Question

What is the midpoint theorem?

Answer 1

Hint: In this question, we need to look at the midpoint theorem statement and understand what is a midpoint theorem and what can we find from that.
$$BC\parallel DE$$
$$DE={\displaystyle \frac{1}{2}}BC$$

MIDPOINT THEOREM STATEMENT:
The midpoint theorem states that " The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side."

i.e. $$BC\parallel DE$$ and $$DE={\displaystyle \frac{1}{2}}BC$$

Note:
It is important to note that the midpoint theorem can be used when the ratio of the sides of a triangle are given and asked to find the other side. It is also used in getting the midpoint formula which gives the midpoint of the line joining two points.
Here, the mid-point theorem can be proved by using the congruence conditions of the triangles and the parallel line properties which helps in getting the parallelogram. Then from the conditions and properties of the parallelogram we can get the relation between DE and BC and can also prove the parallel conditions.
We can also find the areas of the triangles by using this condition because the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.