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Geometry with TI-Nspire ™ Technology

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.

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Geometry with TI-Nspire ™ Technology

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  1. Geometry withTI-Nspire™ Technology Module C

  2. Geometry withTI-Nspire™ Technology Module C 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. 11 | Lesson C.2

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

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