Properties of Geometrical Figures - Yr 9

Ryan Smith, Apr 13, 2020

Table of Contents

  1. Lesson 1 - Angles Review
    1. Simple Angles Review
    2. Angles at a Point Review
    3. Triangle Review
  2. Lesson 2 - Parallel Lines Review
    1. Corresponding Angles
    2. Alternate Angles
    3. Co-interior Angles
    4. Overall summary
    5. Angle between two parallel lines
  3. Lesson 3 - Polygon Review
    1. Quadrilateral Review
  4. Lesson 4 - Interior angle sum of polygons
    1. Quick Overview of Polygons
    2. Interior Angles of Polygons
  5. Lesson 5 - Exterior angle sum of polygons
    1. Exterior Angles Relationships of Polygons
  6. Lesson 6 - Congruent Shapes
    1. Congruent Shapes
  7. Lesson ? - Similar Figures
    1. Similar Shapes

1.

Lesson 1 - Angles Review

  • 1. Simple Angles Review
  • 2. Angles at a Point Review
  • 3. Triangle Review

1.1.

Simple Angles Review

Acute and Obtuse Angles
Use the animation below to explore and review the differences between acute and obtuse angles. Use the checkboxes to make the examples visible or invisible. Use the sliders to adjust and change the angles.
Reflex Angles
Use the animation below to explore reflex angles.
Right and Straight angles
Straight angles are the angles formed by three points on a straight line. The angle is equal to 180[math]^\circ[/math]. Right angles have a value of 90[math]^\circ[/math] and they resemble a corner.
Revolution Angles
A revolution is a 360[math]^\circ[/math] angle - one complete revolution or full circle.
Summary of Angles
– Ryan Smith

1.2.

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1.3.

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2.

Lesson 2 - Parallel Lines Review

  • 1. Corresponding Angles
  • 2. Alternate Angles
  • 3. Co-interior Angles
  • 4. Overall summary
  • 5. Angle between two parallel lines

2.1.

Corresponding Angles

When two parallel lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. When the two lines being crossed are parallel, the corresponding angles formed by the transversal are equal. Use the animations below to explore, visualize and verify corresponding angles.
Summary
[size=150]If the two lines are not parallel, then the corresponding angles formed by the transversal are not equal. When the two lines are parallel (the 'arrow' markings tell you this), the transversal forms corresponding angles that are equal.[/size]
– Tim Brzezinski, Ryan Smith

2.2.

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2.3.

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2.4.

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2.5.

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3.

Lesson 3 - Polygon Review

  • 1. Quadrilateral Review

3.1.

Quadrilateral Review

Quadrilaterals - More Detail
[size=150]There are two main ways to determine if a polygon is convex or non-convex. Either by observing the interior angles or the diagonals. [/size]
Convex vs Non-convex Quadrilaterals
Sum of interior angles of a quadrilateral
– Ryan Smith

4.

Lesson 4 - Interior angle sum of polygons

  • 1. Quick Overview of Polygons
  • 2. Interior Angles of Polygons

4.1.

Quick Overview of Polygons

General overview of the names of polygons and the number of sides
– Ryan Smith

4.2.

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5.

Lesson 5 - Exterior angle sum of polygons

  • 1. Exterior Angles Relationships of Polygons

5.1.

Exterior Angles Relationships of Polygons

– Tim Brzezinski, Ryan Smith

6.

Lesson 6 - Congruent Shapes

  • 1. Congruent Shapes

6.1.

Congruent Shapes

Congruence Defined
Two figures are congruent if they are identical in shape and size.[br][br]For congruent figures:[br][list][*]matching sides are equal[br][/*][*]matching angles are equal[br][/*][/list]
Conditions for Congruence
Tests for congruence for triangles
SAS Test Visualized
SSS Test Visualized
SSS Test Visualized
AAS Test Visualized
Right Angle, Hypotenuse, Side test Visualized
– Tim Brzezinski, Ryan Smith

7.

Lesson ? - Similar Figures

  • 1. Similar Shapes

7.1.

Similar Shapes

– Allison, Tim Brzezinski, Ben Graber, Ryan Smith

Information