7.4 Reasoning about Triangle and Quadrilateral Properties (Guided Activity)
Goal:
Form and test Conjectures about Properties of Quadrilaterals.
MIDSEGMENT - a line segment connecting the midpoints of two adjacent sides.
COUNTEREXAMPLE - an example that proves that a hypothesis or conjecture is false.
What figure is formed by the midsegments of a quadrilateral?
Conjecture: The shape formed by the midsegments of a quadrilateral has the same shape as the original quadrilateral. Use the space below to work through this conjecture.
Conjecture: All interior shapes formed by midsegments are parallelograms. Use the space below to test this conjecture.
Reflecting Questions:
A. Explain how Jafar determined that his conjecture was incorrect.
B. Should Maria have tested other quadrilaterals? Explain.
C. Explain house Elani's examples supported the conjectures she tested but did not prove it.
MEDIAN - the line drawn from a vertex of a triangle to the midpoint of the opposite side.
Conjecture: For any Isosceles triangle, the median through the third angle is never perpendicular to the base. Use the space below to test this conjecture.
Make a conjecture about the relationship between the exterior angle of a triangle and the two interior angles opposite it. Then test your conjecture. Use the space below to test your conjecture.