幾何
三角形、圓、解析幾何與證明題。
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14. find the measure of ∠1. 72° 36° 60° 54°
\(72^{\circ}\)
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rotate the given triangle 270° counterclockwise about the origin. \\( \…
The value of the green - boxed element (the \(x\) - coordinate of the rotated second point) is \(-1\), and the value of the element below the green - boxed element (the \(y\) - co…
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find the measure of angle x, given a || b. x = ?°
\(42\)
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find the measure of angle x, given a || b. x =
\(42\)
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12. find the area of the parallelogram that has a base of 4 m and a hei…
\(A = 22\space m^{2}\)
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find the measure of angle x, given a || b. x =
\(53\)
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are lines a and b parallel? 35° 35° a b yes no
Yes
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are lines a and b parallel? 160° 161° no yes
No
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12. find the area of the parallelogram that has a base of 4 m and a hei…
\(A = 22\space m^{2}\)
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12. find the volume. v = lwh type a response
\(56\) cubic inches
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10. in circle p, xy = 2.4 cm. what is the circumference of the circle? …
\(2.4\pi\) cm (the third option)
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27. which is necessary to calculate the perimeter of a triangle? a. the…
D. The length of all three sides
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9. find the measure of \\( \\angle 3 \\). \\( 30 ^ { \\circ } \\) \\( 9…
\(60^{\circ}\)
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26. for a construction project, a concrete slab needs to be poured that…
d. 16 cubic meters
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11. find the area. a = lw 6\\frac{2}{7} 3\\frac{3}{4} type a response
$\frac{273}{14}$
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8. a circle is inscribed in a square. a point in the figure is selected…
about \(20\%\)
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25. calculate the hypotenuse of each right triangle with the given leg …
C. \(a = 12, b = 13\)
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7. what is the area of the circle if xy = 17 in? 72.25π in² 36.75π in² …
\(72.25\pi\) \(in^{2}\) (the first option)
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6. in a circle, a 90° sector has area 36π ft². what is the radius of th…
\(12\) \(ft\)
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23. what is the formula to calculate the sum of interior angles of a po…
C. \( S=(n - 2)\times180^{\circ} \)
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6. the circumference of a circle is 60π cm. what is the length of an ar…
\(23.3\pi\) cm (the fourth option)
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22. if a cylinder has a radius of 4 units and a height of 8 units, what…
A. \( V = 128\pi \) cubic units
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21. what measurement is essential for calculating the volume of a cylin…
B. Radius of the base
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12. find the volume. v = lwh 6 in. 2\\frac{2}{3} in. 3\\frac{1}{2} in. …
\(56\) cubic inches
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4. find the area of the parallelogram that has a base of $2\\frac{1}{2}…
\(3\frac{1}{8}\text{ ft}^2\) (the third option)
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20. which triangle has two equal sides and two equal angles? a. isoscel…
a. Isosceles
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find the area of a trapezoid with bases 2 ft and 3 ft and height \\( \\…
\(\frac{5}{8}\text{ ft}^2\)
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19. the apothem of a polygon is: a. a line from the center to a side, p…
A. A line from the center to a side, perpendicular to that side
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7 a playground is in the shape of an isosceles trapezoid. the top base …
The distance around the playground (perimeter) is \(92\) ft. ---
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18. choose the scenario where the volume calculations result in less th…
C. Cone with a radius of 3 units and a height of 4 units
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17. to paint the walls of a rectangular room that is 10 meters long, 8 …
A. 164
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1. the figure represents the overhead view of a deck surrounding a hot …
\(973.1\space ft^{2}\)
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draw all possible lines of symmetry on this figure.
Draw a vertical line passing through the mid - point of the base of the given figure. This is the only line of symmetry for the given figure.
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11. find the area. a = lw 6\\frac{2}{7} 3\\frac{3}{4} type a response s…
\(\frac{273}{14}\)
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16. how many lines of symmetry are in a regular octagon? a. 9 b. 7 c. 8…
C. 8
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1. the figure represents the overhead view of a deck surrounding a hot …
\(973.1\mathrm{ft}^{2}\)
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15. the perimeter of a square can be calculated by: a. multiplying one …
A. Multiplying one side by 4
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14. to calculate the area of a compound shape, you should: a. use the f…
D. Divide it into simpler shapes and sum their areas
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13. a path around a rectangular field measures 300 meters in length. if…
C. 50 meters
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12. in the pythagorean theorem ($a^{2}+b^{2}=c^{2}$), the term $c^{2}$ …
B. Longest side of the triangle (hypotenuse)
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10. what does the b in the prism volume formula ( v = b\times h ) stand…
d. Area of the base
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9. a designer plans to create a triangular garden area with a base of 8…
D. 20 sq m
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8. for which of the following polygons can the triangle inequality theo…
B. Any triangle
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7. a gardener is planning a circular flower bed with a radius of 3 mete…
A. \(9\pi\) sq m
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5. a square is a special type of: a. rectangle b. circle c. triangle d.…
A. Rectangle, D. Rhombus
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4. how many degrees does each interior angle of a regular pentagon meas…
B. 108 degrees
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reflect the vector $\\langle -3,8\ angle$ across the line $y = -x$.$\\l…
\(3\)
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given ab//cd. prove that △abc≌△cda.
\(\triangle ABC\cong\triangle CDA\) by AAS. The first unknown angle is \(\angle BAC\) (corresponding to \(\angle DCA\)) and the second unknown triangle is \(\triangle CDA\).
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1. how is the volume of a cone calculated? a. volume = \\( \\frac { 1 }…
C. Volume = $\frac{1}{3}\times\pi\times r^{2}\times h$
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15. to install a round sprinkler system that covers a circular area wit…
B. \(49\pi\) sq m
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14. which of the following sets of numbers can form a right triangle? a…
A. 6, 8, 10
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13. when analyzing a triangular prism, which of the following correctly…
C. Two triangular bases and three rectangular lateral faces.
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12. to paint the walls of a rectangular room that is 10 meters long, 8 …
B. 36
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use the regular pentagon shown. what is the least angle of rotation in …
\(72\)
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11. what is the surface area of a sphere with a radius of 6 cm? a. 678.…
A. \(678.24\ cm^{2}\)
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given ( abcong cd ) and ( bccong ad ). prove that ( \triangle abccong\t…
\(\triangle ABC\cong\triangle CDA\) (by SSS congruence criterion)
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10. for a pyramid with a square base, how many faces does it have in to…
d. 5
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use the regular pentagon shown. how many lines of symmetry does the pen…
D. 5
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9. which conditions imply a triangle is right - angled based on the pyt…
C. \(a^{2}+b^{2}=c^{2}\)
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8. a landscaper is designing a semicircular flower bed with a diameter …
C. 15.42 meters
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4. in which quadrant on a coordinate plane will the point (-2, -5) be?
The point \((-2,-5)\) is in Quadrant III.
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given ( abcong cd ) and ( bccong ad ). prove that ( \triangle abccong\t…
$\triangle ABC\cong\triangle CDA$ by the Hypotenuse - Leg (HL) congruence criterion.
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4. for which of these shapes is it possible to apply the pythagorean th…
A. Right triangle
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3 for a construction project, a concrete slab needs to be poured that i…
C. 16 cubic meters
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another look! you can use the distributive property to break an area in…
1. \(3\times5 = 3\times(3 + 2)\), \(3\times5=(3\times3)+(3\times2)\), \(3\times5=9 + 6=15\) 2. \(4\times7=4\times(3 + 4)\), \(4\times7=(4\times3)+(4\times4)\), \(4\times7=12+16 = …
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2. calculate the hypotenuse of each right triangle with the given leg l…
d. \(a = 12,b = 13\)
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find the measures of the indicated angles below. given ab || cd, t = 56…
\(m\angle ABC = 90^{\circ}\), \(m\angle CAB=56^{\circ}\), \(m\angle ACB = 34^{\circ}\), \(m\angle DCA=56^{\circ}\)
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find the unknown angle measure. figure is not to scale. question 4 scor…
\(20\)
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1. the formula ( a^{2}+b^{2}=c^{2} ) compares the length of the hypoten…
Assuming the formula \(a^{2}+b^{2}=c^{2}\) (Pythagorean theorem) with \(c = 13\) and \(b = 8\), \(a=\sqrt{13^{2}-8^{2}}=\sqrt{105}\approx10.2\). But among the given options (if we…
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the area of a rectangle is $(x^{3}-5x^{2}+3x - 15)$, and the width of t…
\(x - 5\) (the fourth option)
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tell if the two given lines are parallel, perpendicular, or just inters…
1. Perpendicular 2. Parallel 3. Intersect 4. Perpendicular 5. \(m =-\frac{1}{4}\) 6. \(m=\frac{3}{2}\)
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in 1 - 4, complete the equations that represent the picture. 1. a = l ×…
1. \(3\times5 = 15\), \(3\times2=6\), \(15 + 6=21\); \(3\times(3 + 2)=(3\times3)+(3\times2)\) 2. \(3\times3 = 9\), \(3\times4 = 12\), \(9+12 = 21\); \(3\times(3 + 4)=(3\times3)+(3…
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which element is not part of aristotles rhetorical triangle theory? o e…
C. anaphora
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here are the endpoints of the segments \\( \\overline { p q } \\), \\( …
(a) \(PQ=\sqrt{13}\), \(WX=\sqrt{13}\), \(YZ=\sqrt{17}\) (b) \(\overline{PQ}\cong\overline{WX}\)
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knowledge check question 18 find the area of this rectangle. square mill
\(\frac{15}{32}\)
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3. put these numbers in order from least to greatest: 4. which statemen…
B. It has both acute and obtuse angles.
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answer the questions below. (a) the perimeter of a rectangular garden i…
(a) \(55\) m (b) \(91\) cm
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5. laylas pet rabbit lives in a rectangular pen with a perimeter of 28 …
48 square feet
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a rectangular window is 3 ft long and 2 ft wide. christine would like t…
\(864\)
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directions: show your work for each problem. circl 1 pt for each correc…
A. \(26m^{2}\)
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verify the asa postulate for triangle congruence by using congruence tr…
\(\triangle EKS\)
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verify the asa postulate for triangle congruence by using congruence tr…
Rotate; \(EK\)
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verify the asa postulate for triangle congruence by using congruence tr…
\(H\)
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question 8: rc 10 which of these statements expresses the most positive…
Mr. Langley asked the boys to take their seats.
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mcr3u trigonometry assignment t /29 4. jason is standing 8.7 km from to…
The height of the hotel is approximately \(167.5\space m\)
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determine if each pair of triangles are congruent. if they are label it…
6. \(\triangle JKM\cong\triangle LMK\) (SAS) 7. \(\triangle ABC\cong\triangle DEC\) (SAS) 8. \(\triangle FGG\cong\triangle HGG\) (ASA) 9. \(\triangle PSR\cong\triangle PQR\) (HL) …
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mcr3u trigonometry assignment t /29 4. jason is standing 8.7 km from to…
The height of the hotel is approximately $167.5$ metres.
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which pair of triangles below are congruent by asa?
The fourth pair of triangles.
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graphing - sequence of transformation which series of transformations w…
A dilation by a factor of \(2\) and A translation \(4\) units left and \(2\) units down.
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geometry determine if the following transformations result in a congrue…
1. Congruent 2. Similar 3. Congruent 4. Congruent 5. Similar
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problem 22: (first taught in lesson 31) find a. after you enter your an…
\(85\)
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problem 21: (first taught in lesson 42) find x. after you enter your an…
\(42\)
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a fish pond is shaped like a circle with a diameter of 40 ft. what is t…
The radius of the fish - pond is \(20\) ft. The area of a circle equals \(r^{2}\) (where \(r = 20\)) multiplied by \(\pi\). Therefore, the area of the fish - pond is \(400\pi\) \(…
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problem 20: (first taught in lesson 30) △mno is equilateral. find x and…
\(x = 7.5\), \(y=150\)
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problem 19: (first taught in lesson 30) find m + n. after you enter you…
\(140\)
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problem 18: (first taught in lesson 49) in △ijk, ij = 4 and jk = 6. is …
\(\angle I\)
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problem 17: (first taught in lesson 49) from this given statement, sele…
The theorem that in a triangle the larger angle is opposite the longer side.
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problem 16: (first taught in lesson 46) from this given statement, sele…
The exterior angle theorem.
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problem 15: lesson 45) from this given statement, select the definition…
Triangle Inequality Theorem.
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in the diagram below, \\( \\overline { a b } \\parallel \\overline { c …
$m\angle AJG = 61^{\circ}$