Geometry with TI-Nspire™ Technology

Module C

Geometry with TI-Nspire™ Technology

Module C

Lesson 2: Thales’ theorems

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

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

Thales’ Intercept Theorem

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

=BD CE

DA EA

5 | Lesson C.2

Location of point A

• Is Thales’ Intercept Theorem still correct if point A has a different location?

6 | Lesson C.2

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

=BD CE

DA EA

7 | Lesson C.2

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

Location of point B

• Is Thales’ Triangle Theorem still correct if point B has a different location?

9 | Lesson C.2

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

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.

11 | Lesson C.2

Congratulations!

You have just finished lesson C.2!

12 | Lesson C.2