Triangle Inequality Theorem
Objectives
Start
Story
Triangle Inequality Theorem
Formation of Triangles
Practice
Summary
Story
Triangle Inequality Theorem
Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
a + b > c
Example 1:
Given the triangle:
Here:
a and b
are any two sides.
2+4>5 5+4>2 5+2>4
is the other side.
Let's see some examples:
Example 2:
Given sides 3, 4, 7 show that it's not possible to form a triangle.
Example 1: In the given the triangle, the inequality theorem holds.
7+4>3 7+3>4
but 3+4=7
Formation of Triangles
Click here to draw >
Formation of Triangles
Can you form a triangle with the lengths 2, 6, and 5? Drag the elements to figure out.
2+5>6 5+6>2 2+6>5
Yes!, it's possible to form a triangle.
Solution
Click here to draw >
Formation of Triangles
Can you form a triangle with the lengths 2, 2, and 5? Drag the elements to figure out.
2+5>2 5+2>2 but 2+2<5
It's not possible to form a triangle.
Solution
Practice
Click here to draw >
Formation of Triangles 2
Check the results with inequalites
Can you form a triangle with the lengths 2, 5, and 6? Drag the elements to figure out.
04:00
Try it by yourself:
Summary
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
8TH-TRIANGLE-INEQUALITY-THEOREM-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
- Grid paper.
- A Protactor.
- Pencils of different colors.
- Eraser.
- A rule.
- A compass.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
"MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles." MA.8.GR.1.3 Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides. ELA.K12.EE.1.1 Cite evidence to explain and justify reasoning.
WEEK 30-TRIANGLE-INEQUALITY-THEOREM
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Created on October 9, 2024
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Transcript
Triangle Inequality Theorem
Objectives
Start
Story
Triangle Inequality Theorem
Formation of Triangles
Practice
Summary
Story
Triangle Inequality Theorem
Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
a + b > c
Example 1: Given the triangle:
Here:
a and b
are any two sides.
2+4>5 5+4>2 5+2>4
is the other side.
Let's see some examples:
Example 2: Given sides 3, 4, 7 show that it's not possible to form a triangle.
Example 1: In the given the triangle, the inequality theorem holds.
7+4>3 7+3>4
but 3+4=7
Formation of Triangles
Click here to draw >
Formation of Triangles
Can you form a triangle with the lengths 2, 6, and 5? Drag the elements to figure out.
2+5>6 5+6>2 2+6>5
Yes!, it's possible to form a triangle.
Solution
Click here to draw >
Formation of Triangles
Can you form a triangle with the lengths 2, 2, and 5? Drag the elements to figure out.
2+5>2 5+2>2 but 2+2<5
It's not possible to form a triangle.
Solution
Practice
Click here to draw >
Formation of Triangles 2
Check the results with inequalites
Can you form a triangle with the lengths 2, 5, and 6? Drag the elements to figure out.
04:00
Try it by yourself:
Summary
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
8TH-TRIANGLE-INEQUALITY-THEOREM-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
"MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles." MA.8.GR.1.3 Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides. ELA.K12.EE.1.1 Cite evidence to explain and justify reasoning.