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48 Cards in this Set
- Front
- Back
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Complementary angles add up to . . .
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90 degrees
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Supplementary angles add up to . . .
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180 degrees (one will always be acute and the other obtuse)
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Scalene triangles have . . .
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no congruent sides or angles (all sides and angles are different)
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Isosceles triangles have . . .
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two congruent sides (same length) and 2 congruent base angles (angles opposite the equal sides are equal.)
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Equilateral triangles have . . .
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all three sides are the same length and all angles are congruent (60 degrees each)
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area of a circle |
π(r^2) |
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Circumference |
c=d(π) C=2π(r) |
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volume of pyramid |
v=1/3 (l)(w)(h) |
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volume of cone |
v=1/3πr^2h |
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volume of sphere |
v=4/3πr^3 |
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volume of prism |
v=bh |
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volume of cylinder |
v=(π)(r^2)(h) |
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pythagorean theorem |
a^2 + b^2 = c^2 |
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Area of a Rectangle |
(A = length x width) |
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Area of a Triangle (cut a square in half...) |
A = ½ B x H (A = ½ base x height) |
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Area of a Trapeziod |
½ x height (base1+ base2) |
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Perimeter of a Rectangle |
P = 2h + 2w (P = 2 x height + 2 x width) |
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Perimeter of a Triangle |
Sum of all sides |
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What is a hypotenuse? |
The longest side in a right triangle. The side opposite the right angle. |
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Perimeter of a Trapezoid |
Sum of all sides. P=a+b+c+d |
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Area of a Square |
A = (Side)(side) |
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Perimeter will always be... |
one dimensional (centimeters, inches, feet, yards, etc.)
Think: If I was in a room this shape and I walked around the outside edges how far would I travel? |
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What is the Perimeter of a Circle |
Circumference |
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What measurement will always be two dimensional? |
Area: centimeters^2, inches^2, feet^2, yards^2, etc. Think: If i was buying carpet for this room, how much would i need? |
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Volume of a cube |
V=s^3 |
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volume of a rectangular prism |
V=(w)(h)(l) (width)(height)(length) V= (3cm)(4cm)(5cm)=60cm^3 |
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three dimensional measurement |
Volume: centimeters^3, inches^3, feet^3, yards^3, etc. |
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Interior Angles of a Triangle |
will always add up to 180 degrees |
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Right Triangle |
One of the angles is 90 degrees |
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When can you use Pythagorean Theorem? |
With a right triangle: if you know two sides of the triangle, you will be able to find the third side. |
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what is the special rule for triangle side lengths? |
The triangle inequality rule |
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The triangle inequality rule |
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. In other words, as soon as you know that the sum of 2 sides is less than (or equal to ) the measure of a third side, then you know that the sides do not make up a triangle. |
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Acute Angle |
An Acute Angle is less than 90° |
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obtuse Angle |
An obtuse angle is one which is more than 90° but less than 180°In other words, it is between a right angle and a straight angle. |
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Right Angle |
A right angle is equal to 90 degrees. |
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Define Congruent |
Sides are the same length. |
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Any triangle that follows the Pythagorean Theorem is what? |
A Right triangle! |
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When given two sides of a right triangle... a=3 b=4 Find C? |
Use Pythagorean Theorem (3)(3) + (4)(4) = C^2 C= 5 |
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The arch has 5 nearly congruent stones, each of which is in the shape of a right prism with trapezoid bases. Based on the approximate measurements provided, which of the following best approximates the volume of the entire arch? (The area of a trapezoid with bases b1 and b2 and height h is 1/2(b1+b2)(h)
A. 900 cubic feetB. 1,050 cubic feet C. 1,140 cubic feetD. 2,160 cubic feetE. 4,320 cubic feet |
Option (D) is correct. The volume of a right trapezoidal prism is equal to the height of the prism times the base area of the trapezoid, and is given by the formula V=1/2(b1+b2)(h)(l), where b1 and b2 are the trapezoid bases, h = the height of the trapezoid, and l = the height of the prism. By substituting the values given:V=1/2(b1+b2)(h)(l) V=1/2(14+ 10)⋅12⋅3 V= 432 One trapezoidal stone is 432 cubic feet. Since there are 5 nearly congruent stones, 432⋅5=2,160. Therefore, the entire arch is approximately 2,160 cubic feet. |
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Define Mean |
The "mean" is the "average", where you add up all the numbers and then divide by the number of numbers. |
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Define median |
The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, (so you may have to rewrite your list before you can find the median. ) |
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Define mode |
the value that occurs most often. If no number in the list is repeated, then there is no mode for the list. |
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Define Range |
a list of numbers is just the difference between the largest and smallest values. |
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Using the following numbers find the Mean: 13, 18, 13, 14, 13, 16, 14, 21, 13 |
The mean is the usual average, so I'll add and then divide:(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 Note that the mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers. |
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Using the following numbers find the Median: 13, 18, 13, 14, 13, 16, 14, 21, 13 |
The median is the middle value, so first I'll have to rewrite the list in numerical order:
13, 13, 13, 13, 14, 14, 16, 18, 21 There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number: So the median is 14. |
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Using the following numbers find the mode:13, 18, 13, 14, 13, 16, 14, 21, 13 |
13, 13, 13, 13, 14, 14, 16, 18, 21
The mode is the number that is repeated more often than any other, so 13 is the mode. |
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Using the following numbers find the Range: 13, 18, 13, 14, 13, 16, 14, 21, 13 |
13, 13, 13, 13, 14, 14, 16, 18, 21 The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8. |
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What is the Volume of a right trapeziodal prism? |
The area of a trapezoid with bases b1 and b2 and height h is Volume = 1/2(b1+b2)(h)(l) |
