle. please sho…
\(46.2^{\circ}\)
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consider the diagram. what is the length of segment ab? 7 9 18 25
9
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use the given information to prove that ( overline{ps} cong overline{rs…
\(\overline{PS}\cong\overline{RS}\) is proved as above.
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for the right triangle below, find the measure of the angle. please sho…
\(46.6^{\circ}\)
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consider the diagram. lines ac and rs are coplanar. parallel. perpendic…
skew.
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for the right triangle below, find the measure of the angle. please sho…
\(56.4^{\circ}\)
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complete the square and write the given equation in standard form. then…
The equation of the circle in standard form is \((x + 4)^{2}+(y - 2)^{2}=32\) The center of the circle is \((-4,2)\) The radius of the circle is \(r = 4\sqrt{2}\)
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in the diagram, the length of segment tq is 40 units. what is the lengt…
40 units
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check your answers by referring to the checkpoint 4 materials located a…
- a. Area: \(28.26\space cm^{2}\), Circumference: \(18.84\space cm\) - b. Area: \(78.5\space ft^{2}\), Circumference: \(31.4\space ft\) - c. Area of the shaded sector: \(150.72\sp…
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planes q and r are parallel planes. plane q contains line a. plane r co…
lines \(a\) and \(b\) must be parallel.
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show that the polygons are congruent by identifying all the congruent c…
\(\angle A\cong\angle D\); \(\angle ABC\cong\angle DCB\); \(\angle ACB\cong\angle DBC\); segment \(AC\cong\) segment \(DB\); segment \(AB\cong\) segment \(CD\); \(\triangle ABC\co…
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in the diagram shown, the distance between points a and c is the same a…
perpendicular.
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consider the diagram. which line segment has the same measure as st? rx…
\(\overline{SR}\)
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fluency 1. the function ( y = f ( x ) ) is shown graphed below. answer …
(a) \( f(-2)=8 \), \( f(6)=2 \) (b) \( f(2)-f(-6)=-10 \) (c) Zeros: \( x=-4,x = 9 \) (d) \( y \)-intercept: \( -2 \) (e) Minimum: \( -4 \), Maximum: \( 8 \) (f) Turning points: \(…
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in the diagram, tq is 18 units in length. what is the length of rs? 46 …
16 units
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explain what the slope and y - intercept mean in each situation. part a…
- **Part A**: The slope \(3\) means the perimeter increases by \(3\) units per 1 - unit increase in side length. The \(y -\)intercept \(0\) means perimeter is \(0\) when side leng…
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analyzing a statement marissa says that lines a and d will eventually i…
no, because they are parallel
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what is the measure of ac? 5 units 13 units 26 units 39 units
# Explanation: ## Step1: Use the property of mid - segment in a triangle In a triangle, if a line segment connects the mid - points of two sides of a triangle, then it is parallel…
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graph $xgeq1\frac{1}{2}$.
Graph a closed - circle at \(1.5\) on the number line and draw an arrow to the right.
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solving for an unknown segment length what is the length of segment lm?…
\(23\)
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for the right triangle below, find the measure of the angle. please sho…
$39.8^{\circ}$
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for each figure, use rigid motions to verify that the triangles are con…
\(\triangle ABC\cong\triangle CDA\) by the SAS (Side - Angle - Side) congruence theorem.
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determining segment lengths the length of tr is 17 units. what are the …
\(SV = 10\) units, \(QT=5\) units
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c. given: tr intersects np, tu ≅ ru, and nu ≅ pu verify that △tun ≅ △ru…
\(\triangle TUN\cong\triangle RUP\) by the SAS (Side - Angle - Side) congruence criterion.
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find the angle between 0 and 2π in radians that is coterminal with the …
\(\frac{2\pi}{3}\)
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find the radian measure for each of the following angles. enter each an…
\(70^{\circ}=\frac{7\pi}{18}\) radians, \(160^{\circ}=\frac{8\pi}{9}\) radians, \(140^{\circ}=\frac{7\pi}{9}\) radians, \(90^{\circ}=\frac{\pi}{2}\) radians.
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a. given: parallelogram abcd and (overline{ab}paralleloverline{cd}) ver…
\(\triangle ABC\cong\triangle CDA\) by the SSS congruence criterion.
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planes q and r are parallel. explain how you know lines a and b are ske…
Lines \(a\) and \(b\) are skew because they are non - intersecting (as planes \(Q\) and \(R\) are parallel) and non - parallel.
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standard 13 homework score: 5/27 answered: 4/22 progre question 5 conve…
\(\frac{2}{3}\pi\)
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examining lines in three dimensions are the lines in the diagram perpen…
\( l \) and \( m \): skew; \( l \) and \( n \): skew; \( m \) and \( n \): perpendicular
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planes m and n intersect at line d. line a forms a right angle with lin…
c and b, e and c, a and c
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use the diagram to complete the statements. segment ad must be congruen…
Segment \(AD\) must be congruent to segment \(AE\). Segment \(BC\) must be congruent to segment \(DE\).
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each column of the matrix ( a=left\begin{array}{llll}1 & 6 & 6 & 1 \\ 1…
A. (4, 4), (24, 4), (24, 20), (4, 20)
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standard 13 homework score: 1/27 answered: 1/22 progress saved done que…
In radians: \(\frac{1}{2}\) In degrees: \(28.65\)
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for the right triangle below, find the measure of the angle. round your…
$23.2^{\circ}$
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on a circle of radius 2 feet, what angle would subtend an arc of length…
In radians: \(\frac{9}{2}\) In degrees: \(257.83\)
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for the right triangle below, find the measure of the angle. round your…
\(40.0^{\circ}\)