Introduction to Geometry

GreenMaths, pchou, Nov 30, 2015

Simple applets useful for introducing Geometry to first year students.

Table of Contents

  1. Planes and Lines
    1. Planes, lines etc
    2. Planes, lines etc completed
  2. Angles
    1. Angles as rotations
    2. Straight angles and full circle angles.
    3. Angle Size and Arm Length
    4. Measuring with a protractor
    5. Vertically Opposite Angles 2
    6. To Show That Vertically Opposite Angles Are Equal
  3. Parallel Lines
    1. Showing Alternate Angles
    2. Showing Corresponding Angles
    3. Showing the Sum of Interior Angles
    4. Parallel Lines and Alternate and Corresponding Angles
    5. Non-Parallel Lines and Alternate and Corresponding Angles
    6. More Exercises with Parallel Lines
  4. Triangles
    1. The sum of the angles in a triangle?
    2. Sum of the angles in a triangle
    3. Triangle Exterior Angle Sum Theorem
    4. Isosceles Triangles
  5. Constructions
    1. Construction - Divide a line segment into equal parts

1.

Planes and Lines

  • 1. Planes, lines etc
  • 2. Planes, lines etc completed

1.1.

Planes, lines etc

Follow the instructions on your worksheet and use the tools to complete this diagram.[br]You can use the text tool to add the names to your diagram.[br]The worksheet based on the project Maths activity is [url=https://drive.google.com/file/d/0B7OAETs6H0CncUV2TElEQ3JYZnc/edit?usp=sharing]here[/url]
– GreenMaths

1.2.

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2.

Angles

  • 1. Angles as rotations
  • 2. Straight angles and full circle angles.
  • 3. Angle Size and Arm Length
  • 4. Measuring with a protractor
  • 5. Vertically Opposite Angles 2
  • 6. To Show That Vertically Opposite Angles Are Equal

2.1.

Angles as rotations

Angles are rotations.
Angles as rotations
– GreenMaths

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Parallel Lines

  • 1. Showing Alternate Angles
  • 2. Showing Corresponding Angles
  • 3. Showing the Sum of Interior Angles
  • 4. Parallel Lines and Alternate and Corresponding Angles
  • 5. Non-Parallel Lines and Alternate and Corresponding Angles
  • 6. More Exercises with Parallel Lines

3.1.

Showing Alternate Angles

Move the slider to see if the angles are the same. [br]Change the parallel lines by moving theblue points and check the angles again.
Showing Alternate Angles
– GreenMaths

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Triangles

  • 1. The sum of the angles in a triangle?
  • 2. Sum of the angles in a triangle
  • 3. Triangle Exterior Angle Sum Theorem
  • 4. Isosceles Triangles

4.1.

The sum of the angles in a triangle?

Move the slider GreenAngle to change the sizes of the angles. [br]For different shapes of triangles what do you notice about the three angles?[br]There are more things to try below.
The sum of the angles in a triangle?
– GreenMaths

4.2.

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4.3.

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4.4.

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5.

Constructions

  • 1. Construction - Divide a line segment into equal parts

5.1.

Construction - Divide a line segment into equal parts

This applet shows how to divide a line segment into 3, 4 or 5 equal parts. Use a set square to draw the parallel lines.[br]Move the point C to change the angle and the slider to change the radius of the arc.[br]More constructions are shown [url=https://sites.google.com/a/loretothegreen.ie/maths/geometry/constructions]here[/url].
Construction - Divide a line segment into equal parts
– GreenMaths

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