Question

An 8 in. by 8 in. square air vent is shown where AG = 8 inches. BF is the midsegment of ADG and CE is the midsegment of DBF. Which of thefollowing is measure of CE?

Answer 1

Given:

AG = 8 inches

BF is the mid-segment of triangle ADG.

CE is the mid-segment of triangle DBF.

Solution.

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

From the mid-segment theorem, the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

Hence,

`\begin{gathered} BF\text{ = }(1)/(2)\text{ }*\text{ AG } \\ =\text{ }(1)/(2)\text{ }*\text{ 8} \\ =\text{ 4 inches} \end{gathered}`

Similarly, CE is a mid-segment of the triangle DBF, hence:

`\begin{gathered} CE\text{ = }(1)/(2)\text{ }*\text{ BF } \\ =\text{ }(1)/(2)\text{ }*\text{ 4} \\ =\text{ 2 inches} \end{gathered}`

Answer: 2 inches (option A)