1. Chapter 1: Square Roots and the Pythagorean Theorem
1.3 Measuring Line Segments

2. Investigate (p. 17)
Work with a partner. You will need 1-cm grid paper. Copy the squares you see on page 17. Without using a ruler, find the area and side length of each square.
Remember that you can estimate the area of a “tilted” square (C and D) by counting grid squares inside the shape.

3. How did you find the area and side length of each square?
What is the area and side length of squares A and B?
Square A: Area = 9 cm2, side length = 3 cm
Square B: Area = 16 cm2 side length = 4 cm
How did you write the side lengths of squares C and D?

4. How did you write the side lengths of square C?
I needed a number that when multiplied by itself has the product 8. √8 x √8 = 8, so the side length is √8 cm.
Square D?
√10 cm
What patterns did you find in your measurements?
The area of each square is the square of its side length. The side length of each square is the square root of its area.

5. Connect (p. 17)
We can use the properties of a square to find its area of side length.
Area of a square = length x length or length2
When the side length is L, the area is L2
When the area is A, the side length is √A
We can calculate the length of any line segment on a grid by thinking of it as a side length of a square.

6. Therefore, side length = 8cm Side length2 = A So 82 = area
√A = side length
So, √64 = side length
Therefore, side length = 8cm
Side length2 = A
So 82 = area
Therefore, area = 64 cm2
8 cm
64 cm2
8 cm

7. Key Math Learnings
The area of a square is the square of its side length. The side length of a square is the square root of its area.
The length of a line segment on a grid can be found by thinking of it as a side of a square.

8. Example 1 (p. 18) Find the length of line segment PQ.
You will need a ruler and a protractor to construct a square on line segment PQ. Then, the length of the segment is the square root of the area.

9. Discuss the Ideas (p. 19)
1. Is the area of every square a square number?
No; the area of every square is not a square number. For example, the area of square may be 20, which is not a square number.
When will the length of a line segment not be a whole number?
When the area of the square is not a square number.

10. Extra Practice 3 Complete #1 – 4
Note: For #3, do not copy onto grid paper.
Due Friday, Sept 24
Don’t forget: Quiz on Friday on Square Roots and Square Numbers.