Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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33. given: ∠v ≅ ∠y, wz is the perpendicular bisector of vy. can you use…
by AAS only
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32 suppose ( overline{ab} cong overline{ae} ). can you use the sss post…
both apply
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31. how many triangles are shown? the triangles may overlap. 6 8 7 9
8
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30. if $\\triangle dec\\cong\\triangle bec$, which is true by cpctc? $\…
\(\overline{BE}\cong\overline{ED}\)
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problem 1 click and drag to graph all the solutions to the inequality |…
The solution of the inequality \(|x|\leq3\) is the set of all real numbers \(x\) such that \(-3\leq x\leq3\). On the number - line, we have closed circles at \(x=-3\) and \(x = 3\…
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one vertex of a polygon is located at (3, -2). after a rotation, the ve…
\(R_{0,90^{\circ}}\), \(R_{0,-270^{\circ}}\)
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29. in \\( \\triangle yps \\), \\( \\overline{ps} \\) is included betwe…
$\angle S$ and $\angle P$
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28 in the figure, ( mangle1 = mangle2 = 22 ) and ( mangle3 = mangle4 = …
33
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triangle xyz is rotated to create the image triangle xyz. which rules c…
\(R_{0,180^{\circ}}\), \((x,y)\to(-x,-y)\)
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27. \\( \\angle \\mathrm { npm } \\) is congruent to which angle? \\( \…
\(\angle CAB\)
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triangle abc was transformed using the rule $(x,y)$ $-(-y,x)$. the vert…
The transformation was a \(90^{\circ}\) rotation about the origin.
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26. use the information in the figure. if $mangle f = 116$, find $mangl…
32
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25. name the postulate or theorem you can use to prove the triangles co…
HL Theorem
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a pentagon is transformed according to the rule $r_{0,180^{circ}}$. whi…
\((x,y)\to(-x,-y)\) (the first option)
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24. from the diagram, what can you conclude about $\triangle cad$? it i…
It is an isosceles triangle.
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triangle xyz has vertices x(1, 3), y(0, 0), and z(-1, 2). the image of …
\(R_{0,90^{\circ}}\)
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23. which side correspond to \\( \\overline { t a } \\) ? \\( \\overlin…
\(\overline{OD}\)
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parallelogram abcd is rotated to create image abcd. which rule describe…
\((x,y)\to(y, - x)\)
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23. which side correspond to \\( \\overline{ta} \\)? \\( \\overline{og}…
\(\overline{NI}\)
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find the graph of this function as the value of n increases, starting f…
The third graph (the one where the points lie on a unit - circle centered at the origin) is the correct graph. As \(n\) increases, the points \(f(n)\) lie on the unit circle \(x^{…
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find the graph of this function as the value of n increases, starting f…
The second graph (the one where all the points lie on a unit - circle centered at the origin) is the correct graph.
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22. in the figure, ( \triangle ghfcong\triangle ehd ). which statement …
\(\overline{DH}\cong\overline{HF}\) (assuming the first option is the correct one based on CPCTC and side - correspondence in \(\triangle GHF\cong\triangle EHD\))
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21. tv = 10x - 26 and vx = 5x + 9. what is the value of x? 35° -17° -7°…
\(7\)
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a triangle has vertices at ( r(1,1) ), ( s(-2,-4) ), and ( t(-3,-3) ). …
A. \((-4,2)\)
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20. identify the angle or side that is common to \\( \\triangle npm \\)…
\(\overline{MP}\) (the third option)
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19. what additional information is needed to prove the triangles are co…
\(\angle XWY\cong\angle ZWY\) (the third option)
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given: \\( \\overline{qr} \\cong \\overline{st} \\), \\( \\triangle qts…
HL Theorem
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17. if ( mangle ywz = 17 ), what is ( mangle wxy )? 17 56 73 34
73
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15. to use the hl theorem to prove two triangles are congruent, the tri…
The triangles have congruent hypotenuses and one pair of congruent legs.
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in the diagram, $\triangle mtdcong\triangle gls$. which statement is tr…
\(\angle M\cong\angle G\)
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a triangle is rotated 90° about the origin. which rule describes the tr…
\((x,y)\to(-y,x)\) (the second option)
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you have learned that when you simplify expressions you follow the orde…
En \(10\div2 + 6\), se realiza primero la división \(10\div2\). En \(3\cdot10 - 7\), se realiza primero la multiplicación \(3\cdot10\). En \(8 + 9\cdot10\), se realiza primero la …
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14. in this figure, $\\triangle afc\\cong\\triangle efc$. which stateme…
\(\overline{CF}\perp\overline{AE}\)
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13. given: ∠1 ≅ ∠2, ∠3 ≅ ∠4, overline{ts} ≅ overline{tr} name the postu…
AAS Theorem
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rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3, -6), and d(-6, …
\(T_{-4,3}(x,y)\)
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12 use the information given in the diagram. tell why $overline{uw}cong…
Reflexive Property; Given
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rectangle efgh is translated according to the rule ( t_{-5,9}(x,y) ). i…
\((-7,6)\) (corresponding to the second option)
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11. what additional information is needed to prove the triangles are co…
\(\overline{AB}\cong\overline{AD}\)
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if a translation of ( t_{2,-7}(x,y) ) is applied to ( \triangle abc ), …
\((3,-12)\) (the fourth option)
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10. find the values of x and y that make these triangles congruent by t…
\(x = 6,y = 3\)
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a rectangle on a coordinate plane is translated 5 units up and 3 units …
\((x,y)\to(x - 3,y + 5)\) (the third option)
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9. which statement is given in the diagram? ∠acb ≅ ∠abc ∠abc ≅ ∠ade ∠ac…
$\angle ACB\cong\angle ADE$ (the third option)
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8. if ( \triangle abccong\triangle adc ), which is not true by cpctc? (…
$\overline{BE}\cong\overline{DE}$
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which statements are true about triangle abc and its translated image, …
The rule for the translation can be written as \(T_{3,-3}(x,y)\) (second option if \(T_{3,-3}(x,y)\) is the second option in the original numbering, assuming the options: If the o…
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7. name the postulate or theorem you can use to prove the triangles con…
HL Theorem
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solve the inequality and graph the solution on the line provided. 21 - …
Inequality Notation: \(x>1\) For graphing on the number - line: Place an open circle at \(x = 1\) (because \(x = 1\) is not included in the solution, since the inequality is \(x>1…
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5. if ( mangle c = 66^{circ} ), find the values of ( x ) and ( y ). ( x…
\(x = 90^{\circ},y = 24^{\circ}\) (the second option)
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solve the inequality and graph the solution on the line provided. -2 + …
Inequality Notation: \(x\leq - 2\) To graph on the number - line: Place a closed circle at \(-2\) (because the inequality is \(\leq\)) and shade to the left of \(-2\) (since \(x\)…
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line segment pr is graphed below. if pr is one side of parallelogram pr…
\((10,11)\) and \((7,3)\)
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trail 3 (swift fox) 3. a. write a plan of attack. how are you going to …
We need to find either angle \( A \) (to use \( \text{slope}=\tan(A) \)) or the values of rise (\( h \)) and run (\( x \)) (to use \( \text{slope}=\frac{h}{x} \)). If we find angl…
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line segment pr is graphed below. if pr is one side of parallelogram pr…
\((10,11)\) and \((7,3)\)
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suppose \\( \\overline { b d } \\cong \\overline { c a } \\) and \\( \\…
by SSS only
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4.3 pollys problems mrs. gallas neighbor, polly ngo-miel, is learning a…
\(2x^{3}+9x^{2}-2x - 3\) 1. b.
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3. if ( mangle c = 47 ), find the values of ( x ) and ( y ). ( x = 43, …
\(x = 90,y = 43\) (corresponds to the third option)
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2. if bcde is congruent to opqr, then (overline{cd}) is congruent to (o…
\(\overline{PQ}\)
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solve the inequality and graph the solution on the line provided. -2 + …
Inequality Notation: \(x\leq - 2\) For the number line: Plot a closed circle at \(-2\) (since the inequality is \(\leq\)) and shade to the left of \(-2\) (towards the negative inf…
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1. which additional congruence statement could you use to prove that ( …
\(\overline{AB}\cong\overline{AD}\)
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how many cubic meters of water can be stored in a cylindrical tank that…
Approximately \(3.98\) cubic meters.
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answer attempt 1 out of 2
$\frac{4}{3}$
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what is the circumference of a circle that has an area of 36 m2?
The circumference of the circle is approximately \(21.26\) (rounded to two decimal places)
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r 36 45 s 27 t
The triangle is a right - triangle as it satisfies the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 27\), \(b = 36\), \(c = 45\))
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solve the inequality and graph the solution on the line provided. 57 + …
Inequality Notation: \(x\geq - 2\) For the number - line: Place a closed circle at \(x = - 2\) (because the inequality is \(\geq\)) and shade to the right of \(x=-2\) since \(x\) …
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a storage container for paint is in the shape of a cylinder with a heig…
The equation is \(V = 10\times3\pi\) and the volume is \(94.2\) cubic inches.
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solve the inequality and graph the solution on the line provided. 4x + …
Inequality Notation: \(x\leq6\) For the number - line: Place a closed circle at \(x = 6\) (because the inequality is \(\leq\)) and shade to the left of \(6\) (towards the negative…
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solve the inequality and graph the solution on the line provided. 3x - …
Inequality Notation: \(x\lt - 7\) For the number - line: Plot an open circle at \(-7\) (since the inequality is strict, \(x eq - 7\)) and draw an arrow to the left (because \(x\)…
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5. two side lengths of right triangle abc are given. what is the length…
5. A. \(20\) cm 6. C. \(12\) kilometers
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what is the volume of the rectangular prism below? note: figure may not…
\(315\space cm^{3}\)
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solve the inequality and graph the solution on the line provided. 2x - …
Inequality Notation: \(x > - 4\) On the number - line, we draw an open circle at \(-4\) (because the inequality is strict, i.e., \(x eq - 4\)) and draw an arrow to the right of \…
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the vertices of rhombus defg are d(1, 4), e(4, 0), f(1, -4), and g(-2, …
\(20\)
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which steps will verify that a parallelogram is a rectangle? check all …
- Calculate the lengths of the diagonals, and show that they are equal. - Calculate the slopes of every side, and show that adjacent sides are perpendicular.
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solve for ( x ) and graph the solution on the number line below. ( -4 g…
Inequality Notation: \(x\leq7\) To graph on the number - line: Place a closed circle at \(x = 7\) (because the inequality includes equality, i.e., \(\geq\) is equivalent to \(\leq…
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block below. click \grade answer\ to have your answer graded. triangle …
\(49.7\)
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problem 2 click and drag to graph all the solutions to the inequality |…
The solutions of the inequality \(|x + 2|>4\) are \(x>2\) or \(x<-6\). On the number - line, we have an open circle at \(x = 2\) (since \(x\) is not equal to 2) and the line exten…
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find the missing side. 28° 15 cos (28°) = \\frac{15}{z} z = ? round to …
\( 17.0 \)
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practice using coordinate algebra to solve problems. mary thinks the tr…
Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
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1) what is the circumference of a circle that has an area of 36 m²?
The circumference of the circle is \(12\sqrt{\pi}\space m\approx21.26\space m\)
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find the missing side. enter sin, cos, or tan. z 28° 15 ?(28°)=\\frac{}…
$\cos$
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find the trig ratio. 29 20 21 tan(θ)= ? enter as a decimal. round to th…
$0.95$
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3) △gik is equilateral. complete the proof that △ijk ≅ △ihg
\(\triangle IJK\cong\triangle IHG\) is proved using the ASA (Angle - Side - Angle) congruence criterion with the reasons: \(\angle IKJ=\angle HGI\) (Vertical Angle Theorem), \(IK …
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1 agik is equilateral 2 ∠ikj ≅ ∠hgi 3 ∠jik ≅ ∠gih 4 overline{ik} ≅ over…
1. Given (the problem states \(\triangle GIK\) is equilateral) 2. Vertical - angles theorem 3. Alternate - interior angles theorem 4. Given (from the equilateral triangle \(\trian…
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what is the type of two - dimensional solid created by a vertical cross…
triangle, area = \(90\) \(ft^{2}\)
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which solids have the same types of vertical cross sections through the…
a rectangular prism and a cylinder
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1 \\( \\angle rts \\cong \\angle tru \\) 2 \\( \\angle srt \\cong \\ang…
The reason for \(\triangle RTU\cong\triangle TRS\) is the ASA (Angle - Side - Angle) congruence criterion.
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rectangle abcd has a perimeter of 32 units and will be rotated about li…
6 units
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3. find the value of x, (8x - 35)° (6x - 5)° (3x - 1)° x = 5. find the …
\(x = 12\)
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rectangle abcd has a perimeter of 32 units and will be rotated about li…
1. Cylinder 2. \(10\)
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∠gjk ≅ ∠hij, gk ⊥ jk, ij ≅ jk, and hi ⊥ ij. complete the proof that △gj…
\(\triangle GJK\cong\triangle HIJ\) (by ASA congruence criterion)
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δabc ~ δdef find the value of x. x =
\(x = 4\)
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through which points should a line of rotation be placed to create a cy…
F and I
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workbook 2. for each picture, name the shape and calculate the area. a)…
a) Rectangle, \(44.2\space m^{2}\) b) Parallelogram, \(44.2\space m^{2}\) c) Right - triangle, \(22.1\space m^{2}\) d) Triangle, \(22.1\space m^{2}\) e) Triangle, \(22.1\space m^{…
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4) fi = gj and ∠i = ∠g. complete the proof that △fgj ≅ △fif. 1 overline…
1. Given; 2. Given; 3. CPCTC (Corresponding Parts of Congruent Triangles are Congruent); 4. AAS (Angle - Angle - Side)
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rotating a rectangle through which points should a line of rotation be …
E and J
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find the graph of the point (-3, -2).
The second graph (the one on the right) represents the point \((-3,-2)\).
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what three - dimensional solid has 6 rectangular faces, 2 equal bases t…
hexagonal prism
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which solids can have horizontal cross sections that are circles? check…
cones, cylinders, spheres
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identifying cross sections of solids use the diagram to answer the ques…
For the horizontal cross - section: hexagon. For the cross - section through the apex: triangle.
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the volume of a cube with side lengths of a units is represented by the…
125 cubic inches
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find the perimeter of the triangle to the right in simplified radical f…
$13\sqrt{3}$ m
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1. for each picture, name the shape and calculate the area. a) b) c)
a) Shape: Circle, Area: \(6079.04\space mm^{2}\) b) Shape: Triangle, Area: \(26.505\space m^{2}\) c) Shape: Parallelogram, Area: \(78.44\space cm^{2}\)
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use the diagram to answer the questions what two - dimensional figure w…
1. Polygon (or more specifically, if base is square - square) 2. Triangle