Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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24 multiple choice 4 points if three angles in one triangle are congrue…
no
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45) through: (4, 4), parallel to $y = 2x - 5$ 46) through: (4, -2), par…
\(y = 2x-4\) ### Problem 46: Find the equation of the line through \((4,-2)\) parallel to \(y=\frac{1}{4}x\)
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state how the triangles are congruent using sss, sas, asa, aas, or hl. …
AAS (assuming the correct congruence) ### Second Triangle Answer:
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13. if m∠7 = -2x - 1 and m∠2 = 9x + 46, solve for x and find m∠7 and m∠…
\( x = -\frac{47}{11}\), \( m\angle7=\frac{83}{11}\), \( m\angle2=\frac{83}{11}\) (or in decimal form \( x\approx - 4.27\), \( m\angle7\approx7.55\), \( m\angle2\approx7.55\))
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14. match the equation to its perpendicular slope draggable item → corr…
- \( y=\frac{1}{2}x + 2 \) corresponds to \( - 2 \) - \( y = -\frac{1}{2}x-2 \) (corrected) corresponds to \( 2 \) - \( y=-2x + 1 \) corresponds to \( \frac{1}{2} \) - \( y = 2x-1…
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slope of line: $m = \\frac{y_2 - y_1}{x_2 - x_1}$; integer coordinates …
\(m = \frac{y_2 - y_1}{x_2 - x_1}\), \((x_1,y_1)\), \((x_2,y_2)\), \(y - y_1 = m(x - x_1)\), \(1\), \((-4,-13)\), \((12,3)\), \(y - 3 = x - 12\)
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1. interior roof structure typical interior roof structures use beams a…
To prove \( \triangle CAB \cong \triangle DEB \): 1. **Given**: \( B \) is the midpoint of \( \overline{AE} \) ⇒ \( \overline{AB} \cong \overline{EB} \) (Definition of Midpoint). …
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which rule explains why these scalene triangles are similar? diagram of…
none of the above; the triangles cannot be proven similar
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angle abc is a right angle. the measure of angle dbc is 55°. the measur…
35
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2. write the equation that is perpendicular to $y = -3x + 2$ and passes…
\( y=\frac{1}{3}x - 4 \)
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state whether δabc and δaed are congruent. justify your answer. options…
A. yes, by either SSS or SAS ### Question 2 (Triangles in the second diagram)
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angle stv is a straight angle. the measure of angle wtv is 25°. the mea…
\(155\)
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write the correct equation for this problem. do not solve. image of a r…
\(\tan(58^{\circ})=\frac{11}{x}\)
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quadrilateral abc is graphed on a coordinate plane. vertex a is located…
B. \((-4, 6)\) (assuming the second option is labeled B, as per the options given: first \((-4,5)\), second \((-4,6)\), third \((0,5)\), fourth \((6,-4)\))
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angle abc is a right angle. the measure of angle abd is 50°. the measur…
\( x = 40 \)
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fill in the blank 5 points state how the triangles are congruent using …
AAS ### Problem 2 (Middle Triangle Congruence: \( \triangle GHI \) and \( \triangle GJI \))
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4.3 extra practice in exercises 1 and 2, determine which of the lines, …
The cable will pass through the road at the point \((3,-4)\)
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line l is shown below. right triangles abc and def are drawn to measure…
s: ## (a) rise: \( 10 \) run: \( 2 \) slope: \( 5 \) ## (b) rise: \( 10 \) run: \( 2 \) slope: \( 5 \) ## (c) Yes. They are equal because the two triangles are similar.
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what else must you know to prove the triangles congruent by asa? option…
\(\boldsymbol{\angle DCA\cong\angle BCA}\) (the option with \(\angle DCA\cong\angle BCA\)) ### Second Sub - Question (Fill in the Blank)
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find the perimeter or the area. 9. $\\parallelogram abcd \\sim \\parall…
36 cm ### Problem 10
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type of angles are supplementary? wing proof: 8 = 180° | given | reason…
The error is in the reasoning for \(m\angle5 \cong m\angle8\); the reason "Linear Pair" is incorrect (linear pair angles are supplementary, not necessarily congruent). The correct…
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state how the triangles are congruent using sss, sas, asa, aas, or hl. …
SAS ### Second Triangle (Middle)
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complex numbers complex numbers review 0 0 5 10 x click for long desc t…
\( y = \frac{1}{2}x - 1 \) (the first option: \( \boldsymbol{y = \frac{1}{2}x - 1} \))
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the circumference of a circle is 37.68 feet. what is the circles radius…
\( 6.00 \)
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the diameter of a circle is 34 yards. what is the circles circumference…
\( 106.81 \)
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6. name all the alternate exterior angles: 7. name all the linear pairs…
### Question 10 Proof: 1. \( a \parallel b \) (Given) 2. \( \angle1 \) and \( \angle2 \) are a linear pair (Definition of linear pair) 3. \( m\angle1 + m\angle2 = 180^\circ \) (Li…
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the radius of a circle is 2 miles. what is the circles circumference? r…
12.57
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write the equation you would set up for this problem. do not solve. ima…
\(\cos(37^{\circ})=\frac{x}{14}\) (or \(x = 14\cos(37^{\circ})\))
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the formula that relates the length of a ladder, l, that leans against …
14.6 feet
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state how the triangles are congruent using sss, sas, asa, aas, or hl. …
SSS ### Second Triangle (L, M, N, O, P)
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possible points: 100 the circular rim of a basketball hoop has a diamet…
56.5 inches (the second option, assuming the options are 26.3, 56.5, 113.0, 254.3; so the answer is the option with 56.5 inches, e.g., if it's labeled as the second option, like B…
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identify $\\angle edc$ by clicking and dragging the small yellow dots t…
To identify \( \angle EDC \), shade the angle with vertex at \( D \), between the segments \( DE \) and \( DC \) by dragging the yellow dots on \( DE \), \( D \), and \( DC \). (N…
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multiple choice 4 points what other information do you need in order to…
\( \boldsymbol{\angle BAC\cong\angle DAC} \) ### Question 5 (Triangles Congruent via SAS)
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d. c = 8\ 65° c 480 x
\(C\approx18.93\) inches (or if we consider angle, but the label \(C\) is on the side, so it's length. If it's angle, then the other non - right angle is \(25^{\circ}\), but the l…
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identify $\\angle acb$ by clicking and dragging the small yellow dots t…
To identify \( \angle ACB \), shade the angle with vertex at \( C \), between the segments connecting \( C \) to \( A \) and \( C \) to \( B \) (by dragging the yellow dots on the…
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identify two segments that are marked parallel to each other on the dia…
\(OH\) is parallel to \(IJ\) (or other valid pairs like \(NG\parallel OH\), \(NG\parallel IJ\))
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identify two segments that are marked congruent to each other on the di…
\( HE \) is congruent to \( FG \) (or \( HG \) is congruent to \( EF \), or \( EI \) is congruent to \( GI \), or \( HI \) is congruent to \( FI \))
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yes no write a similarity statement. △□ ~ △
$\triangle GHD \sim \triangle EHF$
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categorize the following images with the correct equation setup. the li…
- Middle Graph (labeled 23): Equation \(2x + 3+5x = 180\) - Right Graph (labeled 22): Equation \(2x + 3 = 5x\)
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the diagram below shows the floor plan for an apartment complex. the le…
# Explanation: ## Step1: Determine the scale The distance from the study to the kitchen on the plan is \(2 + 3 = 5\) inches (wait, no, the study is 2" and kitchen is 3"? Wait, the…
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yes no write a similarity statement. △□ ~ △
\(\triangle KJG \sim \triangle KIH\) (or \(\triangle KGJ \sim \triangle KHI\), but the most appropriate based on the diagram's vertex labels is \(\triangle KJG \sim \triangle KIH\…
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reflect the given point over the line in the graph.
To reflect a point \((x,y)\) over a vertical line \(x = h\), the reflected point is \((2h - x,y)\). If the vertical line in the graph is \(x=-2\) (from the grid), and the original…
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the diameter of a circle is 8 centimeters. what is the circles circumfe…
\( 25.13 \)
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use the slope and y-intercept to write the equation of the line. first,…
\(\frac{1}{2}\)
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the radius of a circle is 14 feet. what is the circles circumference? r…
87.96
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mid-term assessment in the diagram, the two quadrilaterals are similar.…
\( 0.32 \)
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the graph of a line is shown on the coordinate plane below. the graph o…
A. \(y=\frac{1}{2}x + 1\)
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the diameter of a circle is 12 feet. what is the circles circumference?…
\( 37.70 \)
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are these scalene triangles similar? (image of two triangles with verti…
\(\triangle VWS \sim \triangle TWU\)
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drag each tile to the correct box. arrange the vector operations in inc…
1. \( \mathbf{c}+(-\mathbf{d}) \), where \( \mathbf{c}=\langle 2,7 angle \) and \( \mathbf{d}=\langle 3,5 angle \) 2. \( \mathbf{g}+(-\mathbf{h}) \), where \( \mathbf{g}=\langle 3…
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final exam 100 points possible answered: 19/22 question 18 you must sho…
\(45.6950\)
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write the correct equation for this problem. do not solve.
\(\cos(58^{\circ})=\frac{x}{11}\) (or \(x = 11\cos(58^{\circ})\))
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the circumference of a circle is 106.76 millimeters. what is the circle…
17.00
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which rule explains why these triangles are similar? (image of two tria…
AA (the option labeled "AA")
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in a scale model of a boat, 1 inch represents 9 feet. scale 1 in : 9 ft…
s: (a) \( 7 \) inches (b) \( 90 \) feet
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which of the following best describes the transformation from rectangle…
Reflection across \( x = 0 \) (the option corresponding to "Reflection across \( x = 0 \)")
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question 18 you must show work here for full credit! given the triangle…
\(45.6951\)
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drag a figure into each blank space so that the two figures in the row …
- Not Similar but Corresponding Angles Have Equal Measures: Drag the blue square (5 by 5). - Not Similar but Side Lengths Are Proportional: Drag the blue rhombus (3, 3, 4, 4). - S…
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both u - v and u + (-1v) produce the same resultant vector, which is <5…
\(\langle 0, 0 angle\) (or the zero vector)
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1) a rectangles length is three meters less than twice of width. its ar…
The perimeter of the rectangle is approximately \( \boldsymbol{19.8} \) meters.
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each pair of triangles is similar. find the value of x. 5. 6. 7. 8.
s: Problem 5: \( \boldsymbol{3}\) Problem 6: \( \boldsymbol{15}\) Problem 7: \( \boldsymbol{96}\) Problem 8: \( \boldsymbol{\frac{16}{3}}\) (or \( 5\frac{1}{3}\))
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scale 1 in : 10 ft answer the following. (a) in the scale drawing, the …
(a) The correct length of the real airplane is 80 feet (the given 9 feet is incorrect). (b) The wingspan in the scale drawing is 9 inches.
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hide sample answer -1v = <-1 × -3, -1 ×5> = <3, -5> part c add vectors …
Assuming \( \mathbf{u} = \langle 2, 3 angle \) (or correct \( \mathbf{u} \) from problem), the result is \( \boldsymbol{\langle 5, -2 angle} \) (or based on actual \( \mathbf{u} \…
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in a scale drawing of an airplane, 1 inch represents 10 feet. scale 1 i…
80 ### Part (b)
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introduction to similarity - item 32250 the two statements below are di…
\(\frac{d}{p} = \frac{e}{q} = \frac{f}{r}\)
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part b because we cannot represent subtraction of vectors on a plane us…
To find \(-\mathbf{v}\) (the additive inverse of \(\mathbf{v}\)) using scalar multiplication, we multiply each component of \(\mathbf{v}\) by \(- 1\). If \(\mathbf{v}=\langle v_1,…
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8 ft 6 ft what is the length of the hypotenuse? ft
10
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directions read the instructions for this self - checked activity. type…
\(\langle 5, - 8 angle\)
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write the equation you would set up to solve this problem. do not solve…
\(31^{2}+x^{2}=67^{2}\)
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which rule explains why these triangles are similar? h 33 46 r 45 i p 4…
none of the above; the triangles cannot be proven similar
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fill in the missing values to find the missing value of the triangle. $…
The first missing value (in \(16+\square = c^{2}\)) is \(9\), and the second missing value (in \(\square=c\)) is \(5\). So the completed steps are \(16 + 9=c^{2}\) and \(5=c\).
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write an equation for the transversal. 5x + 50, 2x - 20
\(5x + 50+2x-30 = 180\) (or simplified as \(7x + 20=180\))
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label the picture according to the description below. you will not need…
The ladder (hypotenuse) should be labeled 50, the height on the building (vertical leg) 40, and the distance from the building to the base of the ladder (horizontal leg) 30. (Assu…
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select all the pairs of alternate exterior angles. ∠rsv and ∠rsq ∠uvx a…
$\angle UVX$ and $\angle TSQ$
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this vector lies in the first quadrant because its horizontal and verti…
(Example answer assuming match) Yes, the results in part I (angle \(26.57^\circ\) in the first quadrant) match the predictions in part H (e.g., predicting the vector lies in the f…
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write the equation you would set up for this problem. do not solve.
\(\cos(37^{\circ})=\frac{x}{14}\) (or \(x = 14\cos37^{\circ}\))
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select all the pairs of alternate exterior angles. ∠mln and ∠hig ∠jig a…
The pairs of alternate exterior angles are ∠MLN and ∠HIG, ∠JIG and ∠KLN. (So select these two options: "∠MLN and ∠HIG" and "∠JIG and ∠KLN")
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fill in the missing values to find the missing value of the triangle. (…
The left - hand side box (under \(12^{2}\)) is \(144\), and the right - hand side box (for \(c\)) is \(15\). If we consider the final value of \(c\) (the question might be asking …
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if mnop is a rhombus, find mp. what steps would you take to solve the p…
First: \( 9x - 77 = 3x + 7 \) Then: substitute into either expression
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select all the pairs of alternate exterior angles. ∠mln and ∠hig ∠jig a…
∠JIG and ∠KLN, ∠MLN and ∠HIG (But according to the options, if we have to choose from the given, the correct pairs are ∠JIG and ∠KLN (second option) and ∠MLN and ∠HIG (first optio…
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fill in the missing values to find the missing value of the triangle. (…
The first missing value (in the left box) is \(64\), and the second missing value (in the right box) is \(10\). So the completed equations are \(64+36 = c^{2}\) and \(10 = c\).
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use the pythagorean theorem to calculate the hypotenuse of a right tria…
5
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part f what does the angle comparison that you made in part e tell you …
The new vector ( - 4v) is in the opposite direction of the original vector (v) because the angle between them is \(180^{\circ}\), indicating they are antiparallel.
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given the right triangle below and the angle θ, answer the following qu…
s: - Side \( a \) is: adjacent to \( \theta \) - Side \( b \) is: opposite to \( \theta \) - Side \( c \) is: the hypotenuse
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label the triangle in accordance with the word problem: a ladder leanin…
- Right angle: 90 - Angle with ground: 20 - Remaining angle: 70 (And assign 5 or x to the appropriate side as per the diagram's labels, but based on angle labeling, the angles are…
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use the diagram below to find the distance across the river. round your…
The distance across the river is approximately \(23.9\) feet.
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select all the pairs of corresponding angles. ∠onk and ∠lki ∠onk and ∠j…
The correct pairs of corresponding angles are: - $\angle ONK$ and $\angle LKI$ - $\angle JKI$ and $\angle MNK$ - $\angle ONP$ and $\angle LKN$
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y = \\frac{2}{7}x - 6 click to select points on the graph. (graph with …
To plot the line \(y = \frac{3}{7}x-6\), select the points \((0, - 6)\) (y - intercept) and \((7,-3)\) (using the slope \(\frac{3}{7}\)) on the graph.
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part b now multiply vector v with the negative scalar value -4 and writ…
The problem is incomplete as the component form of vector \(\mathbf{v}\) is not provided. If \(\mathbf{v}=\langle v_1, v_2 angle\), then \(-4\mathbf{v}=\boldsymbol{\langle -4v_1, …
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name a. jurn loger date 12-12-25 hour 1 7. given: line j is parallel to…
\(\angle 1\cong\angle 2\cong\angle 3\) is proven as shown above.
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a tree standing vertically on level ground casts a 20 foot long shadow.…
49.6
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select all the pairs of corresponding angles. ∠pqt and ∠stv ∠utv and ∠r…
∠PQT and ∠STV, ∠UTV and ∠RQT, ∠UTQ and ∠RQO
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Question was provided via image upload.
1. Second part of Statement 1: \(\boldsymbol{\overline{DE} \perp \overline{BC}}\) 2. Reason for Statement 2: \(\boldsymbol{\text{perpendicular}}\) 3. Statement 3: \(\boldsymbol{\a…
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select all the pairs of vertical angles. ∠lkn and ∠jki ∠onk and ∠mnp ∠l…
The pairs of vertical angles are \( \angle LKN \) and \( \angle JKI \), \( \angle ONK \) and \( \angle MNP \), \( \angle LKI \) and \( \angle JKN \).
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use the following figure to complete the following sentences. select al…
s: ### For "The side with length \( a \) is": - adjacent to \( \angle B \) - opposite of \( \angle A \) ### For "The side with length \( b \) is": - adjacent to \( \angle A \) - o…
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a. write similarity statements for three pairs of similar triangles. b.…
(Part a): \( \triangle KJN \sim \triangle LMN \), \( \triangle KLM \sim \triangle JPM \), \( \triangle KJN \sim \triangle KLM \)
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which angles are corresponding angles? ∠noq and ∠poq ∠noq and ∠pol ∠noq…
$\angle NOQ$ and $\angle KLO$ (the option: $\angle NOQ$ and $\angle KLO$)
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which angles are alternate exterior angles? image of two parallel lines…
\( \angle PQO \) and \( \angle UTV \) (the last option: \( \angle PQO \) and \( \angle UTV \))
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5. find the slope of the line below. (type a response)
\(1\)
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which angles are consecutive interior angles? ∠tux and ∠wxu ∠tus and ∠y…
$\angle TUX$ and $\angle WXU$ (the first option)