Triangles (NCERT Ch. 7)

• Apply congruence criteria: SSS, SAS, ASA, RHS.
• Use CPCTC after proving congruence.
• Prove angles opposite equal sides are equal.
• Understand inequalities in triangles (side-angle relationship).
• Solve NCERT proof-style problems with neat diagrams.

1. Congruent triangles — Same shape and size; correspondence of vertices matters.
2. SSS — Three sides equal.
3. SAS — Two sides and included angle equal.
4. ASA / AAS — Two angles and a side.
5. RHS — Right angle, hypotenuse, one side (right triangles).
6. CPCTC — Corresponding parts of congruent triangles are equal.
7. Theorem — Angles opposite equal sides in an isosceles triangle are equal.
8. Inequality — Greater side has greater angle opposite.

In △ABC, AB = AC. Prove ∠B = ∠C.

Draw median/angle bisector from A to BC or use congruence of △ABD and △ACD.
NCERT: △ABC with AB = AC → ∠B = ∠C (isosceles triangle theorem).

• Skipping given-to-prove structure in geometry proofs.
• Using wrong congruence criterion (SSA is not valid).
• Forgetting units in length/angle statements.

• State one NCERT result from Triangles.
• Draw a neat diagram for a typical Triangles problem.

Open the Practice tab for graded questions on Triangles (NCERT Ch. 7).