几何
三角形、圆、解析几何与证明题。
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in this section, youll solve problems involving geometric constructions…
Square
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in the figure, ( a parallel b ) and ( mangle 1 = 34^circ ). what is the…
\(34\)
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graph the line $x = -1$
To graph \( x=-1 \), draw a vertical line passing through \( x = - 1 \) on the \( x \)-axis (parallel to the \( y \)-axis, intersecting the \( x \)-axis at \( (-1,0) \) and extend…
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in the figure, ( x parallel y ) and ( a ) is a transversal that crosses…
$\boldsymbol{\angle 1 \text{ and } \angle 5}$
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the local restaurant website includes restaurant reviews and places cus…
Both shapes are quadrilaterals.
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$\\angle vyx \\cong \\angle vwx$ and $\\angle wvy \\cong \\angle wxy$. …
Statement 6: \( \overline{WX} \parallel \overline{VY} \) Reason 6: Consecutive Interior Angles Theorem (If two consecutive interior angles are supplementary, then the lines are pa…
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what is the name of the relationship between $\\angle 1$ and $\\angle 5…
corresponding angles
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applying trigonometric ratios to estimate side lengths rounded to the n…
2.7
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what is a pair of supplementary angles if line m and n are parallel? ○ …
$\boldsymbol{\angle5 \text{ and } \angle8}$
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the last step before going live is selecting and setting up your lighti…
Three
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triangle 5: choose a number between 30-50 for the opposite side, and be…
Let's take Opposite \( = 40 \), Theta \( = 53.13^\circ \) (approximate angle where \( \sin\theta = 0.8 \), \( \cos\theta = 0.6 \)) - Adjacent Side \( = 30 \) - Hypotenuse \( = 50 …
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a video that you posted shows you preparing an order of nachos. you pre…
40 centimeters
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find the value of \\(\\sin d\\) rounded to the nearest hundredth, if ne…
$0.58$
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practice what you’ve learned an illusionist develops a plan to create a…
$136$
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express cos m as a fraction in simplest terms.
$\frac{3}{5}$
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identifying trigonometric ratios to estimate side lengths what are the …
$\sin(20^{\circ})=\frac{LN}{8}$, $\cos(70^{\circ})=\frac{LN}{8}$ (i.e., the first and the fifth options)
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in this section, you’ll solve problems involving geometric construction…
B. Square
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question 1 (11.11 points) listen in this section, you’ll identify, clas…
The two equilateral triangles form a rhombus (or a parallelogram with all sides equal, which is a rhombus).
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check the slope box and click and drag one of the labeled coordinate po…
\((1, - 2)\)
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which angles are adjacent angles?\ $\\angle xwt$ and $\\angle utr$\ $\\…
\(\boldsymbol{\angle XWT}\) and \(\boldsymbol{\angle VWT}\)
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erik states that the two cones below have the same volume because of ca…
No, the heights of the cones are not the same, so Cavalieri's principle does not apply.
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which angles are alternate interior angles?\ $\\angle pqn$ and $\\angle…
\( \angle PQN \) and \( \angle ONQ \)
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which angles are corresponding angles? \\(\\angle vux\\) and \\(\\angle…
\(\boldsymbol{\angle VUX}\) and \(\boldsymbol{\angle YXZ}\)
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which option best describes the relationship between ∠1 and ∠8? - alter…
Alternate exterior angles
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using the slope formula, find the slope of the line through the given p…
A. The slope of the line is \(-1\)
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find the slope of the line containing the pair of points. (-2, -7) and …
A. The slope is \(\frac{9}{5}\)
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using the side lengths of $\\triangle pqr$ and $\\triangle stu$, which …
\(\angle P\)
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comparing volumes look at the two stacks of coins. each stack contains …
- The two stacks have equal volume.
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two students describe the sides of right triangle abc in relation to ∠b…
Tomas is correct; \( \overline{AC} \) is opposite \( \angle B \) and \( \overline{BC} \) is adjacent to \( \angle B \)
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match the description with the correct response. a vertical line choose…
B. \( x=-5 \)
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problems 1–2: the hangers and the graph represent the same system of eq…
1. The solution is $(x,y) = (1.5, 4.5)$ 2. A triangle weighing 1.5 lb and a circle weighing 4.5 lb will balance both hangers. 3. Red line: $y = -\frac{1}{2}x + 4$; Blue line: $y =…
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syllable pattern vce syllable pattern vce is a pattern that contains a …
### Part 1: Circle VCe Pattern Words To identify VCe pattern words (vowel - consonant - silent e, with long vowel), we analyze each word: - **impose**: V (i) - C (m, p, s) - e (si…
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find the circumference of each circle using the formula $c = 2\\pi r$. …
1. $47.1$ cm 2. $18.84$ yd 3. $40.82$ ft 4. $163.28$ m 5. $389.36$ ft 6. $226.08$ yd
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polygon interior angles theorem\ polygon exterior angles theorem
- **Polygon Interior Angles Theorem**: For a polygon with \( n \) sides, the sum of the interior angles \( S_{interior}=(n - 2)\times180^\circ \). - **Polygon Exterior Angles Theo…
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find the area of the figure. 8 cm
$64\ \text{cm}^2$
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homework 9.5 & 9.6 - area of rectangles, parallelograms & triangles sta…
23 mm²
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describe the combination of transformations in the images below. $\\tri…
First, $\triangle ABC$ is reflected across the y - axis to obtain $\triangle A'B'C'$. Then, $\triangle A'B'C'$ is reflected across the x - axis to obtain $\triangle A''B''C''$. (I…
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given right triangle def, what is the value of sin(e)? ○ \\(\\frac{3}{5…
$\frac{4}{5}$ (the option corresponding to $\frac{4}{5}$)
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write the ordered pair location of the new point after the given transf…
\((9,9)\)
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write the ordered pair location of the new point after the given transf…
\((4, -1)\)
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check for understanding do you remember how to solve problems about unk…
- Angle $\angle AWB$: $138^\circ$ - Angle $\angle DWA$: $42^\circ$ - Angle $\angle BWC$: $42^\circ$
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$\\overline{pq}$ is reflected across the line $x = -3$. the coordinates…
D. \((-8, 4)\)
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find the measure of one interior angle in each regular polygon. round y…
\( 144^{\circ} \) ### 15) Regular 22 - gon (Interior Angle)
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given the triangle below, what is the length of the hypotenuse? 3 cm 5 …
B. \(\sqrt{34}\space cm\)
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in the figure shown, which pair of angles must be complementary? ○ ∠cob…
$\angle COD$ and $\angle DOB$
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solve for ( x ). round to the nearest tenth, if necessary.
\( 4.2 \)
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the measure of an angle is 63°. what is the measure of its supplement? …
D. $117^\circ$
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calculator what is ( mangle lqk )? enter your answer in the box.
$45^\circ$
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find area; find area of shaded rectangle; find area of shaded parallelo…
30 ### Second Problem (Shaded Rectangle Area):
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what is the area of the triangle below? 3 meters 4 meters a 12 m b 12 s…
C. 6 square m
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calculator the lines s and t intersect at point r. what is the value of…
$y = 29$
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which pair of angles are vertical angles? ∠mrc and ∠krm ∠kre and ∠ert ∠…
D. $\angle ERT$ and $\angle MRC$
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find the value of x in the regular nonagon. (8x + 12)° x = (type an int…
\( 16 \)
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what is the perimeter of the parallelogram? units
20
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first graph the equations, and then mark the point of intersection. $y …
The point of intersection is \((-6, 4)\)
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given ∠x and ∠y are complementary angles. the measure of ∠y is 10° more…
$m\angle Y = 50^\circ$ and $m\angle X = 40^\circ$
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complete the table to show the number of triangles that each polygon ca…
| Number of Sides of the Polygon | Number of Triangles Formed | Interior Angle Sum | |--------------------------------|----------------------------|--------------------| | 12 | 10…
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what is the relationship between $\\angle por$ and $\\angle ros$? \\big…
Supplementary angles
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1. in the figures below, identify as many examples of the terms listed …
To solve this, we analyze each term using circle definitions: ### a. Chord A chord is a line segment with both endpoints on the circle. - $\overline{RS}$: Endpoints $R, S$ on circ…
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use your understanding of triangles to answer the questions below. 8. i…
8. C. $82.8^\circ$ 9. $58.2^\circ$
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m∠e = 104°; m∠f = 96° are the two angles complementary, supplementary, …
neither
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use your understanding of triangles to answer the questions below. 8. i…
8. C. $82.8^\circ$ 9. $58.2^\circ$
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6 solve the system of equations below by graphing each line on the coor…
The solution of the system is the point \((2,1)\)
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m∠c = 97°; m∠d = 83° are the two angles complementary, supplementary, o…
supplementary
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determining a tangent ratio what is the value of \\(\\tan(60^{\\circ})\…
$\boldsymbol{\sqrt{3}}$ (corresponding to the option with $\sqrt{3}$)
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express (sin g) as a fraction in simplest terms.
\( \frac{3}{5} \)
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m∠a = 72°; m∠b = 18° are the two angles complementary, supplementary, o…
Complementary
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what is the measure of the supplement of the angle? 3° enter your answe…
$177^\circ$
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use the diagram of triangle xyz to answer the questions. what is the le…
s: - Length of side XY: \(10\) - \(\sin(X)\): \(\frac{4}{5}\) - \(\cos(X)\): \(\frac{3}{5}\) - \(\tan(X)\): \(\frac{4}{3}\)
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what is the measure of the complement of the angle? 62° enter your answ…
$28^\circ$
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what is the measure of the supplement of the angle? 142° enter your ans…
$38$
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what is the measure of the supplement of the angle? 62° enter your answ…
$118^\circ$
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the measure of angle a is 5 times the measure of its supplement. what i…
The measure of angle A is $150^\circ$. The measure of its supplement is $30^\circ$.
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example 1: find the sum of the measures of the interior angles of the i…
\( 1260^{\circ} \) #### b) Dodecagon (12 - sided polygon)
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$\\angle g$ and $\\angle h$ are complementary angles. the measure of $\…
$m\angle G = 41^\circ$ $m\angle H = 49^\circ$
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bc = round your answer to the nearest hundredth.
$4.92$
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2x + 4y = 8 2y = 3x - 12 **choose the correct line to graph: line 1 is …
To graph \(2x + 4y = 8\) (rewritten as \(y=-\frac{1}{2}x + 2\)), use the line (e.g., Line AB) passing through \((0,2)\) and \((4,0)\). To graph \(2y = 3x-12\) (rewritten as \(y=\f…
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2x + 4y = 8\ 2y = 3x - 12\ **choose the correct line to graph: line 1 i…
If the equation to graph is \(2x + 4y = 8\), the correct line is Line AB. If the equation to graph is \(2y=3x - 12\), the correct line is Line CD. (If we assume the question is to…
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solve the problem. use what you learned from the model. von makes a des…
### Step 1: Draw the Diagram Let's assume two parallel lines \( a \) and \( b \), and two transversal lines \( c \) and \( d \). So we have: - Line \( a \) (top parallel line) - L…
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estimate solutions to systems of equations graphically determine the nu…
1. **How many solutions?** one at $(-2, 2)$ **How do you know?** Lines intersect once. 2. **How many solutions?** none **How do you know?** Lines are parallel, no overlap. 3. **Ho…
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one pair of angles in your map to illustrate each angle relationship me…
For example, \( \angle 1 \) and \( \angle 5 \) are corresponding angles (if \( m \parallel n \)) and are equal. \( \angle 1 \) and \( \angle 3 \) are vertical angles and equal. \(…
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consider parallelogram pqrs below. note that pqrs has vertices ( p(-3, …
### (a) Length of $\overline{PQ}$: $\boldsymbol{\sqrt{53}}$ Length of side adjacent to $\overline{PQ}$: $\boldsymbol{\sqrt{53}}$ ### (b) Slope of $\overline{PQ}$: $\boldsymbol{\fr…
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4. which geometric sequence has a first term equal to 55 and a common r…
{55; -275; 1,375; -6,875; ...}
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which angles are corresponding angles? ∠qpn and ∠qps ∠qpn and ∠rsu ∠qpn…
$\angle QPN$ and $\angle RSU$ (the option with $\angle QPN$ and $\angle RSU$)
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a flat screen television is advertised as being 46 inches on its diagon…
40.4
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a rectangular park is x feet long and y feet wide. the new design of th…
The perimeter of the redesigned park (including the pathway) is \( 2.74x + 2.24y+56 \) feet.
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fill in the blanks to complete the sentences. then find the measures of…
2 pairs of corresponding angles: \(a\) and \(b\), \(c\) and \(d\) If \(AB \parallel CD\), then \(a = b\) and \(c = d\) ### Part 2: Alternate Angles
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which angles are supplementary angles? ∠ijh and ∠nmo ∠ijh and ∠kjh ∠ijh…
\(\boldsymbol{\angle IJH}\) and \(\boldsymbol{\angle KJH}\) (the option: \(\angle IJH\) and \(\angle KJH\))
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bus below, find the measures of $\\angle 1$, $m\\angle 1$ $m\\angle 2$ …
$m\angle 1 = 42^\circ$ $m\angle 2 = 48^\circ$ $m\angle 3 = 42^\circ$ $m\angle 4 = 48^\circ$
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(b) what is the solution?
(3, 0)
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are ∠3 and ∠5 congruent? explain.
Assuming a typical diagram (e.g., vertical angles or parallel lines with a transversal), \(\angle3\) and \(\angle5\) are congruent. The reason is that vertical angles are congruen…
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answer the parts below. (a) plot 3 and 2 on the number line below. (b) …
3 is located to the right of 2 (the option with this text, e.g., if it was option B, then B. 3 is located to the right of 2) ### Part (C)
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find the perimeter and area of the right triangle shown below. 13 cm 10…
Perimeter = 31.31 cm Area = 41.55 $\text{cm}^2$
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9 you are solving a system of two linear equations in two variables, an…
A. Blue
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find the measures of angles 3, 8, 9, and 14 to show that the sum of the…
The angles are \(\frac{540}{17}^\circ\) (or \(\approx31.76^\circ\)), \(\frac{1440}{17}^\circ\) (or \(\approx84.71^\circ\)), \(\frac{1620}{17}^\circ\) (or \(\approx95.29^\circ\)), …
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9 you are solving a system of two linear equations in two variables, an…
A. Blue
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what is the minimum length the ladder must be to reach the roof? round …
4.5
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what is the area of the quadrilateral shown below? 7 25 4
132
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8 you are solving a system of two linear equations in two variables, an…
B. Green
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in the figure shown, which composition of rigid transformations will ma…
B. a reflection followed by a translation