Module C

Lesson 3: Exercises

Geometry with TI-Nspire™ Technology

Module C

Geometry with TI-Nspire™ Technology

In the previous lesson you learned …

• To check Thales’ Intercept Theorem and Thales’ Triangle Theorem.• How to use the Geometry application to check a theorem.• How to construct lines, circles, triangles, midpoints, …• How to change the line or fill color.• How to measure lengths, angles, …• How to calculate formulas in the Geometry application.• That the constructions can be used in a dynamic way.

3 | Lesson C.3

TI-Nspire™ Technology

In this lesson you will:

• Use the TI-Nspire™ software, installed on your computer to do some exercises.

• Check two theorems by using TI-Nspire™ Technology.

• Investigate the height of a pyramid.

• Practice the things you learned in the previous lessons.

4 | Lesson C.3

Exercise 1

Use TI-Nspire™ Technology to illustrate the next theorem by an example:

“The sum of the angles of a polygon with n sides, where n is 3 or more, is 180°× (n - 2).”

Example: A rectangle has 4 sides, this means n = 4The sum of the angles should be 180°× (4 - 2) = 360° .

5 | Lesson C.3

Exercise 2

Use TI-Nspire™ Technology to illustrate by an example that the next formulation of Thales’ Intercept Theorem is also correct:

If A is the intersection of two lines AB and AC andif BC and DE are parallel, the ratio of BA to DA,the ratio of CA to EA andthe ratio of BC to DE are equal:

= =BA CA BC

DA EA DE

6 | Lesson C.3

Exercise 3

Find a solution by using TI-Nspire™ Technology:

According to some historical sources the Greek mathematician Thales applied the intercept theorem to determine the height of the Cheops' pyramid. He used a stick and measured the length of its shadow.

Question: Can you find the height AB of the given pyramid by using the stick CD?

7 | Lesson C.3

Congratulations!

You have just finished lesson C.3!

8 | Lesson C.3