The midsegment is a line segment that connects the midpoints of 2 sides.
The midsegment is a line segment that connects the midpoints of 2 sides.
Below is an isosceles trapezium.
EF is parallel to the base of the trapezium.
True or false: EF is the midsection of the trapezoid.
We can demonstrate that a midsegment exists in a triangle if at least one of the following conditions is met:
The midsegment of a trapezoid divides the two sides it originates from into two equal parts, and is also parallel to both bases of the trapezoid and measures half the length of these bases.
Given an isosceles trapezoid, is the dashed segment a middle segment of the trapezoid?
Given that DE is a middle section in triangle ABC, what is the length of side DE?
Given that DE is a middle section in triangle ABC, what is the length of side DE?
We can demonstrate that there is a midsegment in a trapezoid provided that, at least, one of the following conditions is met:
The midsegment is a segment that connects the midpoints of 2 sides.
It's very simple to remember the meaning of this term since the word "middle" already tells us that it is about the midpoint, so when we come across the concept of "midsegment" we'll remember that it connects the midpoints of two sides.
We're here to teach you everything you need to know about the midsegment, from the proof to the wonderful properties of the segment that will help us solve exercises.
First, we'll talk about the midsegment of a triangle and then we'll move on to the midsegment of a trapezoid.
Given that DE is a middle section in triangle ABC, what is the length of side DE?
Given that DE is a middle section in triangle ABC, what is the length of side DE?
Given that DE is a middle section in triangle ABC, what is the length of side DE?
The midsegment of a triangle crosses through the midpoint of the two sides from which it extends, but, beyond this, it has two remarkable properties that we can utilize after proving that this segment is, indeed, a midsegment of the triangle.
The midsegment of a triangle is half the length of the third side
and is also parallel to it.
If
then
Given that DE is the middle section in triangle ABC, what is the length of side DE?
Given that DE is the middle section in triangle ABC, what is the length of side DE?
Given that DE is the middle section in triangle ABC, what is the length of side DE?
The theorem discusses the properties of the midsegment and its definition.
We can determine that we are looking at a midsegment of a triangle if at least one of the following conditions is met:
That is, if we know that:
Then, we can determine that:
is a midsegment of a triangle and, consequently,
That is, if we know that:
and also
Then, we can determine that:
is a midsegment of a triangle and, consequently,
and also
That is, if we know that:
and also
Then, we can determine that:
is a midsegment of a triangle and, consequently,
and also
Some notes for guaranteed victory
The mid-segment of a trapezoid has properties very similar to those of the mid-segment of a triangle... It makes sense since, after all, we're still talking about the mid-segment.
Given that DE is the middle section in triangle ABC, what is the length of side DE?
Given that DE is the middle section in triangle ABC, what is the length of side DE?
Given that DE is the middle section in triangle ABC, what is the length of side DE?
The midsegment of a trapezoid bisects the two non-parallel sides it emerges from and is parallel to both bases of the trapezoid, as well as being half the length of these.
Notice, as we have already mentioned, its properties are similar to those of the midsegment of a triangle.
The two expressions that you should remember are: parallel and measures half.
But, don't be mistaken, in the trapezoid the midsegment measures half the length of the bases - that is, half the length of both bases combined.
You will be able to use these properties after proving that there is a midsegment in the trapezoid.
Let's look at the properties of the midsegment illustrated:
If Midsegment
then:
The Midsegment Theorem in a trapezoid is about the properties of midsegments.
If at least one of the following conditions is met, we can determine that it is a midsegment in a trapezoid:
That is, if we know that:
and also
Then we can determine that:
is a midsegment of the trapezoid
Therefore:
If there is a straight line in a trapezoid that comes off one side and is parallel to one of the bases of the trapezoid, we can determine that it is a midsegment and, therefore, is parallel to both bases of the trapezoid, measures half the length of these two, and also cuts the second side it touches in half.
That is, if we know that:
and also
Then we can determine that:
is a midsegment of the trapezoid and, as a result:
Below is an isosceles trapezium.
EF is parallel to the base of the trapezium.
True or false: EF is the midsection of the trapezoid.
True
Given an isosceles trapezoid, is the dashed segment a middle segment of the trapezoid?
Not true
Given that DE is a middle section in triangle ABC, what is the length of side DE?
9
Given that DE is a middle section in triangle ABC, what is the length of side DE?
11
Given that DE is a middle section in triangle ABC, what is the length of side DE?
4.5
Given that DE is the middle section in triangle ABC, what is the length of side DE?
In which figure is the dashed line the midsection of the trapezoid?
Below is an isosceles trapezium.
EF is parallel to the base of the trapezium.
True or false: EF is the midsection of the trapezoid.