What this guide covers
Selected Sec 2 G2 skills: similarity, correspondence, enlargement and area ratio. This does not cover every congruence test or construction.
Length changes once; area twice
If corresponding lengths are multiplied by k, corresponding areas are multiplied by k². Congruent figures have equal corresponding lengths; similar figures may be larger or smaller.
Use a named correspondence
Two similar triangles have corresponding short-to-large sides 8 cm and 12 cm. Another short side is 10 cm, and the smaller area is 24 cm². Find the matching large side and the larger area.
- The large-to-small length multiplier is 128=32.
- Matching large side =10×32=15 cm.
- The area multiplier is (32)²=94, so larger area =24×94=54 cm².
Check: The larger side and area are both larger; the area changes by more than the length factor.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
A rectangle 4 cm by 7 cm is enlarged by length factor 2. Find its new sides and area.
New sides are 8 cm and 14 cm, so area is 8×14=112 cm². Original area 28 cm² multiplied by 2²=4 also gives 112 cm².
Triangles with corresponding side lists (3,5,7) and (6,10,14) have the same vertex correspondence. Are they similar, congruent, both or neither? Explain.
Each large side is twice its corresponding small side, so they are similar by proportional sides. They are not congruent because corresponding lengths differ.
Where this connects
- Related: ratio and scale →
A consistent side order helps identify the multiplier.
- Later: combined correspondence problems →
The Upper Secondary guide applies the same idea inside longer geometry.
Sources and scope
Original Mentora lengths and questions aligned to selected Sec 2 G2 content in the MOE G2/G3 Mathematics syllabus. No third-party triangle diagram was used.