(628)-272-0788 info@etutorworld.com
Select Page

Triangle Inequality Theorem

Grade 7 Math Worksheets

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In other words, if you have a triangle with side lengths a, b, and c, then:

a + b > c

a + c > b

b + c > a

This is represented best in the diagram given below in the link: Check out the image.

These inequalities must hold true for any triangle. If any of these conditions are not met, then it’s impossible to form a triangle with those side lengths.

Personalized Online Tutoring

Triangle Inequality Theorem - Grade 7 Math Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

Sign up with your email ID to access this free worksheet.

"We really love eTutorWorld!"

"We really love etutorworld!. Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)

"My daughter gets distracted easily"

"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.

With the help of Etutorworld, my daughter has been now selected in the Gifted and Talented Program   for the school district"

- Nivea Sharma (via TrustSpot.io)

For example, if you have a triangle with side lengths of 3, 4, and 7, you would check:

3 + 4 > 7 (True)

3 + 7 > 4 (True)

4 + 7 > 3 (True)

So, a triangle can be formed with these side lengths.

If you have side lengths of 1, 2, and 6, then

1 + 2 > 6 (False)

1 + 6 > 2 (True)

2 + 6 > 1 (True)

So, a triangle cannot be formed with these side lengths.

There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

Our kid is doing much better with a higher score.

- Meg, Parent (via TrustSpot.io)

7th Grade Tutoring

eTutorWorld offers Personalized Online Tutoring for Math, Science, English, and Standardised Tests.

Our Tutoring Packs start at just under $22.49 per hour, and come with a moneyback guarantee.

Schedule a FREE Trial Session, and experience quality tutoring for yourself. (No credit card required.)

Example Questions

1. Could a triangle have side lengths of 6 m, 7 m, and 5 m?

Solution

6 + 7 > 5 (True)

6 + 5 > 7 (True)

7 + 5 > 6 (True)

So, a triangle can be formed with these side lengths.

2. If the two sides of a triangle are 3 and 8. Find all the possible lengths of the third side. 

Solution

To find the possible values of the third side of the triangle we can use the formula:

A difference of two sides< Unknown side < Sum of the two sides

8 – 3 < x < 8 + 3

5 < x < 11

There could be any value for the third side between 5 and 11

3. If 4 inches, 8 inches and 2 inches are the measures of three lines segment. Can it be used to draw a triangle?

Solution

4 + 8 > 2 (True)

8 + 2 > 4 (True)

4 + 2 > 8 (False)

So, a triangle cannot be formed with these side lengths.

Do You Stack Up Against the Best?

If you have 30 minutes, try our free diagnostics test and assess your skills.

Triangle Inequality Theorem FAQS

What is the Triangle Inequality Theorem?

The Triangle Inequality Theorem states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Why is the Triangle Inequality Theorem important?

The theorem is fundamental in geometry and helps in determining whether a given set of side lengths can form a valid triangle.

Can any three lengths form a triangle?

No, not every combination of three lengths can form a triangle. The Triangle Inequality Theorem provides a condition for the validity of a triangle based on its side lengths.

What happens if the sum of the lengths of two sides equals the length of the third side?

If the sum of the lengths of two sides equals the length of the third side, the triangle formed is said to be a degenerate triangle, which appears as a straight line.

Can the Triangle Inequality Theorem be applied to any polygon?

No, the Triangle Inequality Theorem specifically applies to triangles. It does not extend to other polygons.

How does the Triangle Inequality Theorem relate to the perimeter of a triangle?

The Triangle Inequality Theorem ensures that the sum of the lengths of any two sides of a triangle is greater than the third side. This condition ensures that the triangle can be closed, forming a polygon with finite perimeter.

Does the Triangle Inequality Theorem apply to both the interior and exterior angles of a triangle?

No, the Triangle Inequality Theorem deals only with the lengths of the sides of a triangle, not with its angles.

What are some real-life applications of the Triangle Inequality Theorem?

Real-life applications include designing bridges, determining whether a set of three given measurements (such as the sides of a box) can form a closed figure, and in navigation and surveying.

Does the Triangle Inequality Theorem hold true for all types of triangles?

Yes, the Triangle Inequality Theorem applies to all types of triangles, including equilateral, isosceles, and scalene triangles.

How can the Triangle Inequality Theorem be used to classify triangles?

The Triangle Inequality Theorem can be used to classify triangles based on the relationships between their side lengths, helping to identify whether a triangle is acute, obtuse, or right-angled.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

Affordable Tutoring Now Starts at Just $22.49

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).

What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.

K12 Online Tutoring Free Trial - Step 1K12 Online Tutoring Free Trial - Step 2K12 Online Tutoring Free Trial - Step 3

 

Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a FREE TRIAL Session with us today.

*There is no purchase obligation or credit card requirement

Save 10% on ALL Tutoring Packs with Code BLOOM10
0
Days
0
Hours
0
Minutes
0
Seconds
Save 10% with Code BLOOM10
0
Days
0
Hours
0
Minutes
0
Seconds