8th grade Instructional Unit
Unit 2 – Exponents & Square Roots Review
Unit 3 – Pythagorean Theorem Instructional Unit
by
Nancy Perzel
Day 3 - Length of Line Segments
Warm-Up:
Think back to the largest right triangle we created on the geoboard yesterdayÉ What are the lengths of the legs, or sides of the right triangle? What is the length of the hypotenuse, or the diagonal side?
The answer is not 5!!! This is a common misconception, but the length of this line segment is not 5 units even though it passes through 5 pegsÉ Is the hypotenuse the same, or longer, or shorter than the legs? (A: The hypotenuse is always the longest side!) You can measure the length of the hypotenuse using a ruler or by using the ÔCalculateŐ function on GSP; it should measure approximately 7.1 units. 5x5 Right Triangle GSP file
Activity 1:
Ask students to make this example using rubber bands on their geoboards, or by using GSP as shown below. Both of these segments pass through 2 pegs, but are they the same length? Do they look the same?
Example 1:
Are the two line segments the same length? Why or why not? Discuss. What can you do if you have a diagonal line segment that you donŐt know the length of?
If you are using Geoboards, students can take out rulers and actually measure the length. On GSP students can measure the length of each line segment.
Without using a ruler or the GSP measurement feature, how could you determine the length of the line segment? LetŐs remember back to the first lessonÉ The length of a side of a square is the square root of its area!
LetŐs use this line segment to create a square, then find itŐs area and then perform the square root function to find the length of the segment!
We have constructed a square, all sides of equal measure.
Now, construct the quadrilateral interior, measure the area and use the calculate feature to take the square root of the area. Did our theory work? Discuss why the length of the line segment CF not a whole number.
LetŐs try it again using a line segment of another length. The students can pick one – or you can assign them specific segments (using the idea of slope – give them a starting point and directions to the second point by going left/right and up/down a certain number of units. There are two additional examples on the GSP file: Measure Line Segment (pages 2, 3) and images – Examples 2,3.
Example 2:
Example 3:
Discuss why the length of segment AB is a whole number.
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