Class 10 Maths Chapter 6: Triangles Concept Infographic (NCERT)

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✦ NCF 2023 ALIGNED • VISUAL LEARNING SERIES ✦

Chapter 6: Triangles

Discovering the rules of similarity, proportionality, and geometrical proofs[cite: 7].

📘 Similarity Basics

What is Similarity?

Two figures are similar if they have the same shape but not necessarily the same size[cite: 7]. (All congruent figures are similar, but not vice-versa[cite: 7]).

Polygon Similarity Rule
Two polygons with the same number of sides are similar if:
1. Their corresponding angles are equal[cite: 7].
2. Their corresponding sides are in the same ratio (proportional)[cite: 7].

⭐ Thales Theorem (BPT)

Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio[cite: 7].

If DE || BC,
Then

ADDB

=

AEEC

[cite: 7]

📐 Criteria for Similarity of Triangles

You don't need to check all 6 pairs of parts to prove similarity! Use these 3 golden rules[cite: 7]:

AAA (or AA)

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio[cite: 7].
(Note: Even just 2 equal angles is enough - AA criterion[cite: 7]).

SSS

If sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal[cite: 7].

SAS

If one angle of a triangle is equal to one angle of another triangle AND the sides including these angles are proportional[cite: 7].

⭐ Board Exam Super-Hacks

The Secret "RHS" Similarity

If in two right triangles, the hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are similar[cite: 7]!

Vertex Correspondence is Key

Always write similarity with correct vertex correspondence! If ∠A=∠D, ∠B=∠E, ∠C=∠F, you MUST write ΔABC ~ ΔDEF[cite: 7]. Writing ΔABC ~ ΔEDF is considered wrong in exams[cite: 7].

⚠️ Common Exam Traps

Trap 1: Polygon vs Triangle Rule

For regular polygons (like quadrilaterals), checking ONLY angles or ONLY sides is NOT enough (e.g. a square and a rectangle have equal angles but are not similar)[cite: 7]. But for triangles, one condition implies the other[cite: 7]!

Trap 2: The "Included" Angle in SAS

In the SAS criterion, the equal angle MUST be the one included strictly between the two proportional sides[cite: 7]. If a non-included angle is equal, you cannot prove similarity.

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