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# Show and proof mid point theorem

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Show and proof mid point theorem

Priyanka Devi 1 month, 4 weeks ago

A line joining midpoints of any two sides of a triangle is parallel to the third side and a half of third side. GIVEN- a triangle ABC in which D and E mid points of AB and AC. TO PROVE- DE parallel to BC and DE =1 by 2 BC .CONSTRUCTION-draw a line CF parallel to AB and then produce DE to F. PROOF-in 🔺️ ABC and in 🔺️CEF ≈angle 1= angle 2(alternate angles),angle3=angle4(vertically opposite angles),AE=CE(given),so 🔺️ ABC congruence to 🔺️ CEF by AAS congruence condition AD=CF by cpct(1).AD=BD -given (2).from (1)nd (2) DF parallel to BC. DE parallel to BC. DF=BC. DE+EF=BC. (🔺️ ADE congruent to 🔺️ CEF, DE=EF by cpct). 2DE=BC. DE =1/2BC

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