Revision Notes for Class 7 Maths Chapter 9: Geometric Twins

Quick revision notes summarizing all key concepts from Class 7 Maths Chapter 9 “Geometric Twins”. These Class 7 Mathematics Chapter 9 notes are ideal for quick revision just before exams.

• Congruent figures are figures that are identical in shape and size — one can be superimposed exactly on the other.
• Two circles are congruent exactly when they have the same radius (or diameter).
• Two rectangles are congruent exactly when they have the same length and the same breadth.
• Congruence criteria for triangles: SSS (all three sides equal), SAS (two sides + the included angle equal), ASA (two angles + the included side equal), AAS (two angles + a non-included side equal), RHS (right angle + hypotenuse + one side equal, for right triangles only).
• SSA (two sides + a non-included angle) is NOT a valid congruence criterion in general — it can produce two different triangles (the ambiguous case), except in the special right-angle case where it becomes RHS.
• AAA (all angles equal) only proves similarity, not congruence — congruence needs matching size (at least one side), not just matching shape.
• The order of vertices in a congruence statement (e.g. ΔABC ≅ ΔDEF) shows the exact correspondence of vertices, sides, and angles; any single pair of congruent triangles can be written correctly in six different vertex orders.
• CPCT (Corresponding Parts of Congruent Triangles) means that once two triangles are shown congruent, all their corresponding sides and angles are automatically equal.
• In an isosceles triangle, the angles opposite the two equal sides are equal (base angles equal). In an equilateral triangle, all three sides and all three angles (60° each) are equal.
• Angle-chasing in compound figures uses: angle sum of a triangle = 180°, angles on a straight line (linear pair) = 180°, and vertically opposite angles are equal.

See also: NCERT Solutions for Class 7 Maths Chapter 9

Practice more: Extra Questions for Class 7 Maths Chapter 9

For the full chapter, see the Class 7 Maths book page and the Class 7 Maths Formulas Handbook.

Written by Satish

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