Desmos or GeoGebra Challenge: Create a quadrilateral \(QUAD\). Find the midpoints of each side and label them \(T, Y, P\) and \(E\) respectively. What kind of figure is \(TYPE\)? Justify your answer.
1) \(GEOM\) is a quadrilateral with diagonals of lengths \(20\) cm and \(32\) cm. \(T, R, Y\) and \(S\) are the midpoints of \(\overline{GE}\), \(\overline{EO}\), \(\overline{OM}\), and \(\overline{GM}\) respectively.
a) What is the perimeter of \(TRYS\)?
b) What type of figure is \(TRYS\)?
2) Create coordinates for a trapezoid with three congruent segments.
3) Given the line \(y = 2x + 7\) that passes through the ends of the kite, and a vertex at \((0, 4)\) find three other coordinates that make a kite.
4) Given the line \(y = -\frac{1}{5}x - 13\) create four points that make a kite with the short diagonal on the given line.
5) Create four equations of lines, with restrictions, that make a rectangle. None of the lines can be vertical.
6) Create four equations of lines, with restrictions, that make a parallelogram. None of the lines can be vertical or horizontal.
7) Create four equations of lines, with restrictions, that make a rhombus. None of the lines can be vertical or horizontal.
8) Create four equations of lines, with restrictions, that make an isosceles trapezoid. None of the lines can be vertical or horizontal.
9) Create an equation of a circle and find four points on the circle that make a square.
10) Determine four points on the graph of \(f(x) = x^2 + 6x - 55\) that create an isosceles trapezoid.
11) Given quadrilateral \(QUAD\) with coordinates \(Q(-2, 5), U(2, 7), U(4, 30), D(-2, -5)\).
a) What kind of figure is \(QUAD\)? Justify with a coordinate proof.
b) What do you know about \(\overline{QA}\) and \(\overline{UD}\)? Justify with a coordinate proof.
Answer Bank
1) \(GEOM\) is a quadrilateral with diagonals of lengths \(20\) cm and \(32\) cm. \(T, R, Y\) and \(S\) are the midpoints of \(\overline{GE}\), \(\overline{EO}\), \(\overline{OM}\), and \(\overline{GM}\) respectively.
a) What is the perimeter of \(TRYS\)?
b) What type of figure is \(TRYS\)?
2) Create coordinates for a trapezoid with three congruent segments.
3) Given the line \(y = 2x + 7\) that passes through the ends of the kite, and a vertex at \((0, 4)\) find three other coordinates that make a kite.
4) Given the line \(y = -\frac{1}{5}x - 13\) create four points that make a kite with the short diagonal on the given line.
5) Create four equations of lines, with restrictions, that make a rectangle. None of the lines can be vertical.
6) Create four equations of lines, with restrictions, that make a parallelogram. None of the lines can be vertical or horizontal.
7) Create four equations of lines, with restrictions, that make a rhombus. None of the lines can be vertical or horizontal.
8) Create four equations of lines, with restrictions, that make an isosceles trapezoid. None of the lines can be vertical or horizontal.
9) Create an equation of a circle and find four points on the circle that make a square.
10) Determine four points on the graph of \(f(x) = x^2 + 6x - 55\) that create an isosceles trapezoid.
11) Given quadrilateral \(QUAD\) with coordinates \(Q(-2, 5), U(2, 7), U(4, 30), D(-2, -5)\).
a) What kind of figure is \(QUAD\)? Justify with a coordinate proof.
b) What do you know about \(\overline{QA}\) and \(\overline{UD}\)? Justify with a coordinate proof.
Answer Bank