1.)I. Download student sheets and teacher sheets.
2.) Plot the points Q,U, A, and D on grid paper. Label the points with the correct letter and ordered pair. These points are called the vertices of the quadrilateral.
3.)With a straight edge draw line segments between each pair of points.
4.)Find the length of each segment using the distance formula. Simplify all radicals and approximate your answer to the nearest hundredth
5.)Find the midpoint of and using the midpoint formula. Label the midpoints M, N, O, and P respectively. Write the ordered pair next to the midpoint of each segment.
6.)Find the equation of the lines containing Q, U, A, and D. Write your answer in slope intercept form and in standard form. Show that each vertices is the intersection of two line segments by solving the linear systems.
7.)Find the slopes of the sides of QUAD. Verify that the slopes of the lines between the vertices of the quadrilateral by comparing it to the equation of the line segments.
8.)Determine if any two pair of lines are parallel or are perpendicular. Explain how you arrive at your answer.
9.)Draw diagonals from opposite vertices. Label the point that the diagonals intersect Z. Write the ordered pair for this point. Determine the midpoint of and each diagonals. Find the length of the diagonals using the distance formula.
10.)Classify QUAD as accurately as possible using the definitions of the quadrilaterals. You may use the link provided.
( quadrilateral lesson)
11.)Estimate the area of QUAD. Determine the area as accurately as possible. Explain your method and any formulas that you used.
12.) Review student work and provide feedback on Part I. Group students with the same quadrilateral. Allow students to complete I for homework so all groups will begin part II on the same day.After students complete Part I group them with students who have the same quadrilateral. Students should agree on solutions and work cooperatively.
Begin Part II.
13.)Draw line segments connecting the midpoints (M, N, O, and P) of the quadrilateral QUAD. Using the coordinates of the midpoint.
14.)Find the lengths of the line segment sconnecting M, N, O, and P.
15.)Find the slopes of each of these line segments.
16.)Determine which of these line segments if any are congruent, parallel or perpendicular.
17.)Draw diagonals connecting the opposite vertices.
18.)Find the midpoint of the diagonals. Label it C. Which of the segments have the same length? Explain the process you used to determine your answer.
19.)Are the diagonals the same length, perpendicular or parallel?
20.)Classify the quadrilateral MNOP as many ways as possible. Justify your answer.
you use the animation provided at the link provided.
( Quadrilateral Animation)
21.)Which pairs of triangles are congruent? Write a proof for at least one pair of triangles. This step is intended for Geometry classes only.
22.)Find the midpoints of the sides on MNOP. Label them H, J, K, and L. Make an hypothesis about this quadrilateral and quadrilaterals in general
23.)Prepare individual report. Submit individual reports paper clipped to group members. Download guidelines document.
24.)Present posters. Have students write down properties all QUAD(quadrilaterals) have in common. Have students write down all properties of MNOP(parallelograms) in common. List the properties of the the diagonals of the different quadrilaterals (QUAD). ( quadrilateral lesson) Students should complete online lesson and take true/false assessment.
25.)Complete group evaluation.
Students should research Quadrilaterals on the Internet. Students select a quadrilateral and research its properties. ( Kites)
