几何
三角形、圆、解析几何与证明题。
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4 multiple choice 2 points study $\\triangle rst$ on the grid below. gr…
1. $(-4,-8)$ 2. $2, 3, 4$ 3. $13$ 4. $\{6,9,16\}$
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multiple choice 2 points the diagram shows triangle abc. grid with tria…
$\boldsymbol{\{(-2,2),\ (-3,-2),\ (-1,-1)\}}$
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which set of side measurements could be those of a triangle? 3cm, 4cm, …
B. 5 cm, 7 cm, 11 cm
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the sides of $\\triangle abc$ are 2, 3, and 4. which set of numbers cou…
$\{20, 30, 40\}$
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two triangles are similar. the measure of the shortest side of the firs…
6.25 ### Question 2
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what is an equation of the line that passes through the point (4, 8) an…
$y = 2x$ (or equivalent forms like $2x - y = 0$)
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graph the line that passes through the points (-8,6) and (-6,3) and det…
$y = -\frac{3}{2}x - 6$
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define axis of symmetry a line that divides the graph into two equal pa…
A line that divides the graph into two equal parts. i.e. cuts the graph in half
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define vertex where the parabola touches or intersects the x-axis the h…
B. The highest or lowest point on the graph
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what are the green dots called? y - intercepts rate of change verte x -…
D. x-intercepts
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what is the significance of the ordered pair (2, -4) to the graph? it i…
A. It is the vertex
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what is the vertex of the graph? (2, 4) (3, -1) (0, 8) (4, 2)
B. (3, -1)
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name the x-intercept(s)? options: (0, 0); (2, 4); (0, 0) and (0, 4); (0…
D. (0, 0) and (4, 0)
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• contains the following groups: - dashed box with a circle • consists …
1. First blank (top group): Document Formatting 2. Second blank (under Page group): Background
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a parabola has a vertex at (-3,2). where is the axis of symmetry? y = -…
x = -3
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what is the vertex? options: (4,-4), (2,0), (0,2), (6,0)
(4,-4)
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*21. the perimeter of a square room is 80 feet. the area of the room is…
400 square feet
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refer to the figure below. if the triangle is reflected across the x - …
C. (2, -4)
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refer to the figure below. if the triangle is reflected across the y - …
(4, 3)
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if the triangle is translated so that z becomes z(-2, -3), then x becom…
$X'(2,-2)$
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calculate the area of each right triangle below. note that the figures …
1. $141.96\ \text{cm}^2$ 2. $9.375\ \text{km}^2$ 3. $3.84\ \text{in}^2$ 4. $330\ \text{mm}^2$ 5. $\frac{200}{3}\ \text{ft}^2$ (or $66.67\ \text{ft}^2$)
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10. solve for x. area = 45 un² answer:
$x = 9$
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graph the inequality below on the number line. ( y geq 7 )
To graph \( y\geq7 \) on the number line: 1. Place a closed (filled) circle at the point corresponding to 7 on the number line. 2. Draw an arrow starting from the closed circle at…
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4. you and 4 friends split the total cost of one pizza and one pitcher …
### Pizza & Iced Tea a. Variable: \( x \) = cost of iced tea (in dollars). Expression: $\frac{15 + x}{5}$ b. $\$5.40$ ### Arcade Cost a. Variable: \( g \) = number of games played…
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find the area of the right triangle. area = square units
12 square units
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use pascals triangle to expand ((z + 1)^6). ((z + 1)^6 = square)
$z^6 + 6z^5 + 15z^4 + 20z^3 + 15z^2 + 6z + 1$
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use pascals triangle to expand ((3s + 2)^5). ((3s + 2)^5 = square)
$243s^5 + 810s^4 + 1080s^3 + 720s^2 + 240s + 32$
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in exercises 1 and 2, copy and complete the table. write your answers i…
| $x$ | 5 | 4 | $\sqrt{2}$ | $12\sqrt{2}$ | |-----|---|---|------------|--------------| | $y$ | $5\sqrt{2}$ | $4\sqrt{2}$ | 2 | 24 | --- ### Exercise 2 (30°-60°-90° Triangle)
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use pascals triangle to expand ((m + 4)^4). ((m + 4)^4 = square)
$m^4 + 16m^3 + 96m^2 + 256m + 256$
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the volume of a cube depends on the length of its sides. this can be wr…
D. A cube with side lengths of 3 feet has a volume of 27 cubic feet.
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which pairs of figures below are congruent? (the chart part is omitted …
1. First pair: No 2. Second pair: Yes 3. Third pair: No 4. Fourth pair: Yes
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the function f(r) gives the area of a circle with radius r. it can be w…
A. 28.26
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find the missing side length using the trigonometry functions( sine,cos…
1. $x \approx 8.66$ cm (or $5\sqrt{3}$ cm) 2. $y \approx 42.60$ m 3. $a \approx 15.41$ cm
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complete the proof that $\\triangle wxy \\cong \\triangle vuz$. 1. $\\a…
1. Reason for Statement 4: Additive Property of Length 2. Reason for Statement 6: Substitution Property of Equality 3. Reason for Statement 8: ASA (Angle-Side-Angle) Congruence Po…
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$angle rqv cong angle stu$, $angle qvr cong angle tsu$, and $overline{u…
| Statement | Reason | |-----------|--------| | 1. $\angle RQV \cong \angle STU$ | Given | | 2. $\angle QVR \cong \angle TSU$ | Given | | 3. $\overline{UV} \cong \overline{RS}$ | …
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the triangles below are congruent and their corresponding parts are mar…
(a) $\angle A \cong \angle Z$ $\angle B \cong \angle X$ $\angle C \cong \angle Y$ (b) $\overline{AB} \cong \overline{ZX}$ $\overline{AC} \cong \overline{ZY}$ $\overline{BC} \cong …
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2. read the story a second time. this time, underline the main idea and…
a. Bees are smart creatures that work together to make honey. ### Second Sub - Question (How do you know this is the main idea?)
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2. read the story a second time. this time, underline the main idea and…
a. Bees are smart creatures that work together to make honey ### 2. How do you know this is the main idea?
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7. solve. x = 1.5 cm; y = 5.5 cm; find h . options: 8.25 cm, 38.5 cm, 6…
2.9 cm
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△vwz and △xyz are equilateral. complete the proof that △vyz ≅ △wxz. 1\t…
SAS
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c = 7 cm; y = 5.5 cm; find ( s_2 ).
6.2 cm
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j is the midpoint of \\(\\overline{fh}\\) and \\(\\overline{gi}\\). com…
SSS
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16. choose the correct answer if jk = 3 cm. use the value ( s_2 = 6.2 )…
$\frac{3}{7} \approx 0.4$
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17. choose the correct answer if jk = 3 cm. use the value $s_2 = 6.2$ f…
$\frac{3}{7} \approx 0.4$
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the formula for the volume of a cone is $v = \\frac{1}{3}bh$. solve $v …
A. \( b = \frac{3V}{h} \)
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18. choose the correct answer if jk = 3 cm. use the value $s_2 = 6.2$ f…
$\frac{6.2}{3} \approx 2.1$
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6.1 properties and attributes of polygons 1. classify the polygon as co…
1. Concave, irregular pentagon 2. $3600^\circ$ 3. $162^\circ$ 4. $\frac{360}{7}^\circ \approx 51.43^\circ$ 5. $x=12$ 6. $x=114$ 7. $x=50$ 8. $x=32$, $(4x-8)^\circ=120^\circ$, $(3x…
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19. choose the correct answer if jk = 3 cm. use the value $s_2 = 6.2$ f…
$\frac{6.2}{7} \approx 0.9$
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question given: \\(\\overline{ad} \\cong \\overline{db}\\) and \\(\\ang…
$\boldsymbol{\angle CAB \cong \angle CBA}$ is proven as shown above. Filled two-column proof structure: | Step | Statement | Reason | |------|-----------|--------| | 1 | $\overlin…
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cp geometry similar right triangles day 1 assignment #2 name period dat…
1) $\boldsymbol{48}$ 2) $\boldsymbol{20}$ 3) $\boldsymbol{12}$ 4) $\boldsymbol{54}$ 5) $\boldsymbol{3\sqrt{7}}$ 6) $\boldsymbol{8\sqrt{21}}$ 7) $\boldsymbol{9}$ 8) $\boldsymbol{\f…
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3) x = ______ 5) x = ______ ∠abc = ______ ∠acb = ______
\(75^\circ\) ### Problem 5:
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directions: find the measurement of each missing angle in the triangles…
\(80^\circ\) ### Problem 2:
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six equilateral triangles are connected to create a regular hexagon. th…
6(4a² - 3)
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given: \\(\\overline{bc} \\parallel \\overline{ad}\\) and \\(\\overline…
$\angle BCD \cong \angle BAD$
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find a congruence transformation that maps δyxn to δakt which congruenc…
D. $T_{\langle -10,14 angle} \circ R_{x-axis}(\Delta YXN)$
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quick check y = 2x - 6 y = -4x + 3 (a) graph a (b) graph b (c) graph c …
C. <The graph labeled C with lines intersecting at (1.5, -3), one line with y-intercept (0,-6) and the other with y-intercept (0,3)>
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select the correct answer. which equation represents a line that is per…
C. \( y = -2x - 3 \)
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16. which right triangle has a hypotenuse that is greater than 13 feet …
C. The right triangle with legs 14.4 ft and 4.2 ft (since its hypotenuse is 15 ft, which is greater than 13 ft)
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12. what is the length of the unknown leg of the right triangle rounded…
\(8.8\) feet
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which of the following sets of numbers could not represent the three si…
{8,17,27}
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question given: $overline{bc} \\parallel \\overline{ad}$ and $overline{…
$\angle BCD \cong \angle BAD$ is proven.
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select the correct answer. which equation represents the horizontal lin…
D. \( y = 2 \)
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11. use the pythagorean theorem to find the unknown side length of the …
The unknown side length is \(10\space m\).
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9. what is the length of the hypotenuse of the triangle when $x = 2$? $…
13
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an equilateral triangle has a perimeter of $15x^{3}+33x^{5}$ feet. what…
D. $5x^3 + 11x^5$ feet
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what name best describes this shape? square rhombus parallelogram recta…
square
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$\\overline{bc}$ is tangent to circle a and $\\overline{ab}$ is a radiu…
for ∠B: \(90\) degrees
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select all the trapezoids.
- Top-right quadrilateral (with tick-marked parallel sides) - Bottom-left quadrilateral (with arrow-marked parallel sides) - Bottom-right quadrilateral (with arrow-marked parallel…
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in the diagram below, \\(\\overleftrightarrow{ab}\\) and \\(\\overleftr…
\( 54^\circ \) (corresponding to the option with \( 54^\circ \))
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the measure of (overarc{ab}) is (126^circ). what is the measure of (ang…
\(63^{\circ}\) (corresponding to the option with \(63^{\circ}\))
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what is the scale factor of the dilation?
\(\frac{1}{2}\)
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4. $-2y - 5 > \\frac{5}{2}$
$y < -\frac{15}{4}$ (or $y < -3.75$); on the number line, open circle at $-3.75$, shade left.
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what is the measure of $\\angle ace$ shown in the diagram below?\ \ opt…
65° (the option with 65°)
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the pythagorean theorem do the following lengths form a right triangle?…
No ### Problem 2:
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use circle o to identify each segment. \\overline{bd} is a select \\ove…
s: - $\overline{BD}$ is a secant. - $\overline{BC}$ is a tangent.
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explain fraction equivalence using visual models (mp) reason freida onl…
Using visual models (like rectangles divided into equal parts), we see that 2 times $\frac{1}{4}$ cup (where a rectangle divided into 4 equal parts has each part as $\frac{1}{4}$ …
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use the values $sin 45^circ = 0.707, cos 45^circ = 0.707, \tan 45^circ …
### 1. Determine the given and find ## Step 1: Analyze angle \( \angle A \) From the diagram, \( m\angle A = 45^\circ \) (option b). ## Step 2: Analyze length of \( b \) The lengt…
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graph the line that represents this equation. 5 - 4y = 6
The line is graphed by plotting the points \((0, - 2)\) (from \(y\) - intercept) and \((4,3)\) (using slope \(\frac{5}{4}\)) and drawing a straight line through them. The equation…
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4 in the figure below net of cube is shown. find the surface area of cu…
C. 54 square inches
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find the ordered pair that gives the location of each face. when you ge…
To solve for the ordered pairs of each face, we analyze the x - coordinate (horizontal) and y - coordinate (vertical) of each point: ### 1. Yellow face (top - left yellow) - **Ste…
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1) choose the law and the formula that would be used to solve the trian…
Law: e. Law of Sines Formula: d. \(\boldsymbol{\frac{\sin B}{b}=\frac{\sin C}{c}}\)
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9 what is the circumference of the circle shown below? write your answe…
In terms of \( \pi \), the circumference is \( 84\pi \) millimeters. (If a numerical approximation is needed, it is approximately \( 263.89 \) millimeters.)
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15 find the surface area of the right triangular prism shown below. a 3…
A. 33 square units
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2) choose the law and the formula that would be used to solve the trian…
Law: e. Law of Sines Formula: d. \( \frac{\sin A}{a}=\frac{\sin C}{c} \)
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3) choose the law and the formula that would be used to solve the trian…
Law: c. Law of Sines Formula: b. \(\frac{\sin A}{a}=\frac{\sin B}{b}\)
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triangle nbt is similar to triangle yld. 7. which segment corresponds w…
7. Segment $BT$ 8. $\frac{3}{2}$ 9. 18 10. 20
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4) choose the law and the formula that would be used to solve the trian…
Law: b. Law of Cosines Formula: a. \(a^{2}=b^{2}+c^{2}-2bc\cos A\)
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5) choose the law and the formula that would be used to solve the trian…
Law: d. Law of Cosines Formula: c. \( b^{2}=a^{2}+c^{2}-2ac\cos B \)
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determining parts of quadrilaterals and parallelograms the measure of a…
\( 119.1^\circ \)
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6) choose the law and the formula that would be used to solve the trian…
Law: d. Law of Cosines Formula: c. \(c^{2}=a^{2}+b^{2}-2ab\cos C\)
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chazs new game room is shaped like a cube. it measures 15 feet across. …
D. $900\ \text{ft}^2$
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7) find the length of side b. (there is a triangle abc with angle at a …
2.85 cm (corresponding to the option "2.85 cm")
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8) find the length of a. triangle image with labels: side c = 5 cm, sid…
3.7 cm
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graph the point (1, 9) on the coordinate plane.
The point \((1,9)\) is graphed by moving 1 unit right on the x - axis and 9 units up from the origin, at the intersection of \(x = 1\) and \(y=9\) on the coordinate plane.
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7 a box is to be wrapped in a shiny pink decorative paper. the box is 9…
$202$ in²
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9) find ( mangle b ) to the nearest degree. (image of triangle abc with…
\( 47^\circ \) (corresponding to the option with \( 47^\circ \))
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which point has coordinates (-4, 1.5)?
Z
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what is the measure of (overarc{ac})?
\( 88^\circ \) (corresponding to the first option)
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what is the measure of \\(\\overarc{abc}\\)? (blue arc) options: \\(310…
\( 260^\circ \) (corresponding to the option with \( 260^\circ \))
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what is the measure of ∠abc? 62° 88° 92° 176° 31°
\( 31^\circ \) (so the option with \( 31^\circ \))