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Congruence conditions

Congruence & properties of shapes

Japanese school year: Junior high 2

What you learn

Learn the three conditions for triangle congruence based on the equality of corresponding sides and angles. These conditions form the core foundation for proving various geometric theorems logically. Familiarity with the basic parts of triangles and geometric constructions is helpful before studying this topic.

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Key points

This condition is used to establish that two triangles are congruent (identical in shape and size). If all three pairs of corresponding sides are equal, the two triangles are congruent.

AB=DE,  BC=EF,  CA=FD  ⟹  △ABC≡△DEFAB = DE, \; BC = EF, \; CA = FD \implies \triangle ABC \equiv \triangle DEF

This condition is used to establish that two triangles are congruent. If two pairs of corresponding sides and the included angle between them are equal, the triangles are congruent.

AB=DE,  BC=EF,  ∠B=∠E  ⟹  △ABC≡△DEFAB = DE, \; BC = EF, \; \angle B = \angle E \implies \triangle ABC \equiv \triangle DEF

This condition is used to establish that two triangles are congruent. If one pair of corresponding sides and the angles at both of its ends are equal, the triangles are congruent.

BC=EF,  ∠B=∠E,  ∠C=∠F  ⟹  △ABC≡△DEFBC = EF, \; \angle B = \angle E, \; \angle C = \angle F \implies \triangle ABC \equiv \triangle DEF

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