几何
三角形、圆、解析几何与证明题。
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name: date: ratios directions: write a ratio for each problem in simple…
1. \(3:7\) (yellow) 2. \(125:7\) (red) 3. \(2:5\) (black) 4. \(27:34\) (yellow) 5. \(14:19\) (white) 6. \(2:1\) (but as per options' possible mis - writing, if we assume long - co…
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is pqrs similar to wxyz? justify your answer. yes, because a dilation b…
Yes, because a dilation by a scale factor of 3 centered at point \(P\) maps \(PQRS\) onto \(WXYZ\).
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is stuv similar to bcde? justify your answer. yes, because a dilation b…
No, because \(\frac{BC}{ST}\) is not equal to \(\frac{DE}{UV}\)
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is abc similar to stu? justify your answer. yes, because a dilation by …
Yes, because a dilation by a scale factor of \(\frac{1}{2}\) centered at point \(A\) followed by a rotation \(180^{\circ}\) around the origin maps \(ABC\) onto \(STU\).
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solve the inequality and graph the solution. -16 ≥ 10 + 13f plot the en…
The solution of the inequality is \(f\leq - 2\). On the number - line, we place a closed circle at \(-2\) (because the inequality is \(\geq\) and when we rewrite it as \(f\leq - 2…
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is cdef similar to lmno? justify your answer. yes, because a translatio…
No, because \(\angle C\) and \(\angle L\) do not have the same measure.
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solve the inequality and graph the solutio 3c + 8 < 5 plot the endpoint…
The solution of the inequality \(3c + 8<5\) is \(c < - 1\). On the number - line, we have an open circle at \(-1\) (since \(c=-1\) is not included in the solution) and a ray exten…
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is efgh similar to lmno? justify your answer. yes, because a dilation b…
Yes, because a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin maps \(EFGH\) onto \(LMNO\).
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solve the inequality and graph the solution. -2 + 2p > 10 plot the endp…
The solution of the inequality is \(p>6\). On the number - line, we have an open circle at \(p = 6\) (because \(6\) is not included in the solution set) and a ray extending to the…
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is mno similar to stu? justify your answer. yes, because a dilation by …
Yes, because a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin maps \(MNO\) onto \(STU\).
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self - assessment 2. reasoning a composition of rigid motions maps one …
Reflect $\triangle JKL$ over the $x$-axis and then translate it 3 units to the right and 3 units down.
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solve the inequality and gra 5d - 10 > 5 plot the endpoints. select an …
The solution of the inequality is \(d>3\). On the number - line, we plot an open circle at \(d = 3\) (because \(d = 3\) is not included in the solution set) and draw a ray to the …
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solve the inequality and graph the solution 2q + 2 < 10 plot the endpoi…
The solution of the inequality \(2q + 2<10\) is \(q < 4\). On the number - line, we have an open circle at \(4\) and a ray extending to the left.
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congruence transformations another name for a rigid motion or a combina…
A congruence transformation that maps \( \triangle JKL \) to \( \triangle MNP \) is a \( 180^{\circ} \) rotation about the origin followed by a translation \( 1 \) unit right.
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use a venn diagram to illustrate the relationship between the given set…
Draw a large circle labeled \(Q\). Inside it, draw a smaller circle labeled \(Z\). Inside \(Z\), draw a smaller circle labeled \(W\). Inside \(W\), draw a smaller circle labeled \…
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is efgh similar to pqrs? justify your answer. yes, because a dilation b…
Yes, because a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin maps \(EFGH\) onto \(PQRS\).
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solve the inequality and graph the solution. -8 + 6n < 4 plot the endpo…
The solution of the inequality \(-8 + 6n<4\) is \(n < 2\). On the number - line, we have an open circle at \(2\) and a ray extending to the left.
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complete the paragraph to prove that \\( \\triangle x y z \\sim \\trian…
Start by applying a dilation to \(\triangle XYZ\) centered at \(Y\) with scale factor \(\frac{AC}{XZ}\). This will map \(\triangle XYZ\) to \(\triangle X'YZ'\). Since the dilation…
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solve the inequality and graph the solution. 8 + 3c < 2 plot the endpoi…
The solution of the inequality \(8 + 3c<2\) is \(c < - 2\). On the number - line, we have an open circle at \(-2\) and a ray extending to the left.
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solve the inequality and graph 1 + 5k > -9 plot the endpoints. select a…
The solution of the inequality \(1 + 5k>-9\) is \(k > - 2\). The graph has an open circle at \(-2\) and a ray extending to the right.
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solve the inequality and graph the 1 - 7p < 8 plot the endpoints. selec…
The solution of the inequality \(1-7p < 8\) is \(p>-1\). On the number - line, we plot an open circle at \(p = - 1\) (because the inequality is strict, \(p eq - 1\)) and draw a r…
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now, use the distances you found on your slope triangle to write an exp…
\(\frac{y - 2}{x - 3}\)
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∠4 and ∠5 are complements, and ∠1 and ∠5 are complements by the congrue…
∠1
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chris draws an image of two lines that lie in the same plane and are eq…
A. parallel lines
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review problems 3. select all the pieces of information that would tell…
a. Not proportional. b. Not proportional.
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another look! one way to find the product of 12×24 is to use an array. …
1. \(26\times18 = 468\) 2. \(23\times23=529\)
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select all quantities that are proportional to the diagonal length of a…
B. perimeter of a square, C. side length of a square
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estimate the side length of a square that has a 9 cm long diagonal. cm
\(6.4\)
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write an equation for the graph.
\(x = 3\)
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in each figure below, a plane passes through a geometric solid as shown…
(a) Rectangle; (b) Triangle; (c) Circle
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find the value of x.
\(x = 31\)
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for each object, identify the two shapes that can be combined to model …
(a) Cylinder (third shape in row (a)) and Cone (fourth shape in row (a)); (b) Half - cylinder (first shape in row (b)) and Cube (second shape in row (b)); (c) Cone (first shape in…
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9. aa~ sss~ sas~ not ~ △______~△______ 11. aa~ sss~ sas~ not ~ △______~…
- For problem 9: \(AA\sim,\triangle TSU\sim\triangle VWU\) - For problem 11: \(Not\sim\)
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directions: determine whether the triangles are similar by aa~, sss~, s…
1. **For the first pair of triangles (\(\triangle SRT\) and \(\triangle QPN\))**: - Calculate the ratios of the corresponding sides: - \(\frac{44}{22}=\frac{44}{2\times22} = 2\), …
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find the following angle measures m∠ead = m∠cab =
\(m\angle EAD = 29^{\circ}\), \(m\angle CAB = 119^{\circ}\)
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ea of a right triangle with legs not parallel to the coordinate axes tr…
\(25\)
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is the blue figure a rotation of the red figure about the origin? if so…
yes, 90° clockwise
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the vertices of a rectangle are ( e(-1,1) ), ( f(-1,3) ), ( g(-5,3) ), …
\(E''(2,-1)\), \(F''(2,-3)\), \(G''(-2,-3)\), \(H''(-2,-1)\)
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multiplying and dividing angles multiply or divide each of these exerci…
17. \(108^{\circ}42'\) 21. \(108^{\circ}48'27''\) 25. \(10^{\circ}41'36''\) 27. \(30^{\circ}34'12''\)
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3. how did the triangle trade contribute to the colonial economy? a. by…
C. By providing a steady supply of enslaved labor for plantations
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given ( mangle orp = 80^{circ} )( mangle orn=(3x + 10)^{circ} )prove ( …
$\angle ORP$ and $\angle ORN$ are a linear pair
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what is ( mangle dfc )? ( 45^{circ} ) ( 80^{circ} ) ( 125^{circ} ) ( 13…
C. \(125^{\circ}\)
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which angle is a vertical angle with ∠efd? ∠dfb ∠ced ∠bfc ∠afb
C. \( \angle BFC \)
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given ( mangle edf = 120^{circ};mangle adb=(3x)^{circ},mangle bdc=(2x)^…
vertical angles are congruent
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in which diagram are angles 1 and 2 vertical angles?
The first diagram (the one with two intersecting lines where angles 1 and 2 are opposite each other at the intersection point).
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what is the value of x? 20 35 60 70
A. 20
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given ( mangle ade = 60^circ ) and ( mangle cdf=(3x + 15)^circ ) prove …
Statement: \(60 = 3x + 15\), Reason: substitution
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which pair of angles are vertical angles? \\( \\angle w r u \\) and \\(…
$\angle VRU$ and $\angle TRS$
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marcus states that angle orp and angle lrp are a linear pair which best…
He is incorrect. Ray RO and ray RL are not opposite rays.
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in the diagram, which angle is part of a linear pair and part of a vert…
C. \( \angle GFD \)
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if the ( mangle srw = 85^{circ} ), what are the measures of ( angle vru…
\(m\angle VRU = 85^{\circ}\), \(m\angle URW = 5^{\circ}\)
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given triangle abc and triangle def, with ∠a = 60 degrees and ∠d = 60 d…
1. B. Yes, by SAS similarity 2. d. To prove the similarity of triangles 3. a. To ensure that the scale factor between the triangles is consistent 4. a. 6cm
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which of the following statements is true for similar triangles? a. non…
1. c. Corresponding angles are congruent and sides are proportional 2. c. Triangles PQR and STU are similar by SAS similarity 3. c. $AB/DE = AC/DF$ 4. b. $7.5$ cm 5. d. Yes, by SA…
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what is the measure of \\( \\angle dae \\)? \\( 45 ^ { \\circ } \\) \\(…
45°
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given ( mangle qvr = 49^{circ} ) prove ( x = 15 ) complete the steps of…
$3x + 4 = 49$
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what is ( mangle srw )? 18 54 126 108
126
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given ( mangle elg = 124^{circ} ) prove ( x = 28 ) complete the steps i…
4. angle addition postulate; 6. \(2x = 56\)
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what is the value of x? 30 45 55 60
45
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which angles are linear pairs? check all that apply ∠srt and ∠trv ∠srt …
- $\angle SRT$ and $\angle TRU$ - $\angle VRW$ and $\angle WRS$
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what are the numerical measures of each angle in the diagram? ∠1 and ∠3…
\( \angle 1\) and \( \angle 3\) measure \( 53\) degrees. \( \angle 2\) and \( \angle 4\) measure \( 127\) degrees.
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adding and subtracting angles add or subtract each of these exercises a…
1. \(131^{\circ}\) 5. \(19^{\circ}23'44''\) 9. \(14^{\circ}9'\) 13. \(3^{\circ}11'48''\)
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why is it important to maintain proportional relationships in architect…
1. C. To accurately represent the final structure 2. C. They triple in length 3. D. \(\frac{1}{3}\) 4. D. To ensure proportional relationships
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what happens to the perimeter of a triangle when it is scaled by a fact…
1. b. It triples 2. a. Create accurate maps 3. c. To scale objects proportionally 4. c. Triangles with sides 3, 4, 5 and 5, 6, 7 5. b. To confirm proportionality 6. d. \(\frac{2}{…
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the ratio of the lengths of corresponding sides of similar triangles is…
1. scale factor 2. similar 3. proportional 4. cartography 5. scale 6. scale 7. ratios 8. SSS similarity theorem 9. SSS (or similarity) 10. proportionality 11. similar 12. geometry…
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9. the pitch of a roof on a lean - to that dianna is building is 2:5. i…
\(h = 1.92\) m
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9. the pitch of a roof on a lean - to that dianna is building is 2:5. i…
\(h = 1.92\)m
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15. if ( \triangle wxy cong \triangle hji ), complete each part, a) ( j…
a) \(16m\) b) \(15m\) c) \(37^{\circ}\) d) \(114^{\circ}\) e) \(29^{\circ}\)
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which are vertical angles? check all that apply □ \\( \\angle eab \\) a…
- $\angle EAB$ and $\angle CAD$ - $\angle CAB$ and $\angle DAE$
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which are linear pairs? check all that apply ∠dae and ∠ead ∠bac and ∠ca…
B. \( \angle BAC \) and \( \angle CAD \), D. \( \angle EAD \) and \( \angle DAC \)
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10. find the value of x. (8x - 23)° 34°
\(x = 12\)
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5. find the value of x and m∠a.
\(x = 15\) and \(m\angle A = 48^{\circ}\)
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4. find the value of x and m∠a. (9x + 17)° (3x - 4)° (6x - 31)°
\(x = 11\) and \(m\angle A=116^{\circ}\)
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a two - column proof uses a visual representation of the logical flow o…
B. contains a table with a logical series of statements and reasons that reach a conclusion
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given that ba bisects ∠dbc, which statement must be true? ○ m∠abd = m∠a…
A. \( m\angle ABD = m\angle ABC\)
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a paragraph proof uses inductive reasoning to prove a statement contain…
contains a set of sentences explaining the steps needed to reach a conclusion
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which statement is true about the diagram? 10 5 4 a k b t k is the midp…
A. \(K\) is the midpoint of \(\overline{AB}\)
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what is the missing justification? \\( \\angle a \\cong \\angle b, \\an…
transitive property
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3. find the value of x.
\(x = 18\)
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given: ( mangle aeb = 45^{circ}) (angle aec) is a right angle prove: (o…
angle addition postulate
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which statement is true about the diagram? ∠def is a right angle m∠dea …
\(m\angle DEA = m\angle FEC\)
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which statement is true about the given information? bd = \\frac{1}{2}b…
\(\overline{BD}\cong\overline{CE}\)
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given that (angle abccongangle dbe), which statement must be true? (ang…
$\angle ABD\cong\angle CBE$
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writing a two - column proof identify the missing parts in the proof gi…
B. \(m\angle ABC = 90^{\circ}\) C. angle - addition postulate D. \(2m\angle CBD=90^{\circ}\)
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identify the missing parts in the proof given: \\( \\angle a b c \\) is…
A. angle \(ABC = 90\) B. \(m\angle ABD=m\angle CBD\) C. angle addition postulate D. \(2\times m\angle CBD = 90^{\circ}\)
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given \\( \\angle abc \\) is a right angle and \\( \\angle def \\) is a…
A. definition of a right angle; B. substitution property; C. definition of congruent angles
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given: (overrightarrow{eb}) bisects (angle aec) (angle aed) is a straig…
First blank: \(90\); Second blank: \(AEC\); Third blank: \(angle\ addition\ postulate\)
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given ( mangle abc = mangle cbd ) prove ( overrightarrow{bc} ) bisects …
A: given; B: definition of congruent; C: definition of bisect
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given \\( \\overleftrightarrow{ad} \\). \\( \\overleftrightarrow{eb} \\…
- $\angle CED$ is a right angle - $m\angle CEB = m\angle BEA$ - $m\angle DEB = 135^{\circ}$
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if ( ig = 20 ), ( gh = 19 ), and ( jk = 39 ), find the length of ( over…
\(41.1\)
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8. one of the steepest railways in the world is the lisbon tram in port…
a) The slope is $0.135$. b) The angle of elevation is approximately $7.7^{\circ}$. c) The rise for a run of $15$ m is $2.025$ m.
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which property is shown? if ( mangle abc = mangle cbd ), then ( mangle …
C. symmetric property
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the square below is the image of a square that was dilated by a scale f…
The area of the pre - image is \(400\).
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the rectangle below is the image of a rectangle that was dilated by a s…
\(36\)
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the figure below is a square. find the length of side x in simplest rad…
\(4\)
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find the length of the third side. if necessary, write in simplest radi…
\(3\sqrt{2}\)
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find the length of the third side. if necessary, write in simplest radi…
\(2\)
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find the length of the third side. if necessary, write in simplest radi…
\(2\sqrt{2}\)
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which information do you know is true from the diagram? check all that …
- ∠ABD is a right angle - \(\overrightarrow{BC}\) bisects angle ∠ABD - \(m\angle ABC = 45^{\circ}\) - \(m\angle CBD = 45^{\circ}\) - \(m\angle ABD = 90^{\circ}\)
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use the pythagorean theorem to find the length of the hypotenuse of eac…
9) \(34\) in. 10) \(17\) ft. 11) \(\approx2.2\) ft. 12) \(\approx7.1\) in. 13) \(17\) ft. 14) \(\approx7.8\) km. 15) \(\approx13.4\) ft.
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volume is a way to measure how much space something takes up. length: 1…
48 cm³