If `D` is the mid-point of the hypotenuse `A C` of a right triangle `A B C ,` prove that `B D=1/2A C`

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

Prove that the mid-point of the hypotenuse of a right triangle is equidistant from its vertices.

If D is any point on the base B C produced, of an isosceles triangle A B C , prove that A D > A B .

If D is any point on the base B C produced, of an isosceles triangle A B C , prove that A D > A Bdot

In right triangle A B C , right angle at C ,\ M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Mdot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

In a right triangle ABC, right angled at C, P is the mid-point of hypotenuse AB. C is joined to P and produced to a point D, such that DP = CP. Point D is joined to point B. Show that: Delta APC ~= Delta BPD