Similarity And Congruence

Similar Shapes

Similar figures have the same shape, but different sizes. All circles and all equilateral triangles are similar.

Similar Shapes examples

Maths Fun - Shrink a Coke Bottle

Plastic bottles made with recyclable plastic have a "recyclable" symbol on the label. When placed in very hot water, they will shrink. Drink the Coke in a bottle. Take off the lid. Put the bottle in a sink in case you spill the hot water. One person holds the bottle with tongs. The other person carefully pours boiling water from the kettle into the bottle. It will shrink instantly!

Warning! Boiling water from a kettle is needed for this activity. Ask an adult for permission to do this in a sink. The adult can help you.


Question - Similar Triangles

Apollo 16 Astronaut

The astronaut is 2 metres tall and casts a shadow 1.6 metres long. If the walking stick shadow is 1 metre long, how high is it?

Answer
1.25 metres

Congruent Shapes

Congruent figures are shapes that are exactly the same shape and size.

These tessellations or tiling patterns (left image) from the Alhambra Palace in Spain are an example of Islamic art.

Beehive hexagons (right image) are another example of congruent shapes.

Congruent Shapes examples

Maths Fun - Escher

M.C. Escher, a Dutch graphic artist, created extraordinary tessellations inspired by the Alhambra Palace. Google Image "Escher tessellations" to figure out how he drew his designs.