几何
三角形、圆、解析几何与证明题。
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5. examine the given information in the diagram shown. use the informat…
C. $117^\circ$
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which graph decreases, crosses the y-axis at (0, −7), and then increase…
C. Graph C
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find t. write your answer in simplest radical form. units
\(17\)
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find g. write your answer in simplest radical form. millimeters
\(7\sqrt{3}\)
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5. examine the given information in the diagram shown. use the informat…
A. $146^\circ$
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in exercises 5–8, point ( d ) is the centroid of ( \triangle abc ). fin…
5. $CD=10$, $CE=15$ 6. $CD=22$, $CE=33$ 7. $CD=18$, $CE=27$ 8. $CD=30$, $CE=45$
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2. △efg ~ △_ehg_ by ______
$\triangle EFG \sim \triangle \boldsymbol{EHG}$ by **AA (Angle - Angle) Similarity Criterion** (or ASA, but AA is more appropriate for similarity)
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4. workers at a construction company are building a triangular enclosur…
A. 24 inches, E. 170 inches
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3. examine the given information in the diagram. use the information to…
C. 160°
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sort the words according to the meanings of their shared roots. enclose…
- shut: enclose, closet - angle: polygon, septagon, octagon - place or put: position, pose, dispose
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2. gerald and jessie are deciding which measure to use for the third si…
C. $27 < x < 77$
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Question was provided via image upload.
\( \triangle ABC\cong\triangle \boldsymbol{ADC} \) by \(\boldsymbol{SSS}\) (Side - Side - Side) congruence criterion.
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1. examine the sets of numbers and decide which set are the sides of a …
B. 3 cm, 4 cm, 5 cm D. 5 cm, 6 cm, 9 cm
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20. rotate the coordinate (3, 5) 90° counter - clockwise around the poi…
1. For question 20: $(-12, -6)$ 2. For question 21: $(-4, -7)$
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find the circumference and the area of a circle with diameter 6 m. use …
Circumference: \( 18.84\) meters Area: \( 28.26\) square meters
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rotations about a point (non - origin) whats the process? make your own…
The 3-step process for rotating a shape about a non-origin point $(h,k)$ is: 1. Translate all vertices by subtracting the rotation point coordinates: $(x,y) \to (x-h, y-k)$ 2. App…
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sort the words according to the meanings of their shared roots. cent pe…
- circle: unicycle, recycling, bicycle - hundred: cent, percent, centigrade
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sort the words according to the meanings of their shared roots. subserv…
- Under "serve": subservient, servant, service - Under "circle": encircled, circuit, circus
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sort the words according to the meanings of their shared roots. liberty…
- straight: rectangle, indirectly, direct - free: liberty, liberate, liberal
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in exercises 1–4, point ( p ) is the centroid of ( \triangle lmn ). fin…
1. $QP=3$, $PN=6$ 2. $QP=7$, $PN=14$ 3. $QP=10$, $PN=20$ 4. $QP=14$, $PN=28$
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the vector that translates a(-2, 7) to a(6, 4) is < , >.
\(\langle8, - 3 angle\)
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analyzing a real - world volume problem a carpenter designs two cabinet…
- The cabinets have the same base area. - The cabinets may have the same base dimensions. - The cabinets may have different base dimensions.
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refer to the graph. a translation select choice map $\\triangle abc$ to…
To solve this, we analyze the translation (shift) of triangle \( \triangle ABC \) to \( \triangle EFG \). ### Step 1: Identify Coordinates (Assume Grid Units) Let’s find coordinat…
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a type of cracker, rectangular in shape, is stored in a vertical column…
$\frac{1}{8}$ inch
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which is the image of ( p(-5, 11) ) along the vector ( langle 3, -8 ang…
D) \( P'(-2, 3) \)
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determining missing lengths in the right triangular prism below, \\(\\o…
12
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determining missing values in expressions for volume the figure below i…
$a=2$, $b=3$, $c=6$
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18. the coordinates of two points, and their images, are given below a …
A 90° counterclockwise rotation about the origin. --- ### Problem 19
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finding the volume of an oblique prism an oblique hexagonal prism has a…
168 cubic centimeters
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practice solving for the volume of right and oblique prisms. the figure…
$\frac{1}{2}x^3$
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△abc and △cde are shown below. which statement is true? △abc is similar…
$\triangle ABC$ is similar to $\triangle CDE$.
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solve for x. 34 x° 84° 32 x = ?° law of sines (\frac{sin a}{a}=\frac{si…
\( 69.51 \)
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2. if the triangles are similar, find the length of side f. e = \\frac{…
$\boldsymbol{\frac{5}{12}}$ mi (Option C: $\frac{5}{12}$ mi)
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what is the area of this figure? 13 mi 3 mi 7 mi 6 mi 6 mi 6 mi 3 mi 8 …
99 square miles
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1. if the trapezoids are similar, find the length of side w. y = 80 mm,…
112 mm
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13. in the figure below, triangle efg is reflected across the horizonta…
$-1$ --- ### Question 14
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10) use the situation to answer the question. the scale drawing of a re…
$\boldsymbol{\frac{25\ \text{mm}^2}{1\ \text{yd}^2}}$ (corresponding to the second option)
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1. the diagram below shows a parallelogram. image of parallelogram with…
1. D 240 cm 2. A $28\ \text{m}^2$ 3. D 8 ft × 12 ft 4. B 22 in.
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knows the diameters of all the lids in her kitchen. which equation coul…
A. $\frac{60}{\pi}=d$
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8) use the situation to answer the question. the scale drawing of a rec…
Length: 20 yd Width: 50 yd
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the area of a triangular piece of roof siding is 74 square feet. find t…
18.5 feet
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6) find the area of the figure. the area of a parallelogram - shaped ci…
2.3 mm
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variables and algebraic expressions evaluate ( n - 5 ) for each value o…
3 ### Problem 2: Evaluate \( n - 5 \) for \( n = 121 \)
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a large pond takes up 2,700 square meters of land. if the length of the…
45 meters
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4) find the area of the figure. 25 in 125 in² 625 in² 750 in² 165 in²
625 $\text{in}^2$ (Option: 625 $\text{in}^2$)
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3) find the area of the figure. \\(\\frac{16}{3}\\) yd \\(\\frac{3}{4}\…
4 yd²
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2) find the area of the figure. 0.08 m 0.04 m 0.0016 m² 0.0032 m² 0.000…
0.0016 $\text{m}^2$ (Option 1: 0.0016 $\text{m}^2$)
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1) find the area of the figure. 100 cm 55 cm 60 cm 5,500 cm² 4,650 cm² …
4,400 cm²
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1) use the similar triangles for the following problem. use proportions…
b = 6m
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5) the two triangles are similar. set up and solve a proportion to find…
$s = 1\frac{1}{2}$ yd (matches the second option: $\boldsymbol{s = 1\frac{1}{2}}$ yd)
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use a quadratic function to model the area of the rectangle. graph the …
\( 2x^{2}+10x + 8 \)
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use a quadratic function to model the area of the rectangle. graph the …
$f(x)=2x^2+8x+6$
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cd is the perpendicular bisector of ab. g is the midpoint of ab. points…
D. \( \overline{AE} \) and \( \overline{BE} \)
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on a scale map of a city, an area of one square kilometer is represente…
7
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to boil the banana, jack needs 4\\frac{1}{2} cups of water. he measures…
The second model (the lower one with the shorter shaded bar)
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frank draws a square that measures 3 inches on each side. then, he dila…
20.25
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transversal cd cuts parallel lines pq and rs at points x and y, respect…
C. \( 64.36^{\circ}\)
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type the correct answer in the box. use numerals instead of words. if n…
\( 1 : 1 \)
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7 cm 3 cm b what is the length of the missing leg? if necessary, round …
6.3 centimeters
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select the correct answer from each drop - down menu. as per an axiom i…
First drop - down: two Second drop - down: line
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select the correct answer. prove: if two intersecting lines form two pa…
B. The image with perpendicular lines (forming right angles as vertical angles)
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on this map, oxford street is perpendicular to the street intersections…
1. Oxford Street is perpendicular to Rosewood St. (or Womden Bl., or other vertical streets on the map) 2. [Name of vertical street] is perpendicular to George St. (or Oak St., or…
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select the correct answer from each drop - down menu. given (overline{u…
The first error is in Step 3 (the reason "addition property of equality" does not justify the statement, as it misapplies the addition property; the correct reasoning should invol…
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select the correct answer from each drop - down menu. peter and vivian …
To determine the type of proof Peter used, we analyze his reasoning: ### Step 1: Identify the Proof Structure Peter starts with a known theorem (linear pair theorem: \( \angle 1 \…
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6. a line passes through the origin and has a slope of draw the line by…
To draw the line: 1. Plot the point $(0,0)$ (the origin) since the line passes through it. 2. Use the slope $\frac{1}{2}$ (rise over run, which means for a run of 2 units (change …
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savannah ran around an indoor track with a 220-yard perimeter. she comp…
220 0
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for the pair of similar triangles, find the appropriate value(s) of x. …
$432$
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plot the numbers $-2\\frac{5}{6}$ and $\\frac{2}{3}$ on the number line…
- For $-2\frac{5}{6}$: Place a dot 5 units left of -2 on the 6-part interval between -2 and -3. - For $\frac{2}{3}$: Place a dot 4 units right of 0 on the 6-part interval between …
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area of triangle = \\(\\frac{1}{2}bh\\)\ what are the actual base and h…
$40$ ft²
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a 10-ft vertical post casts a 14-in shadow at the same time a nearby ce…
1020
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area of triangle = \\(\\frac{1}{2}bh\\)\ what are the actual base and h…
Actual base = $8$ ft Actual height = $10$ ft
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select the correct answer from each drop - down menu. which are the bes…
1. A statement that has been shown to be true by vigorous application of logic is a(n) $\boldsymbol{\text{theorem}}$. 2. A statement that is assumed to be true without proof is a(…
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what is the length of the missing leg? if necessary, round to the neare…
3.6 miles
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type the correct answer in the box. spell all words correctly. point is…
E
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2x + 8 ≤ 14 what is the value of x? ?graph
The solution to the inequality \(2x + 8\leq14\) is \(x\leq3\). To graph this, we draw a number line, place a closed circle at 3 (since the inequality is "less than or equal to"), …
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find ( mangle w ). write your answer as an integer or as a decimal roun…
$30.8^\circ$
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what is the length of the missing leg? if necessary, round to the neare…
20 meters
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15 yd. a 9 yd. what is the length of the missing leg? if necessary, rou…
12 yards
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find ( mangle w ). write your answer as an integer or as a decimal roun…
\( 126.9 \)
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ex 2 find x. a right triangle with one leg labeled x, the other leg lab…
\(\sqrt{105}\) feet (or approximately \(10.25\) feet)
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drag the tiles to the boxes to form correct pairs. not all tiles will b…
- Contrapositive: If Anissa is not sleeping, it is not after midnight. - Converse: If Anissa is sleeping, it is after midnight. - Inverse: If it is not after midnight, Anissa is n…
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13 select the correct answer. which statement best defines an angle? a.…
A. two rays that share a common endpoint called the vertex
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select the correct answer. given: ( mangle mxy = mangle kxy ) what is t…
C. \( \boldsymbol{m\angle JXY = m\angle NXY} \)
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what is the length of the missing leg? if necessary, round to the neare…
48 meters
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post test: foundations of geometry drag the tiles to the boxes to form …
- $\overline{CD}$: The tile with segment CD (C and D as endpoints, no extended arrows). - $\overrightarrow{CD}$: The tile with ray CD (arrow starting at C, going through D). - $\a…
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Question was provided via image upload.
48.8 centimeters
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which statement best defines a circle? a. the set of all points in a pl…
A. the set of all points in a plane that are the same distance from a given point called the center
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what is the length of the missing leg? if necessary, round to the neare…
60 yards
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type the correct answer in the box. spell all words correctly. consider…
pyramid
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25 mm 24 mm a what is the length of the missing leg? if necessary, roun…
7 millimeters
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17 ft. 15 ft. b what is the length of the missing leg? if necessary, ro…
$b = 8$ feet
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read the excerpt from \justin lebo.\ when he got it home, he wheeled th…
cluttered
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type the correct answer in the box. spell all words correctly. consider…
pyramid
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what is the length of the missing leg? if necessary, round to the neare…
12 kilometers
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which greek mathematician wrote the most definitive text on geometry, o…
C. Euclid
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1. what is intellectual property? a common piece of knowledge a creativ…
B. a creative work or idea (assuming the second option is labeled B; if the original labels were different, adjust accordingly, e.g., if the second circle's option is the second o…
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a building manager needs to order 9 replacement panes that are all the …
The angle measures for each pane are 42,42,96. The side lengths of each pane are 13.5, 13.5, 20 ft. The angles are the same by the definition of similar triangles. The sides are $…
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a building manager needs to order 9 replacement panes that are all the …
42, 42, 96 --- ### Additional note on dimensions (for full context): ## Step3: Find scale factor of panes There are 9 congruent similar triangles. The area scale factor is $\frac{…
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drag each label to the correct location on the flowchart. given: line l…
1. First box: Line \( l \) and line \( m \) intersect 2. Third box: \( \angle 2 \) is supplementary to \( \angle 3 \) 3. Fourth box: \( \angle 1 \cong \angle 3 \) (by congruent su…
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select the correct answer from each drop - down menu. the area of a rec…
The filled equation is $\boldsymbol{2w^2 + (-1)w + (-91) = 0}$ (or formatted as $\boldsymbol{2w^2 - w - 91 = 0}$)