Similarity — Class 10 Maharashtra SSC Mathematics revision notes
A 5-page visual revision sheet for Similarity, written for Class 10 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Similarity in one look
same shape, different size: equal angles force proportional sides, and areas grow as the square
What similar means, exactly
- two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio
- for triangles either condition implies the other, so proving the angles equal is enough and the sides follow free
- similar is written with the symbol ∼, as in △ABC ∼ △PQR, while congruent uses ≅ and means the same shape at the same size
- congruence is the special case of similarity where the ratio of sides is exactly 1
- the order of the letters carries the correspondence: △ABC ∼ △PQR says A matches P, B matches Q and C matches R, and writing them out of order makes every ratio below wrong
The three tests for similarity
- AA: two angles of one triangle equal two angles of the other. The third is then equal automatically, since the angles of a triangle add to 180°. This is the test you will use most
- SAS: two pairs of sides in the same ratio and the included angles equal. The angle must lie between the two sides, not anywhere else
- SSS: all three pairs of corresponding sides in the same ratio. Check the ratio for every pair, since two matching pairs prove nothing on their own
- Not a test: ASA and RHS belong to congruence, not similarity. For similarity the sides are proportional, never necessarily equal
Page 1 of 5. The full sheet, all 5 pages, opens free in the app.
What this Similarity sheet covers
- Similar triangles
- Similarity
- What similar means, exactly
- AA test
- SAS test of similarity
- SSS test of similarity
- The three tests for similarity
- AA
- SAS
- SSS
- Not a test
- Where the equal angles usually come from
- The ratios that follow from similarity
- corresponding sides, for △ABC ∼ △PQR
- perimeters share the same ratio as the sides
- areas grow as the square of that ratio
- altitudes, medians and bisectors also share k
- triangles of the same height, areas by base
- Basic proportionality theorem
- Thales theorem
- The basic proportionality theorem
- Using the basic proportionality theorem
- Going from an area ratio back to a side
- Similar against congruent
- Similar (∼)
- Congruent (≅)
- Symbols in this chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Similarity the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.