prove that medians of equilateral Triangles are equal
Answers
Answer:
Answer
To prove: The medians of an equilateral triangle are equal.
Median = The line joining the vertex and mid-points of opposite sides.
Proof: Let Δ ABC be an equilateral triangle
AD, EF and CF are its medians.
Let,
AB = AC = BC = x
In
BFC and
CEB, we have
AB = AC (Sides of equilateral triangle)
AB =
AC
BF = CE
∠ABC =∠ACB (Angles of equilateral triangle)
BC = BC (Common)
Hence, by SAS theorem, we have
Δ BFC ≅ Δ CEB
BE = CF (By c.p.c.t)
Similarly, AB = BE
Therefore, AD = BE = CF
Hence, proved
Answer:
Gravitational force acts on all objects in proportion to their masses. But a heavy object does not fall faster than a light object. This is because of the reason that Acceleration= Force/Mass or Force = Acceleration x Mass As force is directly proportional to mass, acceleration is constant for a body of any mass.