On graph paper, draw a parallelogram that is neither a rectangle nor a rhombus.
Algebra ABCD is a rectangle. Find the length of each diagonal.
To draw a parallelogram that is neither a rectangle nor a rhombus, we need to create a shape with opposite sides equal in length but not all sides equal.
First, draw a rectangle ABCD on the graph paper. Let's say AB = 6 units and BC = 4 units. Connect points A and C to form diagonal AC. Next, extend the line segments AB and DC until they intersect, and label this point E. Connect points B and E to form diagonal BE.
Now, we have a parallelogram ABCD with diagonal AC and diagonal BE.
To find the length of diagonal AC, we can use the Pythagorean theorem. The length of AC can be found as the hypotenuse of right triangle ABC.
Using the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
AC^2 = 6^2 + 4^2
AC^2 = 36 + 16
AC^2 = 52
Taking the square root of both sides, we find:
AC = √52 ≈ 7.21 units (rounded to two decimal places)
To find the length of diagonal BE, we can use the same method. Diagonal BE can be found as the hypotenuse of right triangle BDE.
Using the Pythagorean theorem, we have:
BE^2 = AB^2 + BC^2
BE^2 = 6^2 + 4^2
BE^2 = 36 + 16
BE^2 = 52
Taking the square root of both sides, we find:
BE = √52 ≈ 7.21 units (rounded to two decimal places)
Therefore, the length of diagonal AC is approximately 7.21 units and the length of diagonal BE is also approximately 7.21 units.