Question

extra credit #3: triangle midsegment
1 identify all pairs of parallel segments

Explanation:

Step1: Recall the triangle midsegment theorem

The triangle midsegment theorem states that a midsegment of a triangle is parallel to the third side of the triangle.

Step2: Identify midsegments and corresponding parallel sides

• In \(\triangle ACE\), \(BD\) is a midsegment (since \(B\) is the mid - point of \(AC\) and \(D\) is the mid - point of \(CE\)). By the midsegment theorem, \(BD\parallel AE\).
• In \(\triangle CEA\), \(BF\) is a midsegment (since \(B\) is the mid - point of \(AC\) and \(F\) is the mid - point of \(AE\)). By the midsegment theorem, \(BF\parallel CE\).
• In \(\triangle CAE\), \(FD\) is a midsegment (since \(F\) is the mid - point of \(AE\) and \(D\) is the mid - point of \(CE\)). By the midsegment theorem, \(FD\parallel AC\).

Answer:

a. \(BD\parallel AE\)
b. \(BF\parallel CE\)
c. \(FD\parallel AC\)