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A tailor cuts two sleeves from the same numbers. Will they match?

This is CBSE's Triangles – Congruence Theorems. Two triangles are congruent when one fits exactly on the other. Turning or flipping is allowed. Measurements fix a triangle when all triangles built from them are congruent.

What you will learn

• SAS — two sides and the angle between them fix one triangle.
• SSA — an angle not between two sides can give two triangles.
• RHS — the hypotenuse (longest side) and a leg fix a right triangle.
• AAS — two angles and any side fix one triangle.
• Equal sides — in a triangle, they give equal opposite angles.
• Equal angles — in a triangle, they give equal opposite sides.
• A counter-example — one failing case ends a claim.
• Matching parts — the measurements decide, not how a triangle is turned.
• The apex bisector — it halves the top angle and the base.

Need a quick recap?

These earlier lessons help. Tap one if you are unsure.

• The exact match — one figure fits exactly on another; they are congruent.
• Three sides — three matching lengths allow only one triangle.
• Two sides and the angle between — the angle must sit between them.
• Two angles and the side between — two angles give the third angle.
• Three corners are not enough — angles give the shape, not the size.
• The 180° total — a triangle's corners add to two right angles.
• Saying why — a reason is steps, each following from the last.