Given that 𝐴𝐸𝐹𝐷 is a parallelogram, where 𝐸 and 𝐹 are the midpoints of 𝐷𝐵 and
𝐷𝐶, respectively, find the length of 𝐶𝐵.
So our goal is to find the length of 𝐶𝐵. So let’s begin going through what we’re given. We are given that 𝐴𝐸𝐹𝐷 is a parallelogram. And we know that 𝐷𝐴 is 2.6 centimeters.
Well, in a parallelogram, opposite sides are congruent.
So that means 𝐹𝐸 would also be 2.6 centimeters. Next, we’re given information about midpoints. 𝐸 is the midpoint of 𝐷𝐵. And F is the midpoint of 𝐷𝐶.
The length of a line segment joining the midpoints of two sides of a triangle is
equal to half the length of the third side. So if we look at this triangle, triangle 𝐶𝐷𝐵, we are told the length of the line
segment joining the two midpoints on the two sides of the triangle will be half of
the length of the third side, side 𝐶𝐵.
So 𝐹𝐸 should be equal to half of 𝐶𝐵. Well, we know that 𝐹𝐸 is equal to 2.6. So to solve for 𝐶𝐵, we can multiply both sides of the equation by two. And two times 2.6 is 5.2.
Therefore, the length of 𝐶𝐵 will be equal to 5.2 centimeters.