Angles in polygons

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

Explore the geometry of these dart and kite shapes!

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Are these statements always true, sometimes true or never true?

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Drawing the right diagram can help you to prove a result about the angles in a line of squares.