Lesson 6Finding Side Lengths of Triangles
Learning Goal
Let’s find triangle side lengths.
Learning Targets
I can explain what the Pythagorean Theorem says.
Lesson Terms
- hypotenuse
- legs
- Pythagorean Theorem
Warm Up: Which One Doesn’t Belong: Triangles
Problem 1
Which triangle doesn’t belong?
Activity 1: A Table of Triangles
Problem 1
Complete the tables for these three triangles:
triangle
D
E
F
triangle
D
E
F
What do you notice about the values in the table for Triangle E but not for Triangles D and F?
Complete the tables for these three more triangles:
triangle
P
Q
R
triangle
P
Q
R
What do you notice about the values in the table for Triangle Q but not for Triangles P and R?
What do Triangle E and Triangle Q have in common?
Activity 2: Meet the Pythagorean Theorem
Problem 1
Find the missing side lengths. Be prepared to explain your reasoning.
Find the missing side lengths. Be prepared to explain your reasoning.
Are you ready for more?
Problem 1
If the four shaded triangles in the figure are congruent right triangles, does the inner quadrilateral have to be a square? Explain how you know.
Lesson Summary
A right triangle is a triangle with a right angle. In a right triangle, the side opposite the right angle is called the hypotenuse, and the two other sides are called its legs. Here are some right triangles with the hypotenuse and legs labeled:
We often use the letters
Here are some right triangles:
Notice that for these examples of right triangles, the square of the hypotenuse is equal to the sum of the squares of the legs. In the first right triangle in the diagram,
It is important to note that this relationship does not hold for all triangles. Here are some triangles that are not right triangles, and notice that the lengths of their sides do not have the special relationship