Find the midpoint of each side of the trapezoid. Connect the

midpoints. What is the most precise
classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?

as with any quadrilateral, you get a parallelogram.

This topic is discussed here:

http://jwilson.coe.uga.edu/EMT669/Student.Folders/Dozier.Cynthia/essay1/Essay.html

Wesley covered this figure with the unit square shown to find the area.

A rectangle and square are shown. The square is labeled 1 square unit. The length of the rectangle is approximately 6 times as long as a side of the square, and the width of the rectangle is approximately 3 times as long as a side of the square.

Which figure shows how he covered the square and the correct area?



A.
An array of squares has 1 row and 2 columns. The entire array has the same size and shape as the rectangle in the problem statement.
B.
An array of squares has 2 rows and 4 columns. The entire array has the same size and shape as the rectangle in the problem statement.
C.
An array of squares has 3 rows and 6 columns. The entire array has the same size and shape as the rectangle in the problem statement.
D.
An array of squares has 4 rows and 8 columns. The entire array has the same size and shape as the rectangle in the problem statement.
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2 of 3 Answered

Kurt found the area of this shape is 18 square units. If he used a larger unit square, would his measurement be greater than 18 square units or less than 18 square units? Explain.

An array of squares has 3 rows and 6 columns. A square below the array that is the same size as the squares in the array is labeled 1 square unit.

A.
Less than 18 square units; if the unit square is larger, then fewer of them are needed to cover the shape.

B.
Less than 18 square units; if the unit square is smaller, then fewer of them are needed to cover the shape.

C.
Greater than 18 square units; if the unit square is smaller, then more of them are needed to cover the shape.

D.
Greater than 18 square units; if the unit square is larger, then more of them are needed to cover the shape.

To find the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid, we first need to determine the properties of this quadrilateral.

1. Start by labeling the trapezoid's vertices as A, B, C, and D (clockwise or counterclockwise).

2. Find the midpoints of each side of the trapezoid. Let's call these midpoints E, F, G, and H. We can find the midpoints by using the formula:
Midpoint = (Average of x-coordinates, Average of y-coordinates)

For example, the midpoint of side AB is E, which can be found by:
E = ((A_x + B_x) / 2, (A_y + B_y) / 2)

3. Connect the midpoints E, F, G, and H to form a quadrilateral.

Now, let's determine the classification of this quadrilateral based on its properties:

1. If the opposite sides of the quadrilateral are parallel, then the quadrilateral is a parallelogram.

2. If the opposite sides of the quadrilateral are equal in length and parallel, then the quadrilateral is a rectangle.

3. If the opposite sides are parallel and all angles are right angles, then the quadrilateral is a square.

4. If the quadrilateral has only one pair of parallel sides, then it is a trapezoid.

So, based on the properties of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid, we need to determine whether the opposite sides are parallel, equal in length, or have right angles at each vertex to accurately classify it.