Geometry Worksheet - Triangle Congruence Extra Practice (SSS, SAS ... - Free Printable

Final Answer:
The correct congruence criteria for the given triangles are:
10) AAS
11) Not enough information
12) ASA
13) AAS
14) ASA
15) HL (or RHS, if using right-triangle notation — but since the diagram shows right angles and hypotenuse-leg markings, HL is appropriate)

Note: In many high school curricula, HL (Hypotenuse-Leg) is accepted for right triangles; if only SSS, SAS, ASA, AAS are listed as options, and the triangle is right-angled with hypotenuse and one leg marked congruent, it's still considered a special case of AAS or can be justified via HL. However, based on standard worksheet expectations and markings (right angle + hypotenuse + leg), HL is the precise answer for #15. If the worksheet restricts to only the four named criteria (SSS, SAS, ASA, AAS), then #15 may be marked AAS (since two angles — right angle and one acute — plus non-included side can imply AAS). But given the tick marks show hypotenuse and leg, and a right angle, the intended answer is most likely HL.

Since the problem asks to fill in the “Reason” blanks and the worksheet explicitly lists only SSS, SAS, ASA, AAS in the header (and HL is not mentioned), and in many textbooks HL is treated separately, but here the student is expected to use only those four — let’s re-evaluate #15:

Triangle EFG and HIJ: both have right angles (∠F and ∠I), EF ≅ HI (leg), EG ≅ HJ (hypotenuse). That’s HL, but if HL isn’t allowed, we can note that the right angle gives one angle, and the hypotenuse-leg does *not* directly give AAS unless we know another angle. So strictly speaking, with only leg + hypotenuse + right angle, it’s HL, and if the worksheet expects only the four, it’s an oversight — but common practice in such worksheets is to accept HL or sometimes label it as AAS incorrectly.

However, looking at the red “X” in #11 labeled “Not enough information”, and the consistent use of only SSS/SAS/ASA/AAS elsewhere, and the fact that #15 has two sides and a non-included angle (right angle is between leg and hypotenuse? No — in right triangle, right angle is between the two legs; hypotenuse is opposite. So given leg, hypotenuse, and right angle → that’s HL, not SAS (because SAS needs the angle *between* the two sides; here the right angle is *not* between leg and hypotenuse).

Thus, safest correct answers per standard geometry:
10) AAS
11) Not enough information
12) ASA
13) AAS
14) ASA
15) HL

But since the header says “Do your students need more practice with SSS, SAS, ASA, AAS?” and HL is not listed, and many curricula teach HL as part of congruence rules, I will give the technically correct answers including HL for #15.

Final Answer:
10) AAS
11) Not enough information
12) ASA
13) AAS
14) ASA
15) HL