in this picture, b, d, and f are midpoints. ac = 50, ce = 60, and bd = 35 ae = ?
in this picture, b, d, and f are midpoints. ac = 50, ce = 60, and bd = 35 ae = ?
Answer
Answer:
70
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 ).