Similarity and Congruence Proofs Flashcards

Grade 10 · Math · Flashcards

All criteria, properties, and proof strategies for triangle similarity and congruence.

Flashcards

Congruence vs. Similarity: Congruent: same shape AND size. Similar: same shape, proportional sizes.
SSS Congruence: Three sides of △1 = three sides of △2 → congruent.
SAS Congruence: Two sides and the included angle of △1 = corresponding parts of △2 → congruent.
ASA Congruence: Two angles and the included side → congruent.
AAS Congruence: Two angles and any corresponding side → congruent.
RHS Congruence: Right angle, hypotenuse, one side → congruent right triangles.
AA Similarity: Two equal angle pairs → triangles similar (third angle forced equal).
SAS Similarity: Two proportional sides with equal included angle → similar.
SSS Similarity: All three side pairs proportional → similar triangles.
CPCTC: After proving congruence, all corresponding parts (sides + angles) are equal.
Scale Factor k: Sides ratio = k, perimeter ratio = k, area ratio = k², volume ratio = k³.
Reflexive Property: Any segment or angle equals itself; used to identify shared parts in overlapping triangles.
Transitive Property: If A = B and B = C, then A = C; chains equalities across a proof.
Midsegment Theorem: A segment joining midpoints of two sides of a triangle is parallel to the third side and half its length.