Triangle Midsegment Theorem: Core Concepts

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7288 | Total Attempts: 9,526,295
| Questions: 20 | Updated: Nov 21, 2025
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) The triangle midsegment theorem states that the midsegment is

Explanation

The triangle midsegment theorem states that a midsegment connects the midpoints of two sides of a triangle and is parallel to the third side, with a length that is half of that side.

Submit
Please wait...
About This Quiz
Triangle Midsegment Theorem: Core Concepts - Quiz

Are you ready to see a triangle’s secret shortcut? In this quiz, you’ll learn about a midsegment—the line that connects the midpoints of two sides. You’ll discover that it’s parallel to the third side and half as long. With quick checks and clear examples, you’ll spot midsegments, find their lengths,... see moreand see how they help us understand triangles and parallelograms.
see less

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) If D and E are midpoints of two sides of â–³ABC, which statement is correct about DE?

Explanation

Since D and E are midpoints, by the Midsegment Theorem, DE is parallel to BC and half its length, confirming that DE is perpendicular to BC.

Submit
3) If BC = 10, the midsegment parallel to BC measures:

Explanation

The midsegment of a triangle is always half the length of the side it is parallel to. Since BC measures 10, the midsegment will measure 10 / 2 = 5.

Submit
4) If a triangle has midsegments drawn, how many smaller triangles are formed inside?

Explanation

When the midsegments of a triangle are drawn, they divide the triangle into four smaller triangles. Each midsegment connects the midpoints of two sides, forming additional triangles within the original triangle.

Submit
5) The midsegment rule helps prove properties of which quadrilateral?

Explanation

Because the midsegment is parallel and proportional, it helps prove sides are parallel, a key property of a parallelogram.

Submit
6) In △PQR, midpoints M and N are connected. MN ∥ QR. If MN = 8, then QR =

Explanation

According to the midpoint theorem, if M and N are the midpoints of sides PQ and PR respectively, then segment MN is parallel to side QR and MN is half the length of QR. Since MN is given as 8, QR must be 16.

Submit
7) The line segment joining two midpoints of sides of a triangle always divides the triangle into:

Explanation

The line segment connecting the midpoints of two sides of a triangle forms a new triangle that is similar to the original triangle, and it divides the original triangle into two smaller triangles that each have half the area of the original, thus they are equal in area.

Submit
8) A midsegment always forms what shape with the third side?

Explanation

A midsegment connects the midpoints of two sides of a triangle and is parallel to the third side, forming a trapezoid shape.

Submit
9) How many midsegments does a triangle have?

Explanation

A triangle has three midsegments, each connecting the midpoint of one side to the midpoint of another side, forming three distinct segments.

Submit
10) If the midsegment of a triangle is 6 units long, the base it is parallel to measures:

Explanation

In a triangle, the midsegment is half the length of the base it is parallel to. Therefore, if the midsegment is 6 units long, the length of the base must be 12 units.

Submit
11) The midsegment rule is often used in proofs involving:

Explanation

The midsegment rule states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. This is particularly relevant in proofs involving parallel lines, as it establishes relationships between different segments.

Submit
12) In â–³XYZ, midpoints A and B are connected. Which is always true?

Explanation

Since A and B are midpoints, the line segment AB is always perpendicular to YZ, indicating that AB is a vertical segment connecting the midpoints of XYZ.

Submit
13) A triangle’s midsegment creates which type of triangle when drawn with other midsegments?

Explanation

A triangle's midsegments are parallel to the base and half its length, resulting in triangles that are similar to the original triangle by the triangle midsegment theorem.

Submit
14) The three midsegments of a triangle form a:

Explanation

The three midsegments of a triangle connect the midpoints of each side, creating a smaller triangle that is similar to the original triangle. This similarity arises because the midsegments are parallel to the corresponding sides of the triangle and half their length.

Submit
15) If a triangle has side lengths 8, 6, 10, what is the midsegment parallel to the 10 side?

Explanation

The midsegment of a triangle that connects the midpoints of two sides is parallel to the third side and is half its length. Since the side length parallel to the midsegment is 10, the midsegment is half of that, which is 5.

Submit
16) Which of the following is NOT a property of a triangle midsegment?

Explanation

A triangle midsegment is a line segment connecting the midpoints of two sides of a triangle. It is parallel to the third side and its length is half that of the third side. It does not pass through the centroid, which is the point where all three medians intersect.

Submit
17) The midsegment theorem can be proven using:

Explanation

The Midsegment Theorem is proven by showing that the triangles formed by the midsegment and the third side are similar by AA similarity.

Submit
18) The midsegment divides the triangle into two:

Explanation

The midsegment connects the midpoints of two sides of a triangle, creating a smaller triangle that is similar to the original triangle, along with a trapezoid formed by the remaining area.

Submit
19) In â–³DEF, DE = 5, EF = 8, DF = 6. The midsegment parallel to EF measures:

Explanation

The midsegment in a triangle is parallel to the base and its length is half the length of the base. Since EF is 8, the midsegment will measure 4.

Submit
20) A midsegment of a triangle connects:

Explanation

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

Submit
×
Saved
Thank you for your feedback!
20)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
The triangle midsegment theorem states that the midsegment is
If D and E are midpoints of two sides of â–³ABC, which statement is...
If BC = 10, the midsegment parallel to BC measures:
If a triangle has midsegments drawn, how many smaller triangles are...
The midsegment rule helps prove properties of which quadrilateral?
In △PQR, midpoints M and N are connected. MN ∥ QR. If MN = 8, then...
The line segment joining two midpoints of sides of a triangle always...
A midsegment always forms what shape with the third side?
How many midsegments does a triangle have?
If the midsegment of a triangle is 6 units long, the base it is...
The midsegment rule is often used in proofs involving:
In â–³XYZ, midpoints A and B are connected. Which is always true?
A triangle’s midsegment creates which type of triangle when drawn...
The three midsegments of a triangle form a:
If a triangle has side lengths 8, 6, 10, what is the midsegment...
Which of the following is NOT a property of a triangle midsegment?
The midsegment theorem can be proven using:
The midsegment divides the triangle into two:
In â–³DEF, DE = 5, EF = 8, DF = 6. The midsegment parallel to EF...
A midsegment of a triangle connects:
Alert!

Advertisement