Geometry

We use a semi-circle between two lines to mean "angle".

Review

• what is the (common) unit of angle? It’s symbol?
• How many degrees in a full turn/one rotation?
• How many degrees to "face the opposite way"/go the other direction on a line?

Angles at a Point

Add up to 360°.

Angles on a Line

Add up to 180°. (Note: this assumes you’re staying on the same side of the line!)

Angles that add up to 180° are called supplementary.

Right Angles

Are 90°. Use a "square" instead of a semicircle between two lines to indicate this.

Angles that add up to 90° are called complimentary.

Quiz from last week

What’s a (closed) polygon? – connected straight edges that has the end of last line connecting to the start of the first. Encloses/contains a distinct area.

What is a regular polygon? – equal line segment length & angles.

What is the perimeter? The length of all the line segments added together.

Mathematicians are Lazy! (Symbols)

Σ = "sum" = add up all these numbers!

Aside: a + b + c + … = z – ‘a’, ‘b’, ‘c’ etc are called addends. ‘z’ is the sum.

Exterior Angles of a Polygon Add to 360°

Think about starting pointing in a direction, and walking around a polygon

• turn to face the direction of the first line of the polygon
• at the end of the line, turn, ready to do the next line
• repeat the above for the rest of the lines of your polygon

Now imagine doing the same thing, but this time, all the sides have no length.

You’d be turning around a point, ending up facing the same direction as you started!

So the exterior angles of a polygon always add up to 360°!

(Works for regular, irregular, convex, and concave polygons)

Exploration

• make interesting geometric patterns with Rad lines
• looked at the giant picture Paul’s drawing robot made
• Programming geometric shapes with Turtle Blocks

And the know obligatory prefix song.