Advertisements
Advertisements
प्रश्न
In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:
RT = `(1)/(3)"PQ"`
Advertisements
उत्तर
Proof:
R and T are the mid-points of NS and MS respectively.
⇒ RT = `(1)/(2)"MN"`
M and N are the mid-points of LT and PR respectively.
⇒ MN = `(1)/(2)"PQ"`
So, RT = `(1)/(2)(1/2 "PQ")`
⇒ RT = `(1)/(4)"PQ"`.
APPEARS IN
संबंधित प्रश्न
In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC
intersects FE at Q. Prove that AQ = QP.
In the given figure, `square`PQRS and `square`MNRL are rectangles. If point M is the midpoint of side PR then prove that,
- SL = LR
- LN = `1/2`SQ
L and M are the mid-point of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.
If the quadrilateral formed by joining the mid-points of the adjacent sides of quadrilateral ABCD is a rectangle,
show that the diagonals AC and BD intersect at the right angle.
Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
In ΔABC, P is the mid-point of BC. A line through P and parallel to CA meets AB at point Q, and a line through Q and parallel to BC meets median AP at point R. Prove that: BC = 4QR
In ΔABC, D, E and F are the midpoints of AB, BC and AC.
If AE and DF intersect at G, and M and N are the midpoints of GB and GC respectively, prove that DMNF is a parallelogram.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if ______.
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = `1/3` AC.
Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.
