Triangles Notes: Class 10 Maths Chapter 6
Class 10 Maths Chapter 6 Triangles covers similar figures and similar triangles, criteria for similarity of triangles (AA, SAS, SSS), the Basic Proportionality Theorem, areas of similar triangles, and the Pythagoras Theorem.
Overview of Topics & Subtopics (Click to Jump)
1. Similar Triangles
Short Note:
• Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (proportional).
• AA Similarity: if two angles of one triangle are equal to two angles of another, the triangles are similar. SSS Similarity and SAS Similarity criteria also apply.
2. Basic Proportionality Theorem (Thales Theorem)
Short Note:
• 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.
• Converse: if a line divides any two sides of a triangle in the same ratio, the line is parallel to the third side.
3. Areas of Similar Triangles
Short Note:
• The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
4. Pythagoras Theorem
Short Note:
• In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: (hypotenuse)² = (base)² + (perpendicular)².
• Converse: if the square of one side of a triangle equals the sum of the squares of the other two sides, the angle opposite the first side is a right angle.