Triangle Congruence Worksheet – Geometry Practice

Students determine whether two triangles are congruent from given markings and name the correct congruence theorem (SSS, SAS, ASA, HL, or SAA).

Students recognise when a triangle pair cannot be proven congruent from the given information.

Students write a two-column proof, supplying statements and reasons, to prove a given triangle pair congruent.

Students find the slope, intercepts, and equation of a line, including a line perpendicular to a given one.

Review all five congruence shortcuts (SSS, SAS, ASA, HL, SAA) before assigning the 20-item set, since several pairs are deliberately built to test whether students overuse SSA or AAA, which do not prove congruence.

Use the ‘cannot be proven’ items as a class discussion point, asking students to explain specifically which piece of information is missing rather than just marking the pair as unprovable.

Save the two open two-column proofs for after the multiple-choice-style items, since they require students to apply the same reasoning without answer options to check against.

Triangle congruence reasoning — students apply SSS, SAS, ASA, HL, and SAA to twenty triangle pairs, including cases with no valid proof.

Two-column proof writing — students supply their own statements and reasons to prove two given triangles congruent.

Coordinate geometry — students find slopes, intercepts, and the equation of a line perpendicular to a given line.