Angles, Lines and Polygons

Objectives:
To know that the angles of a triangle add up to 180°
Angle properties of parallel lines
To know that the sum of the interior and exterior angles of quadrilateral add up to 360°
Tangents and triangles in a semi-circle

The angles of a triangle add up to 180°

Angle properties of parallel lines

 

Interior Angles of Polygons

An Interior Angle is an angle inside a shape.

Triangles

The Interior Angles of a Triangle add up to 180°

90° + 60° + 30° = 180°	80° + 70° + 30° = 180°
It works for this triangle!	Let's tilt a line by 10° ... It still works, because one angle went up by 10°, but the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

90° + 90° + 90° + 90° = 360°	80° + 100° + 90° + 90° = 360°
A Square adds up to 360°	Let's tilt a line by 10° ... still adds up to 360°!
The Interior Angles of a Quadrilateral add up to 360°

Because there are Two Triangles in a Square

The interior angles in this triangle add up to 180° (90°+45°+45°=180°)

... and for this square they add up to 360° ... because the square can be made from two triangles!

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Exterior angles of a polygon add up to 360

 

Names of polygons

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The angle between the tangent and radius is 90°

A tangent to a circle is a line which just touches the circle.

Remember:
A tangent is always at right angles to the radius where it touches the circle.

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The triangle drawn on the diameter of a circle is always a right angles triangle

We could also rotate the shape around 180° to make a rectangle! It is a rectangle, because all sides are parallel, and both diagonals are equal. And so its internal angles are all right angles (90°).