ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) `M D_|_A C` (iii) `C M= "M A=1/2A B`

ABC is a triangle right angled at C and M is mid-point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show that: MD is mid-point of AC.

DeltaABC is a right triangle right angled at A such that AB = AC and bisector of /_C intersects the side AB at D . Prove that AC + AD = BC .

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: CP = ( 1)/(2)AB

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

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 DBC ~= Delta ACB

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

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

In right triangle ABC, right-angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that D M\ =\ C M . Point D is joined to point B (see Fig. 7.23). Show that: (i) DeltaA M C~=DeltaB M D (ii) /_DBC is a right angle (iii) Δ DBC ≅ Δ ACB (iv) CM =1/2 AB

In the adjoining figure, DeltaABC is right angled at C and M is the mid-point of hypotenuse AB, If AC = 32 cm and BC = 60 cm, then find the length of CM.

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: Angle DBC is a right angle.