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Resources tagged with Angle properties of shapes similar to Road Maker 2:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > 2D Geometry, Shape and Space > Angle properties of shapes

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Road Maker 2

Stage: 5 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out where the blue-and-red brick roads end?

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No Right Angle Here

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Cyclic Quads

Stage: 4 Challenge Level: Challenge Level:1

Points D, E and F are on the the sides of triangle ABC. Circumcircles are drawn to the triangles ADE, BEF and CFD respectively. What do you notice about these three circumcircles?

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Pent

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Arclets Explained

Stage: 3 and 4

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.

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Pegboard Quads

Stage: 4 Challenge Level: Challenge Level:1

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?

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Pentakite

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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At a Glance

Stage: 4 Challenge Level: Challenge Level:1

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

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Triangles and Petals

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

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A Sameness Surely

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Dodecawhat

Stage: 4 Challenge Level: Challenge Level:1

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.

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Bisecting Angles in a Triangle

Stage: 3 and 4 Challenge Level: Challenge Level:1

Measure the two angles. What do you notice?

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LOGO Challenge 4 - Squares to Procedures

Stage: 3 and 4 Challenge Level: Challenge Level:1

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

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Which Solids Can We Make?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Logo Challenge 3 - Star Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

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Tricircle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Golden Triangle

Stage: 5 Challenge Level: Challenge Level:1

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.

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First Forward Into Logo 7: Angles of Polygons

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

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First Forward Into Logo 9: Stars

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

Turn through bigger angles and draw stars with Logo.