Triangles DEF, GHI and JKL are taken in the same order so that the correspondences are

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Triangles DEF, GHI and JKL are taken in the same order so that the correspondences are D↔G↔JD \leftrightarrow G \leftrightarrow J, E↔H↔KE \leftrightarrow H \leftrightarrow K and F↔I↔LF \leftrightarrow I \leftrightarrow L. It is given that △DEF≅△GHI\triangle DEF \cong \triangle GHI and △GHI≅△JKL\triangle GHI \cong \triangle JKL. (i) List the three pairs of equal sides and the three pairs of equal angles that result from the congruence △DEF≅△GHI\triangle DEF \cong \triangle GHI. (ii) Explain, without performing any fresh calculations, why △DEF\triangle DEF must also be congruent to △JKL\triangle JKL. (iii) Write down all pairs of equal sides and all pairs of equal angles between △DEF\triangle DEF and △JKL\triangle JKL.

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