### June 2010

Using your imagination, show or describe 10 ways to connect dots A and B. 1)    What information is needed for you to calculate the area of the square?

2)    How can the two triangle measurements help you figure out the area of the square?

3)    Figure ADE is a right triangle. Where is the right angle? Where is the hypotenuse?

4)    How can you use the Pythagorean Theorem to figure out the length of line segment AD?

5)    What is the length of line segment AD? What is the length of line segment AB?

6)    What is the area of the square?

Figure ABCD is a square. Figure ADE is a right triangle. What is the area of the square? 1) What information is needed to calculate the perimeter of the triangle? What information do you already have?

2) How can you figure out the length of line segment AD? You are given the area of square ABCD; how can that help you discover the length of AD?

3) How is the area of a square or rectangle usually calculated? How can you calculate this area, if you don’t know the length of any of the sides?

4) But the area has already been calculated. Can you think backwards to figure out what the length of the sides must be?  Are the sides all the same length? How do you know for sure? What number times itself equals 4? What is the square root of 4 square meters? What is the length of AD?

5) How can you figure out the length of line segment AE? You know the length of AD and DE, which are two sides of the triangle. What kind of triangle is it? Which side of the right triangle is the hypotenuse? If this is a right triangle, can you use the Pythagorean Theorem to calculate the length of the hypotenuse? What is the Pythagorean Theorem: Is it a + b = c? Is it a² + b² = c²? Does the Pythagorean Theorem tell you the length of the hypotenuse, or the length of the hypotenuse squared?

6) Extra hint for students who already know about 3-4-5 right triangles: double the measurements of AD and DE; what do you notice?