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Schooling · Class 7 · Mathematics · Geometric Twins · Chapter on a page

CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II

Geometric Twins: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Geometric Twins: Key ideas, Formulas and facts, Watch out forKey ideasCongruent figuresTwo line segments are congruent if…corresponding partsSSS ruleSAS ruleASA ruleRHS ruleFormulas and factsCongruent segmentsCongruent anglesSSS (Side-Side-Side)SAS (Side-Angle-Side)ASA (Angle-Side-Angle)RHS (Right angle-Hypotenuse-Side)If triangle ABC ≅ triangle DEF, then…Watch out forComparing sides without checking if…Writing vertices in wrong order…Thinking any three equal…Applying RHS to triangles that are…Forgetting that congruent means same…Geometric Twins
The mind map as a list
  • Key ideas
    • Congruent figures
    • Two line segments are congruent if…
    • corresponding parts
    • SSS rule
    • SAS rule
    • ASA rule
    • RHS rule
  • Formulas and facts
    • Congruent segments
    • Congruent angles
    • SSS (Side-Side-Side)
    • SAS (Side-Angle-Side)
    • ASA (Angle-Side-Angle)
    • RHS (Right angle-Hypotenuse-Side)
    • If triangle ABC ≅ triangle DEF, then…
  • Watch out for
    • Comparing sides without checking if…
    • Writing vertices in wrong order…
    • Thinking any three equal…
    • Applying RHS to triangles that are…
    • Forgetting that congruent means same…

What this chapter is about

This chapter introduces you to the idea of congruence in geometry. Two shapes are called congruent when they are exactly the same in size and shape. Think of them as geometric twins — if you cut one shape out and place it over the other, they match perfectly.

Key ideas

  • Congruent figures are figures that have the exact same shape and size. One can be placed exactly over the other.
  • Two line segments are congruent if they have equal length. Two angles are congruent if they have equal measure in degrees.
  • When two triangles are congruent, their corresponding parts (matching sides and matching angles) are equal.
  • SSS rule: If all three sides of one triangle equal the three sides of another triangle, the triangles are congruent.
  • SAS rule: If two sides and the angle between them in one triangle equal two sides and the included angle in another triangle, the triangles are congruent.
  • ASA rule: If two angles and the side between them in one triangle equal two angles and the included side in another triangle, the triangles are congruent.
  • RHS rule: For right-angled triangles, if the hypotenuse and one other side of one triangle equal the hypotenuse and one side of another, the triangles are congruent.
  • The order of letters matters when writing congruence. If triangle PQR is congruent to triangle XYZ, then P matches X, Q matches Y, and R matches Z.

Formulas and facts to remember

  • Congruent segments: AB = CD means segment AB is congruent to segment CD.
  • Congruent angles: Angle P = Angle Q means the two angles have the same degree measure.
  • SSS (Side-Side-Side): Three pairs of equal sides prove congruence.
  • SAS (Side-Angle-Side): Two pairs of equal sides with the angle between them equal prove congruence.
  • ASA (Angle-Side-Angle): Two pairs of equal angles with the side between them equal prove congruence.
  • RHS (Right angle-Hypotenuse-Side): In right triangles, equal hypotenuse and one equal side prove congruence.
  • If triangle ABC ≅ triangle DEF, then AB = DE, BC = EF, CA = FD, and angle A = angle D, angle B = angle E, angle C = angle F.

Common mistakes

  • Comparing sides without checking if the angle is between them → For SAS, the angle must be the one formed by the two sides you are comparing.
  • Writing vertices in wrong order, like saying triangle ABC ≅ triangle EDF when A should match D → Always match corresponding vertices carefully.
  • Thinking any three equal measurements prove congruence → Three angles equal (AAA) does not prove congruence; the triangles could be different sizes.
  • Applying RHS to triangles that are not right-angled → RHS works only when both triangles have a right angle.
  • Forgetting that congruent means same size, not just same shape → Similar figures have the same shape but may differ in size; congruent figures must match exactly.

Quick revision

  • Congruent figures are exact copies in shape and size.
  • SSS: three sides equal → triangles congruent.
  • SAS: two sides and included angle equal → triangles congruent.
  • ASA: two angles and included side equal → triangles congruent.
  • RHS: right angle, hypotenuse, and one side equal → right triangles congruent.
  • Matching vertices must be written in correct order when stating congruence.