Angles - points, lines and parallel lines

problem
Octa-flower

Age

16 to 18

Challenge level

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
problem
Isosceles meld

Age

11 to 14

Challenge level

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
problem
Flower

Age

16 to 18

Challenge level

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
problem
Lunar angles

Age

16 to 18

Challenge level

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?
problem
LOGO challenge 7 - more stars and squares

Age

11 to 16

Challenge level

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
problem
LOGO challenge 8 - rhombi

Age

7 to 16

Challenge level

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
problem
LOGO challenge 1 - star square

Age

7 to 16

Challenge level

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.
problem
Take the right angle

Age

7 to 11

Challenge level

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.
problem
Watch the clock

Age

7 to 11

Challenge level

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
problem
Parallel universe

Age

14 to 16

Challenge level

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.