GeometryCongruence rules
Name: Date:
Which rule shows each pair of triangles is congruent?
1 SSSSASASAAASHL
2 SSSSASASAAASHL
3 SSSSASASAAASHL
4 SSSSASASAAASHL
5 SSSSASASAAASHL
6 SSSSASASAAASHL
7 SSSSASASAAASHL
8 SSSSASASAAASHL
Triangle congruence rules worksheets
Two triangles are congruent when their matching parts are equal, and the rules say how few of those you need to be sure. These free printable worksheets mark a pair of triangles and ask which rule — SSS, SAS, ASA, AAS or HL — the marks prove it by.
Kid stuck on one? You don’t just get the sheet.
Triangle congruence rules
The answer key prints on a separate page.
What's on this sheet
The marks are the whole question. A tick across a side says that side equals its match on the other triangle; an arc at a corner says the angle does; a little square says a right angle. No lengths or degrees are printed, because the moment a side carries a number the task turns into measure-and-compare instead of reading the rule.
Why this sheet works
The one thing that goes wrong is the included part. SAS needs the angle BETWEEN its two marked sides, and ASA needs the side BETWEEN its two marked angles — move that same side one corner along and it becomes AAS, which still works but for a different reason. Telling ASA from AAS is the point of the page, so it is worth saying out loud whether the marked side sits between the two angles or off to the side.
How this one works
One question from this sheet, worked through a step at a time.
Which congruence rule?
marks:three pairs of equal sides, and no angles
SSS=side, side, side
SSS
- Read the marks first — they are the givens. Here there are three pairs of equal sides, and no angles.
- Three pairs of equal sides pin a triangle down completely — there is only one triangle with those three lengths.
- So the rule is SSS.