Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side:
given: δabc
prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac.
draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity 0 plus y sub 1, divided by 2 by the slope formula. point e is the midpoint of line segment bc with an ordered pair of ordered pair the quantity of x sub 1 plus x sub 2 divided by 2. the quantity of 0 plus y sub 1 divided by 2 by the slope formula. the slope of line segment de is found to be 0 through the application of the slope formula: the difference of y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of the quantity 0 plus y sub 1, divided by 2, and the quantity 0 plus y sub 1, divided by 2, divided by the difference of the quantity x sub 1 plus x sub 2, divided by 2 and the quantity 0 plus x sub 1, divided by 2 is equal to 0 divided by the quantity x sub 2 divided by 2 is equal to 0 when the slope formula is applied to line segment ac the difference between y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of 0 and 0, divided by the difference of x sub 2 and 0 is equal to 0 divided by x sub 2 is equal to 0, its slope is also 0. since the slope of line segment de and line segment ac are identical, line segment de and line segment ac are parallel by the definition of parallel lines.
which statement corrects the flaw in gina's proof?

To show that polygon abcde is congruent to polygon fghij, a must be used to make the two polygons coincide. a sequence of two transformations that can be used to show that polygon abcde is congruent to polygon fghij is .

Complete the worksheet. use 3.14 for π and round all decimals to the nearest hundredth.find the volume of the composite three-dimensional figure above. important terms are written in bold.1. the pyramid has a square base that is inscribed in the circular base of the cone. draw an image of the composite shape of the base. 2. if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1? 3. now that the diameter has been calculated, what is the circular area of the cone? ignore the square base of the pyramid.? 4. what is the formula for volume of a cone? 5.to calculate the volume of the cone, the height is still needed. if the cone has a lateral surface with a length of 13 units, what is the height of the cone? 6.now find the volume of the cone. do not include the empty space for the pyramid. 7.. the side length of the square base of the pyramid is 8 units long. what is the base area of the pyramid? 8.what is the formula for the volume of a pyramid9. since the cone and the pyramid share the same vertex, what is the volume of the pyramid10.using the volume of the cone and the pyramid, find the volume of the composite shape. remember, the pyramid is empty. 11,. referring to the picture in number 1, what is the area of the composite base knowing that the square is empty? 12what is the formula to find the lateral surface area of a cone? (13find the lateral surface area of the cone14what is the lateral surface area shape of the pyramid? what is the formula for its area? 15to find the lateral surface area of the pyramid the length is still needed. calculate the lateral surface length of the pyramid. 16 now that the lateral surface length is known, what is the lateral surface area of the pyramid17. using the lateral surface areas of the cone and pyramid, along with the area of the composite base, what is the total surface area?

Simplify the rational expression. state any restrictions on the variable. t^2-4t-12 / t-8 the / is a fraction sign.