Triangle Midsegment Theorem Basics

Grade 11th

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

Thames

Community Contributor

Quizzes Created: 6941 | Total Attempts: 9,517,194

| Questions: 20

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Question 1 / 20

0 %

0/100

Score 0/100

1) The triangle midsegment theorem states that the midsegment is:

Perpendicular to the third side:

An angle bisector:

Equal in length to the third side:

Parallel to the third side and half its length:

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.

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

About This Quiz

Triangle Midsegment Theorem Basics - 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) What's your name?

We’ll put your name on your report, certificate, and leaderboard.

2) If D and E are midpoints of two sides of △ABC, which statement is correct about DE?

DE bisects ∠A

DE ⟂ BC

DE ∥ BC

DE = 2·BC

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.

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:

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.

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?

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.

Explanation

Submit

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

Kite

Trapezoid

Parallelogram

Rhombus

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 rule applies to parallelograms, as they can be divided into triangles, confirming that the properties of the midsegment can be used to demonstrate the characteristics of parallelograms.

Explanation

Submit

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

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.

Explanation

Submit

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

Two congruent triangles:

A trapezoid and triangle:

Two smaller parallelograms:

Two smaller triangles of equal area:

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.

Explanation

Submit

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

Rectangle

Trapezoid

Parallelogram

Isosceles triangle

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

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?

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

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:

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.

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:

Congruent triangles

Trapezoids

Parallel lines

Medians

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.

Explanation

Submit

12) In △XYZ, midpoints A and B are connected. Which is always true?

AB ⟂ YZ

AB = YZ

AB ∥ YZ

AB bisects ∠X

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.

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?

Similar triangle

Congruent triangle

Equilateral triangle

Isosceles triangle

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.

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:

Parallelogram

Smaller similar triangle

Trapezoid

Rectangle

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.

Explanation

Submit

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

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.

Explanation

Submit

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

Parallel to a side

Half the length of that side

Passes through the centroid

Connects midpoints

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.

Explanation

Submit

17) The midsegment theorem can be proven using:

Pythagorean theorem

Similar triangles

Triangle inequality

Ceva’s theorem

The midsegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. This can be proven using similar triangles, as the triangles formed by the midsegment and the side of the triangle maintain proportional relationships.

Explanation

Submit

18) The midsegment divides the triangle into two:

A triangle similar to the original and a trapezoid:

Two congruent triangles:

Two similar triangles:

Two congruent quadrilaterals:

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.

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 △DEF, DE = 5, EF = 8, DF = 6. The midsegment parallel to EF measures:

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.

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:

A vertex to the opposite midpoint:

The midpoints of two sides:

The centroid to a vertex:

The altitude to the base:

A midsegment in a triangle is a segment that connects the midpoints of two sides, which is parallel to the third side and half its length. This property is essential in understanding triangle geometry.

Explanation

Submit

View My Results

Quiz Review Timeline (Updated): Oct 12, 2025 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.