幾何
三角形、圓、解析幾何與證明題。
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in 1054, eastern and western rome had different religious beliefs. as a…
- The split was known as the **Great Schism (East - West Schism)**. - Eastern church: **Eastern Orthodox Church**; Western church: **Roman Catholic Church** - 1st difference examp…
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number of triangles 2 3 ? ? perimeter (units) 4 5 ? ?
For the number of triangles: 4, 5; For the perimeter: 6, 7
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parallelogram c is a scaled copy of parallelogram b. parallelogram b ha…
\(\frac{7}{10}\) (or \(0.7\))
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the measure of an angle is 22.9°, what is the measure of its complement…
\(67.1\)
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name the marked angle in 2 different ways.
\( \angle ROP \), \( \angle O \)
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what is the reading of this ruler indicated by the arrow? if you need a…
A. \(1\frac{27}{32}\)"
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what is the value of b? 76.1° 47.7°
\( 28.4^\circ \)
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name the marked angle in 2 different ways.
\( \angle GDE \) and \( \angle D \) (or other valid names like \( \angle EDG \) as long as the order of points around the vertex is correct)
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6. squares s and q are scaled copies of one another. a. what scale fact…
4 ### Problem 6b
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3. find the area of the shape below. justify your answer.
12 (assuming each grid square has a side length of 1 unit)
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the measure of an angle is 176°, what is the measure of its supplementa…
\(4\)
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the measure of an angle is 40°. what is the measure of its complementar…
\(50\)
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the measure of an angle is 87°. what is the measure of its complementar…
The measure of the complementary angle is \( 3^\circ \).
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polygon d is a scaled copy of polygon c. images of polygon c (with side…
\( 0.75 \) (or \( \frac{3}{4} \))
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the measure of an angle is 16°. what is the measure of its supplementar…
\(164\)
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∠3 is a supplement of ∠2, and ( mangle 2 = 147^circ ). find ( mangle 3 …
\(33^\circ\)
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choose the correct answer. what fraction is modeled below? image of a s…
A. 3/4
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what is the value of p?
\( 112^\circ \)
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the measure of an angle is 28°. what is the measure of its complementar…
\(62\)
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quadrilateral t is a scaled copy of quadrilateral s. diagrams: quadrila…
\(2\frac{4}{5}\) (or \(\frac{14}{5}\))
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in the diagram shown, what are the measures of ∠dbc, ∠dbe, ∠ebf, and ∠d…
50
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∠1 is a complement of ∠4, and ( mangle 1 = 33^circ ). find ( mangle 4 )
\(m\angle 4 = 57^\circ\)
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the measure of an angle is 157°. what is the measure of its supplementa…
\(23\)
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the measure of an angle is 43°. what is the measure of its complementar…
\(47^\circ\)
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name the marked angle in 2 different ways.
\( \angle AYZ \) and \( \angle Y \) (or other valid names like \( \angle ZYA \) depending on the angle's orientation, but the key is two distinct naming methods using vertex - sid…
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16, two intersecting lines with one angle labeled 97° and another label…
\(x = 5\)
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quadrilateral e is a scaled copy of quadrilateral d. image of quadrilat…
\( \frac{7}{10} \)
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a. eliminate the unnecessary commas in the following passage. most cana…
Most Canadians recognize Margaret Atwood as one of our country’s finest novelists, but she is also an acclaimed short - story writer, essayist, and poet. Born in Ottawa, she began…
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identify the transformation. is this a reflection, translation, or rota…
reflection
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in the diagram shown, what are the measures of ∠dbc, ∠dbe, ∠ebf, and ∠d…
\( 60 \)
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polygon i is a scaled copy of polygon ii. image: polygon h (blue) with …
\(\frac{3}{2}\) (or \(1\frac{1}{2}\))
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name the marked angle in 2 different ways.
Two ways to name the marked angle are \( \angle B \) and \( \angle EBC \) (or \( \angle CBE \)).
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18. for 90% of the last 30 years, the rainfall at shell beach has varie…
The absolute - value inequality is \( |x - 24|>6.5 \), and its solution is \( x < 17.5 \) or \( x>30.5 \). To graph the solution on a number line: - Draw an open circle at \( 17.5…
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the measure of an angle is 102°. what is the measure of its supplementa…
\(78^\circ\)
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name the marked angle in 2 different ways. diagram of triangle with ver…
\( \angle PNO \), \( \angle N \)
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trapezoid g is a scaled copy of trapezoid f. trapezoid f (blue) has a t…
35
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pentagon i is a scaled copy of pentagon h. pentagon h (green) has sides…
15
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name the marked angle in 2 different ways.
\( \angle IKL \), \( \angle K \)
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name the marked angle in 2 different ways
\( \angle Z \), \( \angle XZY \) (Note: The actual vertex label might vary based on the diagram's unlabeled top vertex; if the top vertex is, for example, \( A \), then it would b…
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in the figure, $overline{sr} cong overline{cb}$ and $overline{ac} cong …
No. The statements must have one segment in common to use the Transitive Property of Segment Congruence, but in this case, the statements are about four different segments.
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use the given figure for 3-5. 3. find the value of z if : m∠1 = z² + 45…
\( z = 10 \) (assuming a typo in the problem, \( z \) instead of \( z^2 \); if \( z^2 \), then \( z = \sqrt{10} \), but likely typo) ### Question 4
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the diagram ( overline{at} parallel overline{kv} ). if ( angle opt = 11…
### Part (i): Find the value of \( r \) #### Explanation: 1. **Identify the relationship between angles**: Since \( BC \parallel AD \), \( \angle CEF \) and \( \angle DCE \) are r…
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15 x y w z 72° (15x - 7)° m∠xyz = 95°
$x = 2$
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question 8 of 10 a rectangles width is 6 feet less than its length. wri…
A. \( A(l) = l^2 - 6l \)
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replace the english word below with the correct translation: generalmen…
B. cruel (Wait, no, the options are labeled with circles, but in the problem, the options are: first "mala", second "cruel", third "antipática". So the correct answer is the secon…
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question 5 of 10 a rectangles width is 5 feet less than its length. if …
26
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perimeter of a rectangle the perimeter of the rectangle is 32 cm. the l…
The length is represented by \( 2w + 1 \). The remaining sides: the two width sides are labeled \( w \) and the two length sides are labeled \( 2w + 1 \).
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proving similarity knowing angle measures given: ( mangle b = 46^circ )…
The sum of the measures of the interior angles of a triangle is \(180^{\circ}\)
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15 x w (15x - 7)° 72° z y m∠xyz = 95°
$x = 2$
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for each set of figures, show how the green colored tiles in the border…
### Part a: Grouping Method 1 (Figure Size 3) #### Explanation: We can group the green tiles by rows. Let's count the number of green tiles in each row from top to bottom. The top…
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given: $overline{xy} parallel overline{zw}$ prove: $\triangle xyw sim \…
1. First angle blank: \( \boldsymbol{\angle X} \) 2. Second angle blank: \( \boldsymbol{\angle Z} \) 3. Third blank: \( \boldsymbol{\text{congruent}} \) 4. Fourth blank: \( \bolds…
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task 3 - real world scenarios: determine which principle is being descr…
s: 1. Circle: Checks & Balances (or Separation of Powers, but more accurately Checks & Balances as it's about the interaction between Executive and Legislative) 2. Circle: Individ…
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given: $overline{xy} parallel overline{zw}$ prove: $\triangle xyv sim \…
First drop - down: \( \boldsymbol{\angle X} \); Second drop - down: \( \boldsymbol{\angle Z} \); Third drop - down: \( \boldsymbol{\text{congruent}} \); Fourth drop - down: \( \bo…
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determine the similarity transformations that verify △abc ~ △abc. the f…
dilation with center C
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a triangle has side lengths of (4m + 3n) centimeters, (8m + 10p) centim…
\(5n + 12p + 12m\) (corresponding to the first option among the choices)
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determine the similarity transformations that verify △abc ~ △abc. the f…
First transformation: dilation (assuming, but based on the diagram, the first is a dilation). Second transformation: dilation with center \( C' \) (from the options, the correct s…
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b. write a two - column proof. statements\treasons \tgiven \tdefinition…
\(RM\cong CD\) (proven through the two - column proof as above)
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12. ____ something that relates to or resembles a line 13. ____ three o…
B. line
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recognizing necessary information for similarity what additional inform…
- \(\boldsymbol{\angle B\cong\angle M}\) - \(\boldsymbol{\triangle ABC}\) was rotated and dilated by a scale factor between 0 and 1. - \(\boldsymbol{\angle C\cong\angle L}\)
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triangle xyz was reflected across m and then dilated to form a similar …
The triangle in the middle (the second option among the three triangles shown)
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name:_________________________ date:__________ review points, lines, an…
1. D. point of intersection 2. K. line 3. I. perpendicular lines 4. B. point 5. J. line segment 6. H. collinear points 7. F. midpoint 8. G. parallel lines 9. C. ray 10. L. plane 1…
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triangle def is similar to triangle def. which similarity transformatio…
rotation and dilation (the option: rotation and dilation)
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example 3 (pp. 7–8) draw and label a figure for each relationship. 5. a…
(Problem 5): - A coordinate plane with a line \( \overleftrightarrow{XY} \) passing through \( X(3,-1) \), \( Y(-3,-4) \), and \( Z(-1,-3) \), and a point \( W \) (e.g., \( W(0,0)…
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in the diagram, (overline{mn} cong overline{lq}) and (overline{lq} cong…
A. The Transitive Property of Segment Congruence should have been used
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1. rectangles p, q, r and s are scaled copies of one another. for each …
### Problem 1 (Rectangles) To determine the scale factor direction (greater than 1, equal to 1, less than 1), we compare the sizes: - **Rectangle P to Rectangle R**: R is larger t…
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given: $overline{fh} perp overline{gh}$, $overline{kj} perp overline{gj…
- For step 4 reason: all right angles are congruent - For step 6 statement: \( \angle FGH \cong \angle KGJ \) - For step 7 reason: AA similarity theorem
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unit 1 test review geometry explain each of the following. draw if poss…
A segment with endpoints $P$ and $Q$, drawn as a line between $P$ and $Q$. ### 2. $\boldsymbol{\overrightarrow{PQ}}$
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problem 14: a horizontal line intersected by a transversal, forming a 1…
\(x = 8\)
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question fill in the parts-whole model for the following equation. (___…
Top box: \( 5y \), Bottom left: \( 4y \), Bottom right: \( y \) (or bottom left: \( y \), bottom right: \( 4y \) depending on model labeling, but the whole is \( 5y \))
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the composition ( d_{o,0.75}(x,y) circ d_{o,2}(x,y) ) is applied to ( \…
# Explanation: ## Step1: Recall Dilation Properties Dilation is a similarity transformation, so angles are preserved (congruent), and triangles are similar (not necessarily congru…
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triangle abc is similar to triangle abc. which sequence of similar tran…
B. dilation and translation
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fill in the parts-whole model for the following equation. (2y) = (_____…
The unknown value is \(-6y\). The parts - whole model has the whole as \(-6y\) (top rectangle) and the parts as \(2y\) and \(-8y\) (bottom two rectangles).
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refer to the figure and the given information to find each measure. 9. …
\( x = 10 \), \( AB = 12 \) m, \( BC = 27 \) m ### Problem 10
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complete the two - column proof for the reflexive property of segment c…
| Statements | Reasons | | --- | --- | | 1. A segment exists with endpoints \( A \) and \( B \). | 1. Given | | 2. \( AB = AB \) | 2. Reflexive Property of Equality | | 3. \( \ove…
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determine whether the points can form a line in the given plane. then, …
Yes
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unit 1 test review geometry explain each of the following. draw if poss…
1. Using two points on the line with a line symbol above them (e.g., $\overleftrightarrow{AB}$). 2. Using a single lowercase letter (e.g., line $l$). ### Question 6: What are the …
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write a compound inequality that represents each phrase. graph the solu…
The compound inequality is \( 25 \leq t \leq 30 \), where \( t \) is the baking time (in minutes). For the graph, we draw a number line, mark 25 and 30 with closed circles (since …
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explain each of the following. draw if possible: 1. $overline{pq}$ 2. $…
To find the distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \), use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For \( P(-2, 2) \) and \( Q…
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given: (overline{nm} parallel overline{xz}) prove: (\triangle xyz sim \…
1. parallel 2. Corresponding Angles Postulate 3. \(\angle NYM\) 4. AA
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decide whether each set of points determines a plane. circle yes or no.…
No
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14, 142°, (-2x + 54)° with intersecting lines (diagram of two intersect…
\(x = 8\)
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prove: ∠3 ≅ ∠7 statements 1. k || l 2. ∠3 and ∠4 are supplementary 3. m…
Row 6 (Statement: \( m\angle 4 + m\angle 7 = 180^\circ \), Reason: Definition of Complementary Angles) is incorrect. The correct reason should be related to supplementary angles (…
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fill in the parts-whole model for the following equation. (____) = (4y …
The blank in the equation is \(\boldsymbol{-6z}\). For the parts - whole model: - Top rectangle: \(-6z\) - Middle rectangle: \(4y - 6z\) - Bottom left rectangle: \(4y\) - Bottom r…
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write the following statement in the \if-then\ form. a side of a square…
A. If the side's measure is 24 inches, then the side of a square measures 2 feet.
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find qr in the following problems. r is between q and s. 7. if rs = 44.…
\( QR = 23.8 \) ### Problem 8
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for each statement, circle true or false. then, explain your answer 1. …
True
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solve for the value of p. (6p+3)° (9p-3)° answer attempt 1 out of 3 p =
12
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2. carmen loves to look at the little sharks in the big tank at the aqu…
Multiplication expression: \( V = 10 \times 10 \times 10 \) Exponential expression: \( V = 10^3 \) The volume of the shark tank is \( 1000 \) cubic feet.
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find the value of the variable and the measure of each labeled angle. $…
\(32\)
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6. if ce = 7in. and ae = 23 in., ac = ______.
16 inches
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question 1/1 complete the following proof using theorems, definitions, …
1. Reason: Given 2. Reason: Linear Pair Theorem 3. Reason: Given 4. Reason: Linear Pair Theorem 5. Reason: Substitution Property 6. Reason: Subtraction Property
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1. carmen goes to the citys aquarium and looks at the seahorses. look a…
Multiplication expression: \( V = 6 \times 6 \times 6 \) Exponential expression: \( V = 6^3 \) The volume of the seahorse tank is \( 216 \) cubic feet.
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find the value of the variable and the measure of each labeled angle. (…
\(x = 22\) \((x + 10)^\circ = 32^\circ\)
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a. rotate the figure around a point 90° clockwise and then rotate it an…
C. Translate the figure 3 units down, then 5 units up, and then 2 units down.
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part 1 of 3 find the value of the variable and the measure of each labe…
\(x = 12\)
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use the figure to the right to answer each question. 11. name five poin…
\( R \), \( S \), \( T \), \( U \), \( V \)
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13, 119°, (-3x + 143)° with two intersecting lines (arrows indicating l…
\(x = 8\)
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6. select all the sequences of transformations that could return a figu…
C. Translate the figure 3 units down, then 5 units up, and then 2 units down. D. Reflect the figure over one line and then reflect over the same line. E. Rotate the figure 90° cou…
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two triangles labeled a (top) and b (bottom) on a square grid, with bla…
The areas of Triangle A and Triangle B are equal (both have an area of 6 square units).
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13, 119°, (-3x + 143)°
\(x = 8\)