Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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points a, b, and c are collinear. point b is between a and c. find the …
\( AC = 28 \) ### Problem 10:
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john and marsha are calculating the width of the lake shown in the figu…
A) 5.2 inches
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the segment addition postulate find the length indicated. 1) ( h \bulle…
9 ### Problem 2
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a construction company is putting cone - shaped tops on top of each bri…
C) 314 \( \text{cm}^3 \)
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you can transform δuvw to δuvw by translating it and then performing a …
Translation: $(x, y) \mapsto (x - 6, y - 10)$ Scale factor: $3$
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review the twenty - ninth and thirtieth paragraphs. 28 soon the gondola…
She suspects that Grandpa has faked his illness.
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you can transform $\\triangle ghi$ to $\\triangle ghi$ by translating i…
Translation: $(x, y) \mapsto (x - 7, y + 6)$ Scale factor: $2$
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review the thirteenth and fourteenth paragraphs. there it was—a boxy, r…
She has traveled into the past.
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points lines and planes exit quiz multiple choices 1. a line and a plan…
a. Point ### Question 2
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9. find ( mangle lmn ).
$108^\circ$
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the graph shows rectangles cdef and cdef. which sequences of transforma…
A common sequence is **Rotate 180° around the origin, then translate 9 units up and 15 units right** (or adjust based on precise coordinates). For example, translating each point …
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points lines and planes bell work 1. complete the following statements …
b. If two distinct lines intersect, then they intersect in exactly one point; c. If two distinct planes intersect, then they intersect in exactly one line ### Question 3 (Which ex…
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. write the equation of the line. b: ______________ m: ______________ e…
b: $-1$ m: $-\frac{1}{3}$ Equation: $y = -\frac{1}{3}x - 1$
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4. write the equation of the line. b: ________________ m: _____________…
b: $0$ m: $\frac{3}{2}$ Equation: $y=\frac{3}{2}x$
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16. if v is the incenter of \\( \\triangle pqr \\), \\( qt = 5 \\), \\(…
\( SV = 7 \) \( QS = 5 \) \( QV = \sqrt{74} \) \( PS = 6\sqrt{22} \)
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reasoning 5. in the diagram shown, (overline{hi}) and (overline{jk}) in…
A rotation about point \( L \) (or a reflection/translation combination) can map \( \triangle HLK \) onto \( \triangle ILJ \). This is justified by the SAS congruence of \( \trian…
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problem solving with addition and subtraction equations 4. adesh writes…
a. $m = 57$ (verified as correct by substitution) b. The solution represents the measure of the unknown angle $m^\circ$ in the right angle diagram. c. Adesh incorrectly added 33 t…
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5. list the sequence of steps required to graph the function ( f(x) = -…
c. horizontal translation 4 units to the left, vertical translation 6 units up, reflection in x-axis
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use the figure below to answer the following questions. 11. if $\\trian…
SSS (Side - Side - Side) postulate ### Question 12
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$\\angle jhk \\cong \\angle hji$, $\\overline{ij} \\perp \\overline{hi}…
Angle-Angle-Side (AAS) Congruence Theorem
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transformations: unit 1 quiz 1 review 1. list characteristics of the fo…
- \( L(2, 1) \) (assuming original coordinates) - \( L'(-1, 3) \) - Rule: \( (x, y) \to (x - 3, y + 2) \) ### Question 3: Rotate the polygon 90° about the origin
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consider right triangle $\\triangle abc$ below. which expressions are e…
B. $\frac{\text{length of side adjacent to } \angle A}{\text{length of hypotenuse}}$ D. $\frac{AC}{AB}$
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uw bisects ∠vux and ∠vwx. complete the proof that ( overline{uv} cong o…
| Statement | Reason | |-----------|--------| | 6. $\triangle UVW \cong \triangle UXW$ | ASA Congruence Criterion | | 7. $\overline{UV} \cong \overline{UX}$ | Corresponding Parts …
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remember for problems 11–14, multiply. 11. $\frac{1}{5} \\times \\frac{…
11. $\frac{1}{40}$ 12. $\frac{1}{50}$ 13. $\frac{1}{56}$ 14. $\frac{1}{36}$ 15a. $12a + 3$ 15b. $16w - 20$ 16. B. All parallelograms are quadrilaterals because all parallelograms …
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two triangles are graphed with the following vertices: a(1, 1), b(0, 1)…
Each base angle measures $65^\circ$. ### Question 9
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geometry worksheet 4.6b – medians & centroids page 1 median – a segment…
1. $8.5$ 2. $22$ 3. $10$ 4. $6.7$ 5. $12$ 6. $24$ 7. $\frac{58}{3}$ 8. $11$ 9. $20$ 10. $6.5$ 11. $4.5$ 12. $5.3$ 13. $6$
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name date practice 18 1. graph the solutions to ( x geq 2 ) on the numb…
1. (Graph: Closed circle at 2, shade right) 2. (Graph: Open circle at 7, shade left) 3. $0$, $5$, $-3$ (any three numbers less than 7 are acceptable) 4. Infinitely many solutions.…
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use the figure shown and the given information. l is the centroid of △m…
14. $\boldsymbol{11}$ 15. $\boldsymbol{15}$ 16. $\boldsymbol{4}$ 17. $\boldsymbol{12}$ 18. $\boldsymbol{24}$ 19. $\boldsymbol{8.5}$ 20. $\boldsymbol{14.6}$ 21. $\boldsymbol{2}$ 22…
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3. a parabola that opens downward has its vertex at (3, 0) and a y - in…
a) The equation of the function is $\boldsymbol{f(x)=-(x-3)^2}$ (or expanded form $\boldsymbol{f(x)=-x^2+6x-9}$) b) Key points for graphing: - Vertex: $(3, 0)$ - Y-intercept: $(0,…
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which statement is true? n is a point of tangency on circle p. pt is a …
$\overleftrightarrow{SR}$ is a secant of circle P.
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based on the diagram, pick the two choices below that represent the exp…
$\sin(32^\circ)$, $\frac{28}{53}$
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for problems 4–6, graph the solutions to the inequality on the number l…
1. For $x>0$: Open circle at 0, shade right. 2. For $y<-3$: Open circle at -3, shade left. 3. For $5>z$ (or $z<5$): Open circle at 5, shade left. 4. For problem 7: $x<5$, $5>x$ 5.…
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use translations to graph the given function. $m(x)=|x - 4|$
The graph of $m(x)=|x-4|$ is a V-shaped graph with vertex at $(4,0)$, passing through points such as $(3,1)$, $(5,1)$, $(2,2)$, and $(6,2)$, formed by shifting the parent absolute…
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in parallelogram (abcd), (mangle aeb = 122^circ), (mangle dac = 62^circ…
\(7\)
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triangle bac was dilated from triangle bde at a scale factor of 2. what…
$\boldsymbol{\frac{3}{2} = \frac{6}{4}}$ (or simplified as $\boldsymbol{\frac{BE}{BD} = \frac{BC}{BA}}$)
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in parallelogram vwxy, ( mangle wzx = 68^circ ), ( mangle vyw = 41^circ…
\( 9 \)
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10. which number is the solution to \\(\\frac{2}{5}x + 9 = x - 3\\)? a.…
10. C. 20 11. Substitute $x=4$ into $x+3=7$: $4+3=7$, which equals the right-hand side, so 4 is the solution. 12. a. $24 = y - 8$ b. $24 = y + 8$ c. $8 = 24y$ d. $24 = 8y$
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solve the compound inequality. use graphs to show the solution set to e…
1. Graph for $4(3-x) < -6$: B. <graph with open circle at 4.5, arrow right> 2. Graph for $\frac{x-2}{3} \leq -2$: B. <graph with closed circle at -4, arrow left> 3. Compound inequ…
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equations in real - world situations 9. match each situation with the e…
a. $15=5x$ b. $15=x+5$ c. $15=x-5$ d. $5=15x$ --- ### Question 10
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how many rays are shown in the drawing? number of rays:
3
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what is the volume of the following triangular prism? 9 m 6 m 13 m 351 …
351 \( \text{m}^3 \) (corresponding to the option: 351 \( \text{m}^3 \)) ### Second Question (Rectangular Prism Volume)
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the base of a solid right pyramid is a regular hexagon with a radius of…
$\boldsymbol{6x^2\sqrt{3}}$ units² (corresponding to the last option)
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to solve: 1. figure out how tall the stack of cards is. □ inch(es). v =…
1. 1 inch(es) 2. 4 inches 3. 25%
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camille has two boxes with the dimensions shown. she wants to use the b…
Box A Volume = $172\frac{1}{2}$ cubic inches Box B Volume = $172\frac{1}{8}$ cubic inches Which box should Camille use? Box A Should she use box C? YES
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a solid oblique cone with a slant length of 17 units is placed inside a…
$640\pi$ cubic units
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an oblique prism with a square base of edge length x units has a volume…
$\boldsymbol{\frac{1}{2}x}$ units (the second option)
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an oblique prism has a volume of 144 cubic units. the area of its base …
C. 6 units
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max observes the zoo and the library from a helicopter flying at a heig…
400 feet
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an oblique cylinder is shown. which represents the volume of the cylind…
300π
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a solid oblique pyramid has a regular pentagonal base. the base has an …
19 ft³
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two ropes, ad and bd, are tied to a peg on the ground at point d. the o…
10 feet
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9. explain why rotating a figure 180° about any point results in a poin…
A \(180^\circ\) rotation about a center \(O\) for any point \(P\) in the figure creates an image \(P'\) such that \(O\) is the midpoint of \(\overline{PP'}\) (as \(\angle POP' = 1…
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a source of laser light sends rays ab and ac toward two opposite walls …
$30 + 40 = 70$ m
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3. consider the given right triangular prism and the cross section form…
a. The cross section is an isosceles triangle with side lengths labeled: two sides of 11 inches and one side of 9 inches (congruent to the given base triangle). b. Yes, the cross …
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13. we can prove that two triangles are similar because their angles ar…
A. AA Theorem
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which angles are congruent to each other? $\\angle 9$ and $\\angle 1$ $…
$\angle9$ and $\angle1$
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solve the compound inequality. use graphs to show the solution set to e…
1. Correct graph for $x>7$: D. <graph with open circle at 7, shading right> 2. Solution set of the compound inequality $x>7$ and $x<-1$: $\emptyset$ (empty set)
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question 2 (5 points) what is significant about the geometric dilution …
Geometric dilution (used in pharmacy/compounding) ensures uniform mixing of potent substances (e.g., drugs) by adding diluent in geometric - ratio steps (e.g., mixing a small amou…
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2. consider the given cube and the cross section formed by a plane inte…
a. The cross section is a square identical to the base: ``` 5.4 cm ┌───────────┐ │ │ 5.4 cm │ │ └───────────┘ 5.4 cm ``` (All four sides are labeled 5.4 cm, matching the base's di…
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how are the binomial factors of $x^2 + 7x - 18$ and $x^2 - 7x - 18$ sim…
The trinomial \(x^2 + 7x - 18\) factors into \((x + 9)(x - 2)\) and \(x^2 - 7x - 18\) factors into \((x - 9)(x + 2)\). The signs in each binomial are reversed for the linear - ter…
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4) the number line is shown with a ray starting from 0 (or near 0) and …
The inequality represented is \( \boldsymbol{x < 0} \) (or all real numbers less than 0).
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find st in rectangle qrst. st = submit
22
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solve for ( x ). round to the nearest tenth, if necessary.
$38.6$
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find m∠f in parallelogram efgh. m∠f = \\boxed{}^\\circ submit
$51$
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5) 51 m, 68 m, 85 m
The lengths 51 m, 68 m, 85 m form a right - angled triangle (by the Pythagorean theorem).
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solve for x. round to the nearest tenth, if necessary.
13.5
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4) 2 yd, 3 yd, √13 yd
These side lengths form a right triangle (by the Pythagorean theorem).
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graph these equations: $y = \\frac{1}{5}x + 7$ $y = \\frac{1}{5}x + 7$ …
The graph is a straight line with y - intercept at \( (0,7) \), and other points such as \( (5,8) \) and \( (-5,6) \) (found using the slope \( \frac{1}{5} \)) plotted on it. The …
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in $\\triangle uvw$, the measure of $\\angle w = 90^\\circ$, $uw = 36$,…
$\frac{77}{85}$
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3) 21 mm, 24 mm, 32 mm
The lengths 21 mm, 24 mm, and 32 mm can form a triangle.
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question in △def, the measure of ∠f = 90°, ed = 53, df = 45, and fe = 2…
$\frac{28}{53}$
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a shipping company uses an inclined conveyor belt to load and unload pa…
$4^2 + 10^2 = c^2$ $16 + 100 = c^2$ $116 = c^2$ $10.8 = c$ The length of the conveyor belt is about $10.8$ feet.
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a triangle has sides with lengths 8 inches, 15 inches, and 17 inches. i…
No, because $8^2 + 15^2 eq 17^2$
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in $\\triangle jkl$, the measure of $\\angle l = 90^\\circ$, $kj = 17$,…
$\frac{8}{15}$
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question in $\\triangle tuv$, the measure of $\\angle v = 90^\\circ$, $…
$\frac{56}{65}$
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1) 4 in., 5 in., 7 in. 2) 5 cm, 12 cm, 13 cm
s: 1) 4 in., 5 in., 7 in. do not form a right triangle. 2) 5 cm, 12 cm, 13 cm form a right triangle.
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determine the value of ( x ). enter the correct value in the box. ( x =…
\(100\)
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directions the lengths of the sides of various triangles are given belo…
No (the triangle with sides 4 in, 5 in, 7 in is not a right triangle)
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determine the value of x. enter the correct value in the box. x = \\squ…
\(x = 42\)
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in $\\triangle vwx$, the measure of $\\angle x = 90^\\circ$, $vx = 45$,…
$\frac{45}{28}$
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plot the point on this function with an x - value of 0. what is the y -…
7
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two dimensions of a right triangle are 5 units and 13 units. a student …
D. No. $5^2 + 13^2 = 25 + 169 = 194$. $\sqrt{194}$ is about 13.9, which is not an integer. B. The student is incorrect. The correct equation is $5^2 + b^2 = 13^2$, $b^2 = 144$, $b…
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y = x + 2 y = x + 1 click to select points on the graph.
The system of equations \( \begin{cases}y = x + 2\\y = x + 1\end{cases} \) has no solution because the two lines are parallel (same slope, different y - intercepts).
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5. two sides of a triangle measure 9 cm and 15 cm. which expression rep…
B. $6 < x < 24$
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4. in △pqr, side pq = 10 cm, qr = 14 cm, and pr = 16 cm. which angle is…
B. $\angle Q$
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in the right triangle, there are segments labeled 20, 25, and a side la…
\( \boxed{30} \)
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timed problem score: 2/10 current time: 29.9 find: \\(\\tan a\\) \\(\\t…
$\boldsymbol{\frac{45}{60}}$ (matches the third option)
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find: \\(\\tan a\\) *the figure is not drawn to scale* answer \\(\\frac…
$\frac{48}{20}$ (matches option B. $\frac{48}{20}$)
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timed problem score: 0/10 current time: 2.0 find: \\(\\cos a\\) *the fi…
$\frac{4}{5}$
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express the trig ratios as fractions in simplest terms. answer attempt …
$\sin K = \frac{3}{5}$ $\cos J = \frac{3}{5}$
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4) a = 9 b = □ c = 36
If we assume a geometric sequence relationship (which gives an integer answer, likely the intended case), \(b = 18\). If we assume the Pythagorean theorem with \(c\) as hypotenuse…
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in the right triangle diagram, there are lengths 18, 22, and an unknown…
\( x = 6\sqrt{11} \approx 19.9 \) (or if we round to a whole number, \( 20 \))
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3) a=□ b=8 c=14
If we leave it in radical form, \(a = 2\sqrt{33}\); if we use a decimal approximation, \(a\approx11.49\) (rounded to two decimal places)
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2) a=□ b=6 c=10
\(a = 8\)
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$\\overleftrightarrow{dy}$ is tangent to circle $o$ at point $d$, and $…
$61^\circ$
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directions: complete each proof. 1. given: $overline{de} \\parallel \\o…
| Statements | Reasons | |------------|---------| | $\overline{DE} \parallel \overline{GH}$ | Given | | $\angle D \cong \angle G$, $\angle E \cong \angle H$ | Alternate Interior A…
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2. in a given triangle, the measurement of each angle is (2x+10), (x+20…
C. 50
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directions use the pythagorean theorem and a calculator to find the mis…
\(7.3\)
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nevaeh leans a 22-foot ladder against a wall so that it forms an angle …
19.77 feet
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directions: complete each proof. 1. given: $overline{de} \\parallel \\o…
| Statements | Reasons | |------------|---------| | $\overline{DE} \parallel \overline{GH}$ | Given | | $\angle D \cong \angle G$, $\angle E \cong \angle H$ | Alternate Interior A…