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- Square pyramid surface area.  Be specific about what S1 represents.  1/2bh should be included.
- Nice explanation on the dimension change question.  Not sure what I thanked you for.

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2*l*w, 2*l*h, 2*w*h
Example: The length is 5, the height is 2, the width is 10. So, the formula would be 2*5*10, 2*5*2, 2*10*2, which equals 160.

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b+(s1*4)
Example: The base is 25, and one side is 400. So, the formula would be 25+(400*4), which equals 1,625.

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2*3.14r²+2*3.14r*h
Example: The radius of the cylinder is 7, and the height is 11. So, the formula would be 2*3.14*7²+2*3.14*7*11, which equals 791.68.

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b*h, l*w, l*w, l*w
Example: The base is 4, the height is 3. The first length and width is 4x7. The second length and width is 5x7. The third length and width is 3x7. So, the formula 4*3, 4*7, 5*7, 3*7, which equals 96.

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1/3*b*h*w
Example: The base of the square pyramid is 20, the width is 20, and the height is 14. So, the formula would be 1/3*20*14*20, which equals 1,866.6 (repeating).

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4/3*3.14r^3
Example: The radius of the sphere is 5. So, the formula is 4/3*3.14*5^3, which equals 523.6.

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1/3*3.14*r²*h
Example: The radius of the cone is 3, and the height is 11. The formula would be 1/3*3.14*3²*11, which equals 103.67.

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3.14*r²*h
Example: The radius is 2, and the height is 3. So, the formula would be 3.14*2²*3, which equals 37.7.

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1/2*b*h*H
Example: The base is 12, the height (of the triangle) is 16, and the height (of the rectangle) is 20. So, the formula would be 1/2*12*16*20, which equals 1,920.

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3.14*radius²

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1/2*h(b1+b2)
Example: Base 1 of the trapezoid is 10, base 2 is 6, and the height is 4. So, the formula would be 1/2*4(10+6), which equals 32.

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b*h
Example:The base of a parallelogram is 6, the height is 2, so the formula would be 6*2, which equals 12.

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l*w
Example: The length of a rectangle is 5, the width is 8. The formula would be 5*8, which equals 40.

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Basic formula: The scale factor that change the dimensions are multiplied. That product is the scale factor and is applied to the original area.

Elaborate formulas:
1) When the length is doubled and the width stays the same, then the area doubles.

Example: the original length of the rectangle is 4cm, the width is 3cm. The area of it was 12 units². It is then changed, so the new length of the rectangle is 8cm, the new width is 3cm. The area of the new rectangle is 24cm².

2) When the length stays the same and the width doubles, then the area doubles.

Example: the original length of the rectangle is 4cm, the width is 3cm. The area of it was 12 units². The new length of the rectangle is 4cm, the new width is 6cm. The area of the new rectangle is 24cm²

3) When the length is doubled and the width is doubled, then the area increases by 4.

Example:  the original length of the rectangle is 4cm, the width is 3cm. The area of it was 12 units². The length of the new rectangle is 8cm, the new width is 6cm. The area of the new rectangle is 48cm²

Circles:
1) When the radius doubles then the area is multiplied by 4.

Example: The radius of the original circle is 1, the area is 3.14 units². The radius of the new circle is 2, the new area is 12.56cm²

2) When the radius triples then the area is multiplied by 9.

Example:  The radius of the original circle is 1, the area is 3.14 units². The radius of the new circle is 3, the new area is 28.26cm².

you're welcome Mr. Greene!

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You find the area of the composite figure, then you find the area of the inscribed figure. After that, you subtract the area of the inscribed figure by the area of the composite figure.

Example:
First, I would find the area of the circle, which is 78.5 units². Next, you find the area of the square, which would be 49 units². Then, you would do 78.5-49= 29.5 units².

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3.14*diameter
Example: The diameter is 30. So, the formula is 3.14*30, which equals 94.25.

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Triangle: 1/2 b*h
Example: The base of a triangle is 3, the height is 10. So, the formula would be 1/2*3*10, which equals 15.

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- 90 degree rotations are incorrect.  You switched them.
- Prime Coordinates are a point after a transformation has been completed.

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This picture shows prime coordinates because it shows how the line goes across (x axis), and then goes up (y axis) to give you the prime coordinate of (4,7).

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https://www.mathsisfun.com/definitions/coordinates.html
This website says and shows what a prime coordinate and gives examples. It also say how there are different types of coordinates and it says how to use prime coordinates.

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This picture shows a rotation because it shows the original shape and coordinates, and shows the shape and coordinate after it was rotated 90 degrees clockwise.

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This picture shows a reflection  because it shows the original shape (in the third quadrant), and it shows the new shape (fourth quadrant). It shows that it was reflected over the y-axis.

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This picture shows dilations because it shows the original shape and original coordinates. It also shows the new shape and coordinates after it was dilated. This is a dilation of 2.

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This picture shows translation because it shows the original shape, and it shows the shape when it was translated. It also shows how much it was translated.

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Example: The original points would be (-4,5), (-1,1), and (-4,-1). The translation of those points would be (2,5), (5,1), and (2,-1). This would be a translation of 6.
Non-Example: The original points would be (-4,5), (-1,1), and (-4,-1). The translation of those points are (3,6), (7,4), and (4,-7). These points do not make the same shape so it is not a translation.

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Example: The original points would be (-2,-2), (1,-1), and (0,2). The dilation of those points would be (-4,-4), (2,-2), and (0,4). This would be a dilation of 2.
Non-Example: The original points would be (-2,-2), (1,-1), and (0,2). The dilation of those points are (-3,-4), (5,-4), and (6,2). These points do not make the same points as the original shape, so it's not a dilation.

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Example: The original points would be (2,2), (5,5), and (4,1). The rotation of those points would be (-2,-2), (-5,-5), and (-4,-1).
Non-Example: The original points would be (2,2), (5,5), and (4,1). The rotation is (2,-2), (5,-5), (-4,-1). This is not a rotation because it is a reflection.

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Example: The original points would be (-2,1), (2,4), and (4,2).  The reflection of those points would be (-2,-1), (2,-4), and (4,-2). This is a reflection of the x coordinate.

Non-example: The original points would be (-2,1), (2,4), and (4,2). The relfection points are (2,-1), (2,-4), and (4,2). This is not a reflection because it is not the same shape if you were to flip one over the other.

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Rotations
90° clockwise (x,y) to (-y,x)
90° counterclockwise (x,y) to (y,-x)
180° (x,y) to (-x,-y)
Reflections:
Over Y-axis (x,y) to (-x,y)
Over X-axis (x,y) to (x,-y)

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Coordinates are a set of values that show an exact position.

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A circular movement. Rotation has a central point that stays fixed and everything else moves around the point in a circle.

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An image or shape as it would be seen in a mirror.

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A translation is a transformation of the plane that slides every point of a figure the same distance in the same direction.

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A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

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This picture shows a transversal line because there are two lines with one line running through both of them. The line that runs through them both creates more angles.

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This picture shows vertical angles because angle AC is vertical to angle DB (they are both 75 degrees). Angle AD is going to be vertical to CB.

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This picture shows supplementary angles because it shows the degrees of both angles (130 and 50) and the sum of them is 180 degrees.

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This picture shows adjacent angles because the common vertex is angle O, and side C is adjacent to side B, and side A is adjacent to side B.

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This picture shows complementary angles because it shows the degrees of both angles (25 and 65) and the sum of them is 95 degrees, which is a right angle.

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This picture shows corresponding angles because it shows that A and E are corresponding because they are the same angles, The same applies with C and G, B and F, and D and H

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Example: There are two horizontal parallel lines next to each other, and there is a slanted line running through them both. This creates 8 angles, making it transversal.

Non-Example: There are two horizontal parallel lines next to each other, and there is a slanted line running through one of them. This makes it not transversal because the slanted line is only running through one line, instead of two.

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Example: There are four angles right next to each other. One of the angles is 81 degrees, so the one across from it is 81. The other angles are both 99 degrees, because they are both across from each other.

Non-Example: There are four angles right next to each other. One of the angles is 81 degrees, but the one across from it is 90 degrees. This is not an example of vertical angles because even though they are directly across from each other, they aren't the same number.

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Example: two angles are next to each (even though they don't have to be), one obtuse and one acute. The acute angle is 60 degrees, the obtuse is 120 degrees, which equals 180 degrees.

Non-example: There was an obtuse angle and an acute angle, one being 130 degrees, the other being 80 degrees. This is not a supplementary angle because it does not equal 180 it equals 210.

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Example: The angles share a common vertex and can equal either 90 degrees or 180 degrees

Non-Example: If they are not next to each other, they are not adjacent.

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Example: One angle is 40 degrees and the one next to it is 50 degrees, which equals a 90 degree right angle.

Non-Example: If one angle is 40 degrees and the one next to it is 70 degrees, it wouldn't because it equals 110 degrees, which is greater than 90. Or, if the angle is not a right angle.

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Example: When a transversal line runs through two parallel lines, which creates angles that are formed in the same position.

Non-Example: There's no real way to not have corresponding angles, unless there is no line running through the two lines, because then it can't create the corresponding angles.

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Intersecting a system of lines.

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Each of the pairs of opposite angles made by two intersecting lines.

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Two Angles are Supplementary when they add up to 180 degrees.

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Two angles that have a common vertex and a common side.

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either of two angles whose sum is 90°

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When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.

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- Similar shapes have congruent corresponding angles and proportional corresponding sides.

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Two shapes can only be similar if the only difference is the size of the figures. They cannot be two different shapes such as it can't be a square and a triangle, it would have to be either two squares or two triangles. One shape can be flipped or turned. This picture shows what I mean.

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The parts of a linear equation are y=mx+b.

Y = y coordinate

M = slope

x = x coordinate

b = y intercept

An example would be y=3x-2.

3 would be the slope, and -2 would y intercept.

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The types of slope include:

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This picture shows scale factors because it shows how the smaller rectangles side lengths are 10 by 15, and if you multiply that by two, then you get a rectangle with the side lengths of 20 by 30. The next rectangle would have side lengths of 20 by 45.

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This picture shows indirect measurements because it shows the measurements of both the sides on each triangle, which creates our equation. Our equation would be h x 4 = 24 x 6, which would equal 4h = 144. You then divide both numbers by 4, giving you the answer h = 36.

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This picture shows proportions because it shows the equation that you have to do to figure out x (which is x/6 = 1/1.5) and that you have to cross multiply. By cross multiplying, you get 1.5x = 6, and if you do both numbers divided by 1.5, you get x = 4.

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This picture shows unit rates because it shows that you drive 300 miles in 5 hours, but if you divide both the numbers by 5, then you find out that you drive 60 miles per hour.

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Example: if you have two squares, one with a side length of 2 inches, and another with a side length of 4 inches. This gives a scale factor of 1 : 2 from the small square to the large square.

Non-Example: You can't have one triangle and one square. They both have to be the same shape or else the answer will not be correct when you try to find the scale factor.

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Example: If you have two triangles:

First triangle:

height = h length of one side = 24

Second triangle:

height = 3 length of one side = 6

You have to do 6 x h = 3 x 24

6h = 72, then divide them both by 6.

h = 12.

Non-Example: You don't want to do

h x 24 = 3 x 6 because you have to multiply the numbers of the same side on both triangles. H and 3 are both on the same side on both of the triangles, so you would multiply them.

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Example: 2/3 = 6/9

Use cross products to verify: 2 x 9 = 3 x 6

18 = 18 Yes, it's a proportion

Non-Example: 2/3 = 7/9 because 2/3 cannot go into 7/9 and 2 x 9 = 3 x 7 equals 18 = 21, which are not the same.

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Example: At a school dance, there are 6 girls for every 3 boys. The ratio of girls to boys as a unit rate:

Girls : boys = 6 : 3 = 6/3 = 6 ÷ 3/3 ÷3 = 2/1

Non-Example: You can't just leave the fraction as 6/3 because the denominator has to be 1.

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a number which scales, or multiplies, some quantity.

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a method of using proportions to find an unknown length or distance in similar figures.

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a part, share, or number considered in comparative relation to a whole.

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a comparison of two different quantities when they are combined together.

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- Missing 2nd question on when to flip the symbol of an inequality.