In the figure, [i]ABC[/i] is a triangle. [br][i]D[/i] is a point on [[i]AB][/i] and [i]E[/i] is a point on [[i]AC][/i].
Observe the length of segments [[i]AD][/i], [[i]DB][/i], [[i]AE][/i] and [[i]EC][/i].[br][br]What does represent the point [i]D for the segment [AB][/i] and point [i]E for segment [AC][/i]?
[i]D[/i] is the midpoint of [[i]AB] [/i]and [i]E[/i] is the midpoint of [[i]AC][/i].
Observe the value of the angles <ADE and <A[i]BC. [br][br][/i]What can you say about the lines (DE) and (BC)?
[math]\angle[/math]ADE = [math]\angle[/math]ABC then [i](BE)[/i] // ([i]BC)[/i] cut by transversal (AB) since corresponding angles are equal
Observe the length of [[i]DE][/i] and [[i]BC][/i]. [br][br]What can you say about the length of [[i]DE][/i] and [[i]BC][/i]?
The length of [DE] is equal to the half of that of [BC] [br][i]DE[/i] = [math]\frac{1}{2}[/math] . [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.
Complete the following sentence to suggest what Midpoint Theorem is.[br][br]"In △[i]ABC[/i], if [i]D[/i] midpoint of [AB] and [i]E[/i] midpoint of [[i]AC][/i], then ..."[br][br][br]
[i](DE)[/i] is parallel to ([i]BC)[/i] and the length of [[i]DE][/i] is equal to half of [[i]BC][/i].