Three matching parts prove two triangles congruent, but only in the right pattern: three sides, two sides with the angle between them, two angles with a side, or a hypotenuse and a leg of right triangles. Two sides and an angle not between them (SSA) proves nothing, and neither do three angles. In a congruence statement the letters line up: the first vertex matches the first.
Which postulate proves the triangles congruent, if any?
Two sides are ticked in each triangle, and the marked angle sits between them.
Side, included angle, side.
The answer is SAS.
Where students go wrong
Reading SSA as SAS. If the marked angle is not between the two marked sides, the pattern proves nothing.
Also called triangle congruence postulates, SSS SAS ASA AAS, hypotenuse leg, CPCTC or congruence statements.
What you can put on this worksheet
SSS, SAS, ASA, AAS, HL, or not enough
Which postulate proves the triangles congruent, if any?→ ASA
Corresponding parts from a congruence statement
△JKL≅△MNO. What corresponds to ∠L?→ ∠O
Questions about these worksheets
Yes. Every congruent triangles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the congruent triangles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: sss, sas, asa, aas, hl, or not enough and corresponding parts from a congruence statement. Tick as many as you want and set how many of each, or let it spread them evenly.
Reading SSA as SAS. If the marked angle is not between the two marked sides, the pattern proves nothing.