CongruencE and Tessellations Slideshow 37, Mathematics Mr Richard Sasaki, Room 307

Objectives Understand the meaning of congruencE and identify congruent shapes Learn some congruent shapes that will tessellate

CongruencE What is congruencE? CongruencE occurs when two (or more) shapes are congruent. Two shapes are congruent when _________________________. They are the same size and shape (Their angles and lengths must be the same.)

CongruencE properties Must congruent shapes be identical? Yes. But… Location and rotation can be different. Flipping is also acceptable.

Example Lastly say something like “∴ They are congruent.” ∠ABC = ∠EDF Show That the two shapes below are congruent. AC = AB= BC= ∠ABC = ∠BAC = ∠BCA = ∠EDF ∠DFE ∠DEF FE DF DE A D 70o 4cm 3cm F 70o 4cm B C E 3cm If we show that each length and angle has a corresponding equal, we can show that these are congruent.

A and 1, B and 4, C and 12, D and 3, E and 11, F and 8, G and 7, H and 5, I and 6, J and 9, K and 10, L and 2 2 1 1 3 2 3

CongruencE - Notation If a triangle with edges abc is congruent to a triangle with edges DEF, we can say… ∆𝐴𝐵𝐶≡∆𝐷𝐸𝐹 We use the “Identical to” symbol and triangle symbols to show this.

TESSELLATIONS Try to make some tessellations! A Shape can tessellate with its congruent self by repeating in all directions with no gaps. An example of a tessellation: Here an equilateral triangle was used. We can see that there would never be any gaps.

Answers All of the shapes should tessellate except for the regular pentagon and regular octagon. Well done if you managed this with the irregular pentagons!

Congruence When we test whether two shapes are congruent, we don’t need to check all three angles and all three sides. All we need is the information required to draw a unique triangle. Have a think about with what information you could construct a unique triangle.

Yes Yes Yes No Yes No No Yes Yes No Yes No Yes No!!