Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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find the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm. 12 24…
12
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if p is the midpoint of ab and ab = 12, what is the length of pb? 6 9 1…
6
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what is the surface area of a cube given that the volume of the cube is…
B. 96
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what is the volume? 5 in 4 in 28 100 196 300
100
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name date determine if the triangles are congruent. write the triangle …
1. not enough information 2. \(\triangle JKL\cong\triangle JML\) (SSS) 3. not enough information 4. not enough information 5. \(\triangle ABC\cong\triangle ADC\) (SAS) 6. \(\trian…
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what is the measure of the hypotenuse of a right triangle with side len…
\(\sqrt{89}\) (the third option)
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which graph represents the solution set for the inequality \\( \\frac {…
The second option (the number - line with a closed circle at 36 and an arrow pointing to the left) is the correct graph.
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5. 7. (overline{bc}) bisects (angle acd)
For problem 5: \(m\angle1 = 35^{\circ}\), \(m\angle2 = 43^{\circ}\), \(m\angle3 = 12^{\circ}\) For problem 7: \(m\angle1 = 42^{\circ}\), \(m\angle2 = 42^{\circ}\), \(m\angle3 = 48…
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3. 79° 104° m∠1 =
\(25^{\circ}\)
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3. 1 79° 104° m∠1 =
\(25^{\circ}\)
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exterior angle theorem an exterior is formed by extending any one side …
For the Triangle Angle Sum Theorem: \(m\angle A + m\angle B + m\angle C = 180^{\circ}\). For the Exterior Angle Theorem: \(m\angle1=m\angle2 + m\angle3\)
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a plane flies 40 miles from a starting point, and at the same time, a s…
\(45^{\circ}\)
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what is the measure of angle b?
\(81.04^{\circ}\)
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shellyara is hiking a straight line up a mountain trail. she hikes a to…
19.47°
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solve the triangle below by finding all the missing sides and angles. c…
c = 4.47, \(A = 26.6^{\circ}\), \(B = 139.4^{\circ}\) (corresponds to the third option: \(c = 4.47,A = 26.6^{\circ},B = 139.4^{\circ}\))
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mia was given the triangle below to solve for x. step a: \\( \\cos ( 1 …
Mia made an error in Step B.
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two ships leave from the same spot. one travels east for 12 miles. the …
4.61 miles
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a giant, 268 - foot tree casts a smaller, 158 foot shadow. what is the …
\(59.48^{\circ}\)
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in the figure below, what is ac? 15.98 cannot be determined 4 1.02
4
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name date class lesson 11 - 2 addition and subtraction equations practi…
1. \(r = 4\) 2. \(w=38\) 3. \(m=\frac{5}{8}\) 4. \(t=-4\) 5. \(x + 139=180\) 6. \(x = 41^{\circ}\) 7. \(x+18 = 90\) 8. \(x = 72^{\circ}\) 9. Problem: There are 3 red apples and \(…
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question 1 in the figure below, what is ab? 0.21 4.24 3.77 4.51
4.24
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christopher is solving the triangle by finding all the missing sides an…
Part 1 calculation of \(x = 13.1\) is correct. Part 2 has an error: the angle opposite \(8\) is approximately \(34.2^{\circ}\) (not \(76.6^{\circ}\)). Part 3 has an error: using t…
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javi is standing at the end of a 100 - foot - long hallway. he looks up…
10.8 feet
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christopher is solving the triangle by finding all the missing sides an…
In Part 2, the error is using \(12.9 = 13.1\sin\theta\) (should be \(8\times\sin67^{\circ}\approx7.36\) instead of \(12.9\)). The correct angle opposite \(8\) is approximately \(3…
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question 5 of 25 an isosceles triangle has angle measures 55°, 55°, and…
D. 8.72 inches
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question 4 of 25 suppose a triangle has two sides of length 42 and 35, …
A. 66.78
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select the true statement about triangle abc. a. \\( \\cos a = \\cos c …
D. \(\cos A=\sin C\)
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question 2 of 25 calculate the length a to two decimal places. a. 13.68…
A. 13.68
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ru || sv. complete the proof that tv ≅ su. statement 1 ∠u ≅ ∠v 2 ru || …
\(\triangle SRU\cong\triangle STV\) (by ASA), so \(\overline{TV}\cong\overline{SU}\) (by CPCTC)
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question 1 of 25 given any triangle abc labeled as shown, the law of si…
D. The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.
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question 10 of 10 given any triangle abc labeled as shown, which equati…
A. \(\frac{\sin A}{c}=\frac{\sin C}{a}\)
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question 9 of 10 use the law of sines to find the length of side c. rou…
B. 32.7
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question 8 of 10 an isosceles triangle has angle measures 56°, 56°, and…
A. \(21.5\) cm
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use the law of sines to find the length of side b. round your answer to…
C. 54.9
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what is the final transformation in the composition of transformations …
a \(180^{\circ}\) rotation about point \(B'\)
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the rule ( t_{5,-0.5}circ r_{0,180^{circ}}(x,y) ) is applied to ( \tria…
\( (4,-1.5) \)
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in triangle abc, m∠a = 25°, m∠c = 61°, and b = 38. solve for the other …
C. \(a = 18.4\)
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question 5 or 10 in triangle abc, ( mangle a = 58^{circ} ), ( mangle b …
A. 49.3
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which rule describes the composition of transformations that maps pre -…
\(T_{-6,1}\circ r_{x - axis}(x,y)\)
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calculate the side lengths a and b to two decimal places. a. a = 16.23 …
A. \(a = 16.23\) and \(b = 18.83\)
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question 3 of 10 in triangle abc, ( mangle a = 81^{circ}, mangle b = 32…
C. 74.9
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to apply the law of sines to find the length of side ( b ) of the trian…
C. \(c,\angle B,\angle C\)
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what is the final transformation in the composition of transformations …
a reflection across line \(m\)
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question 1 of 10 a triangle has two angles measuring 26° and 93°. the s…
A. 11.5, D. 26.3
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exercises: find the volume of each cone. use either 3.14 or \\( \\frac …
1. \(183.17\) in³ 2. \(1056\) cu.yd 3. \(12.56\) ft³ 4. \(154\) yd³ 5. \(942\) in³ 6. \(508.68\) ft³
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which composition of transformations maps figure efgh to figure efgh? a…
a reflection across line \(k\) followed by a translation down
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which rule describes the composition of transformations that maps \\( \…
\(r_{y - axis}\circ T_{6,-5}(x,y)\) (the fourth option)
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exercises: find the volume of each cylinder below. show your work. 1.) …
1. \(6.28\) cu yd 2. \(113.04\) cu in 3. \(1526.04\) cu ft 4. \(769.3\) cu yd 5. \(285.955\) cu yd 6. \(763.02\) cu ft
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which rule describes the composition of transformations that maps figur…
\(r_{l}\circ R_{Q,180^{\circ}}\) (the second option)
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exercises: using the formula ( v=\text{length}cdot\text{width}cdot\text…
1. \(5.33\) cu. yd 2. \(9.2\) cu. ft 3. \(23.33\) cu. in 4. \(306\) cu. in 5. \(198.8\) cu. ft 6. \(1521\) cu. yd 7. \(221\) cu. ft 8. \(32.76\) cu. in
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parallelogram fghj is the final image after the rule $r_{y - axis} circ…
\((-2,2)\)
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determining vertices after a sequence of transformations analyze the pr…
\(A''(3,0)\), \(C''(1,1)\), \(D''(1,-1)\)
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example 3 find the area of a rectangular solid (prism) with length of 3…
1. \(144\) cubic in. 2. \(39\) cubic yd. 3. \(144\) \(in^{3}\) 4. \(180\) \(ft^{3}\) 5. \(40.96\) \(cm^{3}\) 6. \(8.75\) \(ft^{3}\)
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the sequence of transformations, ( r_{o,90^{circ}} circ r_{x - axis} ),…
\((0,3)\)
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question 10 of 10 the law of cosines can only be applied to right trian…
B. False
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question 9 of 10 suppose a triangle has sides 3, 4, and 5. which of the…
A. The triangle in question is a right triangle.
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calculate \\( cos \theta \\) to two decimal places. a. -0.07 b. -0.42 c…
A. -0.07
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question 7 of 10 sitting on a park bench, you see a swing that is 60 fe…
C. 41 feet
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select all the trapezoids.
The blue and orange figures are trapezoids.
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question 6 of 10 suppose a triangle has two sides of length 3 and 4 and…
D. \(\sqrt{13}\)
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using the given diagram, solve for x. x = 20/3
\(x = 12\)
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identifying the rule for a composition of transformations which rule de…
\(R_{0,270^{\circ}}\cdot T_{0,2}(x,y)\)
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question 5 of 10 the law of cosines is $a^{2}+b^{2}-2ab\\cos c = c^{2}$…
D. 37
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solve for x. x = (round to one decimal place as needed. use a comma to …
\(5.1\)
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analyzing a sequence of transformations analyze the diagram. what is th…
The first transformation was a reflection. The second transformation was a translation.
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question 4 of 10 in order to apply the law of cosines to find the lengt…
B. The lengths of two of the triangle’s sides and the measure of the angle between them
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identifying the rule for a composition of transformations which rule de…
\(T_{-5,0}\circ R_{0,90^{\circ}}(x,y)\)
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question 2 of 10 the measure of θ, in degrees, is approximately 48.8°. …
B. False
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analyzing a sequence of transformations kyla applied ( r_m cdot t_{0,3}…
She applied the rotation to the triangle first. She changed the size of the triangle instead of just applying a translation.
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composing transformations which figure represents the final image after…
4
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question 1 of 10 what does the law of cosines reduce to when dealing wi…
B. The Pythagorean theorem
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identifying sequences of transformations what is the final transformati…
a rotation \(180^{\circ}\) about \(Z'\)
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figure bcde was transformed using the composition ( r_{x - axis} cdot t…
\((5,-6)\)
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find the perimeter of the parallelogram.
\( 36 \) units
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the pair of polygons is similar. find the value of x. x =
\(3\)
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a) yes; mnpl - ghjf because the corresponding angles are congruent; 2/5…
D. no; \(\frac{MN}{GH} eq\frac{NP}{HJ}\)
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select the proportion that relates the corresponding sides. a) \\( \\fr…
A. \(\frac{QR}{MN}=\frac{RP}{NP}=\frac{QP}{MP}\)
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in the figure shown, $\triangle mnp sim \triangle qrp$. list all pairs …
B. \(\angle M\cong\angle Q\), C. \(\angle N\cong\angle R\), E. \(\angle P\cong\angle P\)
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answer attempt 1 out of 2 $x = square$ $y = square$
\(x = 4\), \(y=137\)
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answer attempt 1 out of 2 x = submit answer
\(20\)
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answer attempt 2 out of 2 x = submit answer
\(17\)
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in the figure shown, \\( \\triangle fgh \\sim \\triangle jkl \\). selec…
A. \(\angle F\cong\angle J\), C. \(\angle G\cong\angle K\), D. \(\angle H\cong\angle L\)
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select the proportion that relates the corresponding sides. o a) (\frac…
C. \(\frac{WX}{AB}=\frac{XY}{BC}=\frac{YZ}{CD}=\frac{WZ}{AD}\)
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in the figure shown, abcd ~ wxyz. select all pairs of congruent angles.…
A. \(\angle A\cong\angle W\), B. \(\angle B\cong\angle X\), D. \(\angle D\cong\angle Z\), E. \(\angle C\cong\angle Y\)
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question 10 of 10 what is cos 30°? a. √3 b. √3/2 c. 1/√2 d. 1 e. 1/√3 f…
B. \(\frac{\sqrt{3}}{2}\)
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r is the midpoint of qs. complete the proof that ∠u ≅ ∠t. 1 r is the mi…
5. \(\triangle QRT\cong\triangle SRU\), SSS Congruence Criterion; \(\angle U\cong\angle T\), CPCTC.
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question 9 of 10 the ____ of an angle is the ratio of the adjacent leg …
A. cosine
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question 8 of 10 what is cos 45°? a. 1 b. \\frac{1}{\\sqrt{2}} c. \\fra…
B. $\frac{1}{\sqrt{2}}$
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according to this diagram, what is sin 23°? a. \\( \\frac { 13 } { 12 }…
B. \(\frac{5}{13}\)
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question 6 of 10 what is tan 30°? a. √3 b. 1/√3 c. √3/2 d. 2/√3 e. 1 f.…
B. \(\frac{1}{\sqrt{3}}\)
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cell towers a cell phone tower casts a shadow that is 100 feet long. at…
\(135\)
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determine whether the pair of triangles is similar. explain your reason…
$\triangle GIH\sim\triangle KIL$ by AA Similarity.
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carpentry jake is fixing an a - frame. he wants to add a horizontal sup…
\(12\) ft
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sailing the two sailboats shown are participating in a regatta. if the …
\(202.2\)
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graph the image of \\( \\triangle a b c \\) after the following sequenc…
Plot the points \((6,11)\), \((3,3)\), \((-3,11)\) and connect them to form the image of \(\triangle ABC\) after the given sequence of transformations.
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nick built a fence shaped like the triangle below. if it took nick 2.5 …
\( 90 \) minutes
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julius sprinted 68 meters. reece sprinted diagonally across a rectangul…
Reece sprinted a longer distance by \(3\) meters.
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statement 1 ∠rvx ≅ ∠twu 2 ∠r ≅ ∠t 3 overline{wx} ≅ overline{uv} 4 vx = …
1. Vertical angles are congruent; 2. Given; 3. Given; 4. Segment addition postulate; 5. Segment addition postulate; 6. Substitution; 7. Transitive property of equality; 8. AAS (An…
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tw ≅ ux and ∠w ≅ ∠u. complete the proof that sx ≅ st. statement 1 tw ≅ …
1. Given 2. Given 3. Reflexive Property of Congruence 4. AAS (Angle - Angle - Side) 5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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in a certain city, e street, w street, c street, and d street are paral…
\(497\)