Other tags that relate to Triangles and Petals
Visualising. Area - circles, sectors and segments. Circumference and arc length. Regular polygons and circles. Angle properties of polygons. GeoGebra. Locus/loci. 2D shapes and their properties. Angles - points, lines and parallel lines. Pythagoras' theorem.There are 31 results
Broad Topics > Angles, Polygons, and Geometrical Proof > Angle properties of polygons
Triangles and Petals
Age 14 to 16
Challenge Level
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Gibraltar Geometry
Age 11 to 14
Challenge Level
Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?
Pegboard Quads
Age 14 to 16
Challenge Level
Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?
Arclets Explained
Age 11 to 16
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
Angles Inside
Age 11 to 14
Challenge Level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
Angles in Three Squares
Age 14 to 16
Challenge Level
Drawing the right diagram can help you to prove a result about the angles in a line of squares.
Star Polygons
Age 11 to 14
Challenge Level
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
Polygon Pictures
Age 11 to 14
Challenge Level
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Tricircle
Age 14 to 16
Challenge Level
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
Bow Tie
Age 11 to 14
Challenge Level
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
A Sameness Surely
Age 14 to 16
Challenge Level
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
Floored
Age 14 to 16
Challenge Level
A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
Dodecawhat
Age 14 to 16
Challenge Level
Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
Logo Challenge 3 - Star Square
Age 7 to 16
Challenge Level
Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
No Right Angle Here
Age 14 to 16
Challenge Level
Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.
At a Glance
Age 14 to 16
Challenge Level
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
LOGO Challenge 4 - Squares to Procedures
Age 11 to 16
Challenge Level
This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.
Cyclic Quadrilaterals
Age 11 to 16
Challenge Level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Convex Polygons
Age 11 to 14
Challenge Level
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Getting an Angle
Age 11 to 14
Challenge Level
How can you make an angle of 60 degrees by folding a sheet of paper twice?
Terminology
Age 14 to 16
Challenge Level
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Pent
Age 14 to 18
Challenge Level
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Pentakite
Age 14 to 18
Challenge Level
ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.
First Forward Into Logo 9: Stars
Age 11 to 18
Challenge Level
Turn through bigger angles and draw stars with Logo.
First Forward Into Logo 7: Angles of Polygons
Age 11 to 18
Challenge Level
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
NRICH is part of the family of activities in the Millennium Mathematics Project.