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Congruence and similarity: cheat sheet

Angles and shapes · The words and methods from the lessons, with an example of each.

congruence tests

Each set of equal parts fixes a triangle. In SAS the angle is between the two sides; SSA is not a test, because it can give two triangles.

SSS, SAS, ASA or AAS, RHS\text{SSS},\ \text{SAS},\ \text{ASA or AAS},\ \text{RHS}
Two different triangles with the same SSA parts
Two different triangles with the same SSA parts

diagonals of quadrilaterals

A parallelogram's diagonals cut each other in half; a kite's cross at 90°. Prove a property with two congruent triangles.

rectangle: equal, bisectrhombus: bisect at 90∘\text{rectangle: equal, bisect} \quad \text{rhombus: bisect at } 90^\circ
A rectangle with its two equal diagonals
A rectangle with its two equal diagonals

scale factor

Similar shapes: every length times k, every angle the same. Triangles are similar by AA, SSS (sides in one ratio) or SAS.

k=copy lengthmatching original lengthk = \dfrac{\text{copy length}}{\text{matching original length}}
A 3, 4, 5 triangle and a copy twice as big
A 3, 4, 5 triangle and a copy twice as big

parallelogram angles

Neighbouring angles are co-interior between parallel sides. All four add to 360°.

opposite angles equal; neighbours add to 180∘\text{opposite angles equal; neighbours add to } 180^\circ