3-ABC is anequilateral triangle BD and CE are medians show that BD= CE - Maths - Congruence of Triangles

Question

3-ABC is anequilateral triangle BD and CE are medians show that
BD= CE

Lalit Mehra · Accepted Answer

Î”ABC is an equilateral triangle BD and CE are the medians of Î”ABC Î”ABC is an equilateral triangle âˆ´ AB = AC (Sides of an equilateral triangle are equal) $\Rightarrow \frac{1}{2} AB = \frac{1}{2} AC$ â‡’ BE = CD (BD and CD are medians of Î”ABC) In Î”BCE and Î”BCD, BE = CD (Proved) âˆ EBC = âˆ DCB = 60Â° BC = BC (Common) âˆ´ Î”BCE $≅$ Î”BCD (SAS congruence criterion) â‡’ CE = BD (CPCT)

3-ABC is anequilateral triangle.BD and CE are medians. show that BD= CE