Given below is the proof that if the mid-points of sides of a triangle are joined to make another triangle, then the 4 triangles formed are divided into four congruent triangles. Which of the following is the correct missing STEP-4?
Let ABC be a triangle. D, E, F are the mid-points of side BC, AB, AC. Join D, E, F which forms a triangle. To Prove: △AEF≅△EBD≅△FDC≅△DFE STEP-1: EF∥BC (E,F are mid-points of AB, AC) STEP-2: DE∥AC (D,E are mid-points of BC, AB) STEP-3: DF∥AB (D,F are mid-points of BC, AC) STEP-4: STEP-5: △AEF≅△DFE (EF is diagonal of parallelogram AEDF) STEP-6: △EBD≅△DFE (ED is diagonal of parallelogram EBDF) STEP-7: △FDC≅△DFE (FD is diagonal of parallelogram EDCF) STEP-8: ∴ △AEF≅△EBD≅△FDC≅△DFE (from STEP-5,6,7)
(A)
∴ AEDF, EBDF, EDCF are rectangles (from STEP-1,2,3)
(B)
∴ AEDF, EBDF, EDCF are rhombus (from STEP-1,2,3)
(C)
∴ AEDF, EBDF, EDCF are parallelograms (from STEP-1,2,3)
(D)
∴ AEDF, EBDF, EDCF are trapezium (from STEP-1,2,3)
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