Class 10 Similar Triangles: Corresponding Sides and Ratios

Two triangles can have the same shape while facing different ways. The reliable starting point is a correspondence between vertices, not the left and right positions in the drawing.

Sources checked 2 October 2026 · original study guide · CBSE/NCERT context

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Read the order as a mapping

Writing ΔABC ∼ ΔPQR means A matches P, B matches Q and C matches R. Therefore AB matches PQ, BC matches QR and AC matches PR. Draw three small matching arrows on your rough work before substituting lengths.

A matches P, B matches Q, C matches R. The second triangle is rotated 180° and enlarged by 1.5: AB corresponds to PQ, BC to QR, AC to PR. Position on the page does not decide correspondence.

Rotate the drawing, keep the correspondence

The second triangle in the drawing is rotated through 180°. A still matches P, B matches Q and C matches R. Match the listed vertex order or proved angle equalities; leftmost and highest positions are not geometric reasons. The sketch uses scale factor 1.5, separately from the numerical example below.

Choose a similarity reason

Swipe across the table to see all columns.

Criterion	Evidence needed	Insufficient evidence
AA	Two pairs of equal corresponding angles	One equal angle
SSS	All three corresponding side ratios equal	Two proportional sides alone
SAS	Two proportional side pairs and equal included angles	An equal angle outside the two sides

Use the mapping in a calculation

Suppose ΔABC ∼ ΔPQR, AB = 6 cm, BC = 9 cm and PQ = 10 cm. The enlargement factor from ABC to PQR is 10 ÷ 6 = 5/3. Therefore QR = 9 × 5/3 = 15 cm. The second triangle has larger matching sides, which agrees with the factor being greater than one.

Writing 6/10 = QR/9 reverses only one ratio. If you use small/large on the left, use small/large on the right: 6/10 = 9/QR. Either orientation works when you keep it consistent.

Turn the picture into a proof

Record the equal angles or side ratios with their reasons. State the similarity criterion, then write the triangles in matching order. Only after establishing similarity should you use the corresponding-side relation you need. A shape that looks similar is not evidence.

For a triangle crossed by a parallel line, mark the corresponding angles created by that parallel line. This often supplies AA. If your proof uses a given ratio instead, check whether the basic proportionality theorem or its converse is the more direct route.

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Sources and scope

This is a focused learning resource, not a complete chapter or a prediction of board questions. Use your current syllabus and the paper-specific marking scheme for assessment requirements.

PDF documentNCERT Mathematics: source chapterRead the original textbook for the full chapter. The explanations and examples on this page are independently authored, not NCERT solutions.Open PDF External resourceOfficial CBSE Class X sample papers and marking schemesChoose the subject and the matching paper and marking scheme. Basic and Standard Mathematics have separate papers.Visit source

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Choose the specific step that is causing difficulty. Return to this lesson after repairing it; you do not need to complete every foundation page.

Frequently asked questions

Does similar mean congruent?

No. Similar triangles have the same shape; congruent triangles also have the same size. A similarity scale factor of one gives equal corresponding sides.

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