In the diagram, [i]ABC[/i] is a triangle. [br][i]D[/i] is apoint on [i]AB[/i] and [i]E[/i] is a point on [i]AC[/i].[br][math]m[/math] measures the gradient of [i]DE[/i] and [math]m_1_{ }[/math] measures the gradient of [i]BC[/i].
Question 1[br]Observe the length of [i]AD[/i], [i]DB[/i], [i]AE[/i] and [i]EC[/i].[br]What can you say about the point [i]D[/i] and point [i]E[/i]?
[i]D[/i] is the midpoint of [i]AB [/i]and [i]E[/i] is the midpoint of [i]AC[/i].
Question 2[br]Observe the value of [math]m[/math] and [math]m_1[/math]. [br]What can you say about the line [i]BE[/i] and [i]BC[/i]?
[i]BE[/i] and [i]BC[/i] have the same gradient, they are parallel.
Question 3[br]Observe the length of [i]DE[/i] and [i]BC[/i]. [br]What can you say about the length of [i]DE[/i] and [i]BC[/i]?
Length of [i]DE[/i] = [math]\frac{1}{2}[/math] Length of [i]BC[/i]
Drag points [i]A[/i], [i]B[/i] and [i]C[/i] randomly.[br][br]Reflect if the observations made in Question 1 to 3 are still the same after points [i]A[/i],[i] B[/i] and [i]C[/i] are moved.
Question 4[br]Complete the following sentence to suggest what Midpoint Theorem is.[br][br]"In △[i]ABC[/i], if [i]D[/i] and [i]E[/i] are the midpoints of sides [i]AB [/i]and [i]AC[/i] respectively, then ..."[br][br][br]
[i]DE[/i] is parallel to [i]BC[/i] and [i]DE[/i] is half of [i]BC[/i].