Congruency, Enlargement and Combined Transformations · 5.1.3
Solving congruency problems
This standard asks students to apply the SSS, SAS, ASA and AAS congruency conditions to solve problems, finding unknown side lengths or angles, justifying why two shapes are congruent, and using congruent parts to solve related measurement or geometric problems.
The official learning standard (5.1.3)
“Solve problems involving congruency.”
What it means
This standard asks students to apply the SSS, SAS, ASA and AAS congruency conditions to solve problems, finding unknown side lengths or angles, justifying why two shapes are congruent, and using congruent parts to solve related measurement or geometric problems.
How it is examined
In Paper 1, students identify congruent shapes or state the correct congruency condition from a diagram. In Paper 2, structured questions require using given congruency conditions to calculate unknown lengths or angles, often within larger geometry problems, with clear working and justification expected.
Worked example
In triangles ABC and DEF, AB = DE = 8 cm, BC = EF = 6 cm, and ∠B = ∠E = 90° (the angle between the two given sides). Given DF = 10 cm, find the length of AC and state the congruency condition used.
- Compare corresponding parts: AB = DE = 8 cm, BC = EF = 6 cm, ∠B = ∠E = 90° (the included angle between AB and BC).
- Since two sides and the included angle are equal, triangles ABC and DEF are congruent by the SAS condition.
- Corresponding sides of congruent triangles are equal, so AC = DF.
- Given DF = 10 cm, therefore AC = 10 cm.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I know which congruency condition to use?
Compare what information is given, three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), or two angles and a non-included side (AAS). Match the given data to the condition before writing your conclusion.
Do I need to write the condition name in my answer?
Yes, stating "by SSS/SAS/ASA/AAS" is usually required for full marks, as it justifies why the shapes are congruent rather than just similar or coincidentally equal.
What if only some sides match but not the included angle?
Then congruency cannot be confirmed by SAS; check whether SSS, ASA, or AAS applies instead, or the triangles may not be congruent at all, SSA alone is not sufficient to establish congruency.