Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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right triangle relationships and trigonometry what is the area of trian…
111.3 square units
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a right triangle has one angle measuring degrees. the longest side of a…
1. 90 2. hypotenuse 3. legs 4. Pythagorean 5. hypotenuse 6. right triangle 7. legs 8. hypotenuse 9. Pythagorean
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fall 2025 geometry b wwva right triangle relationships and trigonometry…
\(41^{\circ}\)
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the equation ( sin(25^{circ})=\frac{?}{?} ) can be used to find the len…
21.3 in.
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right triangle relationships and trigonometry given right triangle def,…
$\frac{40}{9}$
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if one leg of a right triangle is 5 units and the hypotenuse is 13 unit…
D. 12 units
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which theorem helps in finding the unknown side length of a right trian…
C. Pythagorean Theorem
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if the legs of a right triangle are 6 units and 8 units, what is the le…
B. 10 units
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if the legs of a right triangle are 5 units and 12 units, what is the l…
A. 13 units
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17. half of the diameter of a circle is called the what?
Radius
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the perimeter of the rectangle below is 164 units. what is the value of…
B. \(x = 11\)
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what is the hypotenuse of a right triangle with legs of 7 units and 24 …
D. 25 units
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$\\overline{ab}$ is congruent to $\\overline{cd}$. solve for x. a 3(2x …
\(x = 7\), so the answer is D.
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the perimeter of the triangle shown is 17x units. the dimensions of the…
B. \(17x = 30+7x\)
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in the pythagorean theorem, what does c represent? a. the area of the t…
C. The hypotenuse
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17. half of the diameter of a circle is called the what? 19. solve $1\\…
$\frac{1}{2}$
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which of the following scenarios can be solved using the pythagorean th…
B. Determining the length of a ladder needed to reach a certain height
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if the hypotenuse of a right triangle is 10 units and one leg is 6 unit…
B. 8 units
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a triangle has legs of 7 and 24 and the hypotenuse is 25. is it a right…
C. Yes
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which formula represents the pythagorean theorem? a. ( a^{2}+b^{2}=c ) …
B. $a^{2}+b^{2}=c^{2}$
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7. match each directed line segment with the translation from polygon p…
1. Translation \(1\) → \(D\) (vector \(w\)) 2. Translation \(2\) → \(C\) (vector \(u\)) 3. Translation \(3\) → \(A\) (vector \(v\)) 4. Translation \(4\) → \(B\) (vector \(a\))
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6. here are 4 triangles that have each been transformed by a different …
D
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explore the distance tool and then answer each question to determine th…
\((x_2 - x_1)^2 = 64\) \((y_2 - y_1)^2 = 25\) \((x_2 - x_1)^2+(y_2 - y_1)^2 = 89\) \(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\approx9.43\)
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lesson 16 practice problems 1. for each figure, identify any angles of …
2. A. All sides of the triangle have the same length, B. All angles of the triangle have the same measure 3. A. 45 degrees, B. 90 degrees, C. 135 degrees, D. 180 degrees, E. 225 d…
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reflect the figure over the line x = -1. write new coordinates. 4). ref…
| Parallelogram \(ABCD\) | Parallelogram \(A'B'C'D'\) | |----|----| | \(A(2,1)\) | \(A'(-4,1)\) | | \(B(-2,5)\) | \(B'(0,5)\) | | \(C(-5,-2)\) | \(C'(3,-2)\) | | \(D(-1,-6)\) | \(…
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1). translate the quadrilateral abcd - 2 horizontally and + 3 verticall…
1. | Parallelogram \(ABCD\) | Parallelogram \(A'B'C'D'\) | |---|---| | \(A(-1,4)\) | \(A'(-3,7)\) | | \(B(5,4)\) | \(B'(3,7)\) | | \(C(2,2)\) | \(C'(0,5)\) | | \(D(-4,2)\) | \(D'(…
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3. use the properties of equality to identify the error made in the con…
The error is in the statement “by the Multiplication Property” in the last step. To correct it, we should use the Division Property of Equality. We divide both sides of the equati…
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use the graph of two triangles for items 1 and 2. select all the true s…
A. \(PQ = ST\), C. \(m\angle R=m\angle U\), E. \(QR = SU\), F. \(m\angle Q=m\angle T\)
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use the graph of four triangles. complete the statement below to prove …
\(\overline{MN}\)
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atg 2) use your knowledge of parallel lines and angle relationships to …
The theorem is the Same Side Exterior Angles Theorem. The value of \(x\) is \(1.5\).
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triangle \\( \\triangle a ^ { prime } b ^ { prime } c ^ { prime } \\) i…
A. \(A\) and \(A'\) have the same coordinates, B. The perimeters of \(\triangle ABC\) and \(\triangle A'B'C'\) are the same, C. \(\angle C\) and \(\angle C'\) have the same measur…
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circle ( a ) is the result of rotating circle ( a ) by ( 180^{circ} ) a…
A. Circle \(A\) and circle \(A'\) have the same circumference, B. The radii of circle \(A\) and circle \(A'\) have the same lengths.
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triangle ( \triangle abc ) is the result of reflecting ( \triangle abc …
A. \(\overline{BC}\) and \(\overline{B'C'}\) are both perpendicular to the \(y\) - axis. B. \(\angle B\) and \(\angle B'\) have the same measures. C. The perimeters of \(\triangle…
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rigid transformations: preserved properties segment \\( \\overline { a …
C. \(\overline{AB}\) and \(\overline{A'B'}\) have the same lengths.
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triangle \\( \\triangle a ^ { prime } b ^ { prime } c ^ { prime } \\) i…
A. \(\angle A\) and \(\angle A'\) have the same measures; C. The areas of \(\triangle ABC\) and \(\triangle A'B'C'\) are the same.
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multiple choice question teaching geometry in schools is an example of …
knowledge
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segment \\( \\overline { a ^ { prime } b ^ { prime } } \\) is the resul…
A. \(\overline{AB}\) and \(\overline{A'B'}\) have the same lengths.
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find measures using rigid transformations triangle ( \triangle abc ) is…
\(14.9\)
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quiz interior and exterior angles of triangles and polygons complete: 1…
7) \(x = 65^{\circ}\), \(y = 55^{\circ}\), \(z = 25^{\circ}\) 8) \(x = 30^{\circ}\), \(y = 30^{\circ}\) 9) No 10) \(6 < c<14\) 11) Sum of exterior angles \(=360^{\circ}\), Measure…
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triangle \\( \\triangle a b c \\) is translated 9 units to the left and…
\(8\)
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use the graph below to enter a single translation rule. complete 0 tran…
$(x,y)\to(x + 2,y+6)$
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quadrilateral ( abcd ) is the result of dilating quadrilateral ( abcd )…
- \(BC\) and \(B'C'\) are on the same line: True - The lengths of \(CD\) and \(C'D'\) are equal: False
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use the graph below to write a single translation rule. complete the ru…
\((x + 4,y + 3)\)
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triangle ( abc ) is translated 5 units to the right and 4 units up to c…
\(74^{\circ}\)
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4. here is a shape. what is the area of this shape? area: square units …
\(33\) #### b)
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solve for x in the diagram below.
\(x = 12\)
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solve for $x$ in the diagram below.
\(x = 20\)
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solve for x in the diagram below.
\(x = 20\)
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1. what is the area of triangle a? a. 40 square centimeters b. 16 squar…
1. B. 10 square centimeters 2. C. 9 inches 3. (Draw a parallelogram with base 6 units and height 3 units for Parallelogram 1, and a parallelogram with base 9 units and height 2 un…
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3. draw two different parallelograms that each have an area of 18 squar…
Parallelogram 1: base = 2 units, height = 9 units; Parallelogram 2: base = 3 units, height = 6 units. (The actual drawing is done on the grid according to the base - height pairs)
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1. what is the area of triangle a? a. 40 square centimeters b. 16 squar…
1. B. 16 square centimeters 2. C. 9 inches 3. For parallelogram 1: base \(b = 6\) units and height \(h=3\) units (since \(A=b\times h=6\times3 = 18\)). For parallelogram 2: base \…
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solve for x in the diagram below.
\(x = 25\)
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multiple choice questions circle the correct answer for each of the fol…
1. B. demographics 2. A. baby boomers 3. C. gross domestic product 4. D. recession 5. B. inflation 6. C. consumer price index 7. B. economics
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solve for x in the diagram below.
\( 34 \)
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solve for x in the diagram below.
\(x = 15\)
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integrated 2 similarity quiz name: per. 1) each pair of figures are sim…
a. \(x = \frac{7}{3}\) b. \(x = 7.5\)
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solve for $x$ in the diagram below.
\(x = 20\)
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1) each pair of figures are similar. use this fact to solve for the mis…
a. Similar, \(\triangle ABC\sim\triangle MLK\), Similarity condition: \(AA\) b. Similar, \(\triangle PRT\sim\triangle XWT\), Similarity condition: \(SSS\)
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given m∠qps is a straight angle. m∠qpr = 7x - 4° m∠rps = 9x - 40° find …
\( 94^{\circ} \)
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what fraction of the shapes below are triangles? count the trian goes o…
\(\frac{1}{6}\)
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given m∠abd = 87° m∠abc = 9x - 1° m∠cbd = 6x + 58° find m∠abc:
\(17^{\circ}\)
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find ( mangle mon ). ( mangle mon = 8x + 90^circ ) ( mangle lom = 4x + …
\(m\angle MON = 130^{\circ}\)
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what fraction of the circle is yellow?
$\frac{1}{3}$
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given find m∠mon. m∠mon = 5x - 23° m∠lom = 3x - 15°
\( 57^{\circ}\)
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given \\overline{ol}\\perp\\overline{on} \\( m\\angle lom = 3 x - 15 ^ …
\(57^{\circ}\)
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what is the area of this rectangle? the area of the rectangle is 34.1b²…
\(281.4b^{2}\text{ ft}^{2}\) (corresponding to the third option in the multiple - choice list)
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4. what fraction of the rectangle is purple?
$\frac{1}{4}$
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what is the distance between points (1,2) and (5,5)? 3 4 5 6 question 4…
For the distance question: 5. For the mid - point question: \((0,0)\)
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what is the distance of this line? 8 12 sqrt{60} sqrt{136} 60
\(\sqrt{136}\)
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if we are given coordinates which formula should we use to find the dis…
The formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) (Distance Formula) should be used.
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which number line represents the solution set for the inequality ( 3x <…
The third number - line (with an open circle at \(-3\) and arrow pointing to the left) represents the solution set of the inequality \(3x < - 9\).
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4. triangle qrs has a perimeter of 55 units. segment rt bisects \\( \\a…
\(10\)
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4. triangle qrs has a perimeter of 55 units. segment rt bisects ∠r. wha…
\(25\)
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section 7: transformations & symmetry 46. what type of transformation s…
46. Translation 47. Reflection 48. Rotation 49. Rotational symmetry 50. False
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14. in a right triangle, the measure of one acute angle is 2 times the …
b. \(26^{\circ},64^{\circ}\)
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which lines must be parallel? a r and s b p and q c p and r d q and s e…
B. \(p\) and \(q\)
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section 6: coordinate geometry 41. what are the coordinates of the orig…
41. \((0,0)\) 42. \(5\) 43. \((2,2)\) 44. \(1\) 45. True
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section 5: perimeter, area & volume 36. find the area of a trapezoid wi…
36. \(50\space cm^{2}\) 37. \(26\space cm\) 38. \(27\space cm^{3}\) 39. \(216\space cm^{2}\) 40. \(60\space cm^{3}\)
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27. find the perimeter of a square with side 7 cm. 28. what is the area…
27. \(28\) cm 28. \(40\) \(cm^{2}\) 29. \(720^{\circ}\) 30. True 31. Circumference 32. Diameter 33. Tangent 34. \(A=\pi r^{2}\) 35. \(31.4\) cm
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use the diagram to informally derive the formula for area of a circle. …
\(\pi r^{2}\)
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section 3: quadrilaterals & polygons 21. what is the sum of the interio…
21. \(360^{\circ}\) 22. \(5\) 23. Parallelogram 24. Trapezoid 25. Octagon 26. \(60\mathrm{cm}^{2}\)
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use the diagram to informally derive the formula for area of a circle. …
\(\pi r^{2}\)
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use the diagram to informally derive the formula for area of a circle. …
\(\pi r^{2}\)
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in exercises 2 and 3, determine which lines, if any, must be parallel. …
For Exercise 2: \(g\parallel h\). For Exercise 3: \(j\parallel k\), \(l\parallel m\), \(l\parallel n\), \(m\parallel n\).
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12. in the diagram of the boat harbor, ( mangle 1 = 90^{circ} ). find (…
\(m\angle2 = 90^{\circ}\). Theorem or postulate: Corresponding Angles Postulate.
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part b the slope of side ec is \\( \\frac { 4 } { 3 } \\). complete the…
\(\frac{4}{3}=\frac{AC}{9}=\frac{16 - 5}{14 - 5}\)
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kamryn part a point c has the coordinates (5,5). which proportions show…
\(\frac{ED}{DC}=\frac{CA}{AB}\): False \(\frac{CA}{AB}=\frac{CD}{DE}\): False \(\frac{5 - 2}{5 - 1}=\frac{CA}{AB}\): False \(\frac{5 - 1}{5 - 2}=\frac{17 - 5}{AB}\): False
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triangles acd and eba are similar right triangles. the slope of (overli…
The first box is \(14\), and the \(x\) - coordinate of point \(D\) is \(11\).
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lines a and b are parallel. what is the measure of \\( \\angle 3 \\) if…
C. \(84^{\circ}\)
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triangles ptq, qsr, and pur, shown on the graph below, are similar righ…
Correctly Represents Slopes: \(\frac{PT}{TQ}=\frac{QS}{SR}\), \(\frac{PU}{UR}=\frac{PT}{TQ}\), \(\frac{TU}{US}=\frac{QS}{SR}\) Does Not Correctly Represent Slopes: \(\frac{PT}{UR}…
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triangles abc and triangle cde are similar right triangles. complete th…
\(\frac{1.5}{2}=\frac{3}{4}\)
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jeremiah is using inscribed regular polygons to informally derive the f…
\(r\)
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compute the perimeter of the rectangle using the distance formula. (rou…
B. 34
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c is the midpoint of ab. if ac = 3(c + 2), cb = c + 26 find c and the l…
\(72\)
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find the measure of the missing angles. answer attempt 1 out of 2 d = e…
\(d = 101^{\circ}\), \(e = 21^{\circ}\), \(f = 79^{\circ}\)
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which angle number represents an angle vertical to \\( \\angle f h c \\…
\(5\)
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geometry test (50 questions) section 1: points, lines, and angles 1. wh…
1. Line segment 2. \(180^{\circ}\) 3. Complementary angles 4. Supplementary angles 5. Adjacent angles 6. \(60^{\circ}\) 7. Protractor 8. Obtuse angle 9. \(110^{\circ}\) 10. True
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question what is the image point of (8, -4) after the transformation $r…
\((7,1)\)
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drawing is not to scale. if a,b,c are collinear, ac = 5z + 2, bc = 3z +…
\(z = 6\) \(AC = 32\)
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complete the following sentence. the figure below has rotational symmet…
\(180\)