Congruency Congruent Triangles — Formula Sheet

Two figures are congruent if they coincide exactly when one is placed over the other.

Two lines are congruent only when they are equal in length.

Symbol for congruency: = or ≡

ΔABC ≡ ΔDEF

S.S.S. Congruency Condition: AB = PQ, BC = QR and AC = PR ⇒ ΔABC ≅ ΔPQR [AB,BC,AC = corresponding sides of two triangles]

S.A.S. Congruency Condition: AB = XZ, BC = XY and ∠ABC = ∠ZXY ⇒ ΔABC ≅ ΔZXY [AB,BC = two sides; ∠ABC = included angle]

A.S.A. Congruency Condition: BC = QR, ∠B = ∠Q and ∠C = ∠R ⇒ ΔABC ≅ ΔPQR [BC = included side; ∠B,∠C = two angles]

A.A.S. Congruency Condition: ∠B = ∠Q, ∠C = ∠R ⇒ ∠A = ∠P and AC = PR ⇒ ΔABC ≅ ΔPQR [∠B,∠C = two angles; AC = corresponding non-included side]

R.H.S. Congruency Condition: ∠B = ∠E = 90°, AB = FE and hypotenuse AC = hypotenuse FD ⇒ ΔABC ≅ ΔFED [∠B,∠E = right angles; AB,FE = one side; AC,FD = h

Example 3: AB = CD, ∠BAO = ∠CDO, ∠ABO = ∠DCO ⇒ ΔAOB ≅ ΔDOC

Example 3: AO = DO and BO = CO

Example 4: AB = AC, AO = AO, ∠BOA = ∠COA = 90° ⇒ ΔAOB ≅ ΔAOC

Example 4: ∠B = ∠C and BO = CO