Question

D, E, F are the midpoints of the sides BC, CA and AB respectively of △ ABC. Then △ DEF is congruent to triangle –  ABC AEF BFD, CDE AFE, BFD, CDE

Solution

The correct options are B AEF C BFD, CDE D AFE, BFD, CDE  It is easy to verify that △ DEF is congruent to each one of the triangles △ AEF, △ BFD & △ CDE. Consider ΔAFE∠AFE=∠Band∠AEF=∠C  Since FE is parallel to BC. Similarly in ΔBFD∠BFD=∠Aand∠BDF=∠C  and  ΔDEC∠DEC=∠Aand∠EDC=∠B  We know ∠A+∠B+∠C=180∘ Now, consider ΔDEF∠FED=180∘−∠DBF−∠EDC=180−∠C−∠B=∠A Similarly, ∠DFE=∠C and ∠FED=∠B. By AA similarity So, ΔDEF~ΔAFE~ΔBFD~ΔCDE

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