Midquad Investigation
- See the general quadrilateral below.
- Find the midpoint of each side (Midpoint, 2nd button from left in menu), and label consecutive midpoints as A, B, C, and D, respectively.
- Construct quadrilateral ABCD. (Polygon, 5th button) This is called the midquad of the original quadrilateral.
- Find the length of each side of ABCD. (Distance, 8th button)
- Find the measure of each vertex angle of ABCD. (Angle, 8th button)
- Move length, angle, and vertex labels to appropriate locations in the graphic, as to not impede view.
General Quadrilateral
What do you observe? What type of quadrilateral does ABCD appear to be?
Rhombus
Construct the midquad for the rhombus. Use measuring tools and manipulate the figure to explore the midquad, and describe it as completely as possible.
Kite
Construct the midquad for the kite. Use measuring tools and manipulate the figure to explore the midquad, and describe it as completely as possible.
Isosceles Trapezoid
Construct the midquad for the isosceles trapezoid. Use measuring tools and manipulate the figure to explore the midquad, and describe it as completely as possible.
Rectangle
Construct the midquad for the rectangle. Use measuring tools and manipulate the figure to explore the midquad, and describe it as completely as possible.
Square
Construct the midquad for the square. Use measuring tools and manipulate the figure to explore the midquad, and describe it as completely as possible.
What general conclusions can you make about midquads of quadrilaterals?