Geometry with TI-Nspire

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

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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
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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
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Location of point A

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

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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

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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.
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Location of point B

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

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Investigation
Steps

• Line segment
• Midpoint of the line segment
• Red circle
• Triangle with points on circle
• Measure angle
• Grab and move point on circle

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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.

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