Question

in this picture, b, d, and f are midpoints. ac = 50, ce = 60, and bd = 35 ae = ?

Explanation:

Step1: Identify Midsegment Theorem

In a triangle, the segment connecting the midpoints of two sides is parallel to the third side and half its length. Here, B and D are midpoints, so BD is a midsegment of triangle ACE.

Step2: Relate BD to AE

By the Midsegment Theorem, \( BD=\frac{1}{2}AE \). We know \( BD = 35 \), so we can solve for \( AE \).

Step3: Solve for AE

Multiply both sides of the equation \( 35=\frac{1}{2}AE \) by 2: \( AE = 35\times2 = 70 \).

Answer:

70