O Level MathematicsC4.3 Congruence (use SSS, SAS, ASA, RHS conditions).

🔢 Mirror-Image Triangles? Master Congruence Instantly! 🔍

Edudent Academy
4 Jan 26

Congruence tells us when two shapes are *exactly* the same size and shape. For O-Level exams, recognising congruent triangles quickly can unlock marks in geometry proofs and construction questions. **Think of congruent triangles as perfect photocopies**—they match corner-to-corner!

The Four Must-Know Congruence Tests

**SSS, SAS, ASA, and RHS** give us shortcuts to prove triangles identical without measuring every part. When any one of these sets of conditions is met, the two triangles are guaranteed to be congruent:

  • SSS (Side-Side-Side): All three corresponding sides are equal.
  • SAS (Side-Angle-Side): Two sides and the included angle are equal.
  • ASA (Angle-Side-Angle): Two angles and the included side are equal.
  • RHS (Right-angle-Hypotenuse-Side): For right-angled triangles—hypotenuse and one other side are equal.

Worked Example: SSS in Action

Problem: In
△ABC\triangle ABC
and
△DEF\triangle DEF
,
AB=DE=5 cmAB = DE = 5\text{ cm}
,
BC=EF=8 cmBC = EF = 8\text{ cm}
, and
AC=DF=7 cmAC = DF = 7\text{ cm}
. Prove the two triangles are congruent and state the corresponding vertices.

  • Step 1: Identify the three given side equalities:
    AB=DEAB = DE
    ,
    BC=EFBC = EF
    ,
    AC=DFAC = DF
    .
  • Step 2: Since all three pairs of corresponding sides are equal, apply the **SSS** congruence test.
  • Step 3: Conclude
    △ABC≅△DEF\triangle ABC \cong \triangle DEF
    . Therefore, the correspondence of vertices is
    A↔DA \leftrightarrow D
    ,
    B↔EB \leftrightarrow E
    , and
    C↔FC \leftrightarrow F
    .

By mastering these concise tests, you can swiftly justify equal angles, parallel lines, or symmetrical shapes in exam problems. **Practise daily**: sketch random triangles, label equal parts, and decide which congruence test applies. The more you drill, the faster those marks will roll in!