---
title: "Congruence and similarity: cheat sheet"
subtitle: "Angles and shapes"
---

# Congruence and similarity

> The words and methods from this unit, with an example of each.

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**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.

$$\text{SSS},\ \text{SAS},\ \text{ASA or AAS},\ \text{RHS}$$

_Two different triangles with the same SSA parts_

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

$$k = \dfrac{\text{copy length}}{\text{matching original length}}$$

_A 3, 4, 5 triangle and a copy twice as big_

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**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.

$$\text{rectangle: equal, bisect} \quad \text{rhombus: bisect at } 90^\circ$$

_A rectangle with its two equal diagonals_

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

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

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