Question

1 fill in the blank 1 point
identify all pairs of parallel segments.

1. bd||
2. bf||
3. fd||

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side.

• In \(\triangle ACE\), \(B\) is the mid - point of \(AC\) (since \(AB = BC\)) and \(D\) is the mid - point of \(CE\) (since \(CD=DE\)). So, by the mid - segment theorem, \(BD\parallel AE\).
• In \(\triangle ACE\), \(B\) is the mid - point of \(AC\) and \(F\) is the mid - point of \(AE\) (since \(AF = FE\)). So, by the mid - segment theorem, \(BF\parallel CE\).
• In \(\triangle ACE\), \(F\) is the mid - point of \(AE\) and \(D\) is the mid - point of \(CE\). So, by the mid - segment theorem, \(FD\parallel AC\).

Answer:

1. \(BD\parallel AE\)
2. \(BF\parallel CE\)
3. \(FD\parallel AC\)