Lesson 4 of 8
Congruence and Similarity
Two figures are congruent when they are exactly the same shape and the same size, just maybe turned or flipped. Two figures are similar when they are the same shape but different sizes, like a photo and a smaller copy of it.
FORMULA
Congruent = same shape and same size. Similar = same shape, sizes are proportional (matching angles equal, matching sides in the same ratio).
Triangle congruence shortcuts
- ●SSS (Side-Side-Side): all three pairs of sides equal.
- ●SAS (Side-Angle-Side): two sides and the angle between them equal.
- ●ASA (Angle-Side-Angle): two angles and the side between them equal.
Proportions in similar figures
In similar figures, matching sides keep the same ratio. Set up a proportion and cross-multiply to find a missing side.
Example: two similar triangles, the small one has a side of 4 matching a side of 8 on the big one (ratio 1 to 2). If another small side is 5, the matching big side is 10, because 4/8 = 5/10.