Congruence of Triangles — O/L Mathematics

What must I remember about Congruence of Triangles?

• Two geometric figures are congruent if they possess identical shape and equal size, coinciding exactly when superimposed.
• Case 1: Side-Angle-Side (SAS) — Two sides and the included angle of one triangle are respectively equal to two sides and the included angle of the other.
• Case 2: Angle-Side-Angle (ASA) or Angle-Angle-Side (AAS) — Two angles and any corresponding side are respectively equal.
• Case 3: Side-Side-Side (SSS) — All three corresponding sides of the two triangles are equal in length.
• Case 4: Right angle-Hypotenuse-Side (RHS) — In two right-angled triangles, the hypotenuse and one corresponding side are equal.

Test yourself (1 minute)

1. The non-included angle trap in SAS

   The angle MUST be between the two equal sides; SSA (Side-Side-Angle) is NOT a valid congruence criterion.

2. State reasons for every statement

   In formal geometric proofs (Paper 2 Part B), every stated equality must cite a valid geometric reason (e.g., 'common side', 'vertically opposite angles', 'radii of same circle').

3. Deductions from congruence

   Once triangles are proven congruent, state corresponding elements clearly (e.g., 'AB = XY (corresponding sides of congruent triangles)').

Practise Congruence of Triangles questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 5)

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Grade 10 · Term 1