Advertisements
Advertisements
प्रश्न
In the given figure, T is the midpoint of QR. Side PR of ΔPQR is extended to S such that R divides PS in the ratio 2:1. TV and WR are drawn parallel to PQ. Prove that T divides SU in the ratio 2:1 and WR = `(1)/(4)"PQ"`.
Advertisements
उत्तर
In ΔPQR,
T is the mid-point of QR and VT || PQ
So, V is the mid-point of PR.
Since R divides PR in the ratio 2 : 1 and PV = VR,
so, PV = PR = RS
Since R is the mid-point of SV and RW || VT,
W is the mid-point of ST.
Since V is the mid-point of PR and VT || PQ,
T is the mid-point of UW.
So, UT = TW = SW
⇒ T divides SU in the ratio 2 : 1
Also,
R and W are the midpoints SV and TS respectively.
⇒ WR = `(1)/(2)"VT"`
V and T are the mid-points of PR and UW respectively.
⇒ VT = `(1)/(2)"PQ"`
So, WR = `(1)/(2)(1/2 "PQ")`
⇒ WR = `(1)/(4)"PQ"`.
APPEARS IN
संबंधित प्रश्न
In below fig. ABCD is a parallelogram and E is the mid-point of side B If DE and AB when produced meet at F, prove that AF = 2AB.
BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If
L is the mid-point of BC, prove that LM = LN.
In the Figure, `square`ABCD is a trapezium. AB || DC. Points P and Q are midpoints of seg AD and seg BC respectively. Then prove that, PQ || AB and PQ = `1/2 ("AB" + "DC")`.
In ∆ABC, E is the mid-point of the median AD, and BE produced meets side AC at point Q.
Show that BE: EQ = 3: 1.
A parallelogram ABCD has P the mid-point of Dc and Q a point of Ac such that
CQ = `[1]/[4]`AC. PQ produced meets BC at R.
Prove that
(i)R is the midpoint of BC
(ii) PR = `[1]/[2]` DB
In triangle ABC; M is mid-point of AB, N is mid-point of AC and D is any point in base BC. Use the intercept Theorem to show that MN bisects AD.
In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find DE, if AB = 8 cm
In a parallelogram ABCD, M is the mid-point AC. X and Y are the points on AB and DC respectively such that AX = CY. Prove that:
(i) Triangle AXM is congruent to triangle CYM, and
(ii) XMY is a straight line.
The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is ______.
P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square.
