1. Geometry with TI-Nspire™ Technology
Module C
Geometry with TI-Nspire™ Technology

2. Geometry with TI-Nspire™ Technology
Module C
Geometry with TI-Nspire™ Technology
Lesson 2: Thales’ theorems

3. In the previous lesson you learned about…
The basic terms of geometry.
Angles and angle terms.
Different polygons, rectangles and triangles.
The area, the perimeter and the circumference of the circle.
Coordinates and transformations.
A few important theorems.
The features of TI-NspireTM Technology to teach geometry.
3 | Lesson C.2

4. TI-NspireTM Technology
In this lesson you will:
Check Thales’ intercept and Thales’ triangle theorem.
Use the TI-NspireTM Geometry application to make geometrical constructions.
Explore the Geometry tools.
Thales of Miletus
4 | Lesson C.2

5. Thales’ Intercept Theorem
If A is the intersection of two lines AB and AC and
if BC and DE are parallel,
the ratio of BD to DA and
the ratio of CE to EA are equal:
5 | Lesson C.2

6. Location of point A
Is Thales’ Intercept Theorem still correct if point A has a different location?
6 | Lesson C.2

7. Investigation Steps Three points A, B, C Red lines AB and AC
Black line BC
Point D on line AB
Line parallel to BC
Intersection point E
Type formula
Measure lengths of segments
Calculate both sides of the equation
7 | Lesson C.2

8. Thales’ Triangle Theorem
If A, B and C are points on a circle
where AC is a diameter of the circle,
then the angle ABC is a right angle.
8 | Lesson C.2

9. Location of point B
Is Thales’ Triangle Theorem still correct if point B has a different location?
9 | Lesson C.2

10. Investigation Steps Line segment Midpoint of the line segment
Red circle
Triangle with points on circle
Measure angle
Grab and move point on circle
10 | Lesson C.2

11. In this 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.
In this lesson you learned that…
The values & concepts of TI-Nspire Technology you studied in module A really stimulate a better understanding of Math problems.
You easily can open a document by double click it in My Files.
TI-Nspire helps to solve a classic problem by using multiple representations.
One document can contain different problems, with different pages.
Different pages can be created by different applications.
There are two kinds of toolbars: the standard toolbar on top of the screen and a second toolbar that depends on the current application.
You can use different panels, who are located on the left side of the screen.
You can change view from normal mode to handheld mode.
11 | Lesson C.2

12. You have just finished lesson C.2!
Congratulations!
You have just finished lesson C.2!
Congratulations !
You have just finished lesson C.2
12 | Lesson C.2