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.

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

ABCD is a trapezium in which A B\ ||\ D C , BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of 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 trapezium ABCD, AB/DC, E is mid-point of aD. A line through E and parallel to AB intersects BC at point F. Show that: 2EF=AB+DC

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.

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

E is the mid-point of the side AD of the tarapezium ABCD with AB||DC . A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-points of BC.

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 a triangle ABC, AD is a medium and E is mid-point of median AD. A line through B and E meets AC at point F.