Triangles: An Introduction (1965)

[Music] All around us we see shapes called triangles. What is a triangle? Let's find out. How many sides does a triangle have? 1 2 3. Can you describe the sides? They are all line segments. How many corners does a triangle have? 1 2 3. A triangle is a shape made when three line segments meet at three corners. Look at these shapes. Are they triangles? Yes, they are triangles. Each has three straight sides that meet at three corners. What do you see about the length of the line segments in this triangle? They are all the same length. A triangle with sides that are all the same length is called an equilateral triangle. Some triangles look like this. What do you see about the length of the line segments that make this triangle? only two are the same length. A triangle with only two sides the same length is called an isosles triangle. What do you see about the length of the line segments that make this triangle? They are all different lengths. A triangle with each of its sides a different length is called a scaline triangle. Do you think that any three line segments can make a triangle? Let's see. is this a triangle? No, because the three line segments do not meet at three corners. Do you think these line segments will make a triangle? Is this a triangle? No. The three line segments do not meet at three corners. Let's see if these line segments will make a triangle. Do they? Yes. The three line segments meet at three corners. Can you discover why some sets of line segments make a triangle while others do not? Let's find out. We will put the two shorter line segments end to end. Compare the length of the two shorter line segments in each set with the length of the longest line segment. In the first set, the length of the two shorter line segments together is shorter than the length of the longest line segment. Do they make a triangle? No. How do the two shorter line segments of the second set compare with the longest segment? Together they are exactly the same length. Do they make a triangle? No. How do the two shorter line segments of the third set compare with the length of the longest line segment? Together they are longer than the longest line segment. Do they make a triangle? Yes. What can we say then about the length of the line segments that are used to make a triangle? If the two shorter line segments are placed end to end and together they are shorter than the longest line segment or are exactly the same length, they will not make a triangle. But if the two shorter line segments together are longer than the longest line segment, they will make a triangle. A triangle is a shape made when three line segments meet at three corners. Triangles are often named according to the length of their sides. Some triangles have sides that are all the same length. They are called equilateral triangles. Some triangles have two sides the same length. They are called isosles triangles. Other triangles have sides that are all different lengths. They are called scaline triangles. But three line segments do not always make a triangle. Three line segments will make a triangle only when the two shorter line segments placed end to end are longer than the longest line segment. How would you bend this pipe cleaner to be sure it will make a triangle? [Music]