ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.
The diagonals of a quadrilateral intersect each other at the point such that . Show that is a trapezium.
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that :
All the values of for which both roots of the equation are but lie in the interval
The logical statement is equivalent to
AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB=10 cm, AC=6 cm and BC=12 cm, find CE.
A cm long rod moves with its ends on two mutually perpendicular straight lines and . If the end be moving at the rate of cm/sec, then when the distance of from is cm, the rate at which the end is moving, is
cm / sec
cm / sec
cm / sec
None of these
In triangle ABC, if DE is parallel to BC, then which of the following is stated by Basic Proportionality Theorem?
M and N are points on the sides PQ and PR respectively of a ΔPQR. For each of the following cases, whether MN || QR:
(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ =1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm
In the given figure, side BC of ΔABC is bisected at D and O is any point on AD, BO and CO produced meet AC and AB at E and F respectively, and AD is produced to X so that D is the midpoint of OX. Prove that AO : AX = AF : AB and show that EF || BC.
In Fig. 7.141 DE || BC such that AE=(14)AC. If AB = 6 cm, find AD.
The following figure is a parallelogram. Find and. (Lengths are in )
is a rhombus and and are mid-points of the sides and respectively. Show that the quadrilateral is a rectangle.
If LM ∥ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?
D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC
Find the value of x, when
(i) AD = x cm, DB = (x - 2) cm,
AE = (x + 2) cm and EC = (x - 1) cm.
(ii) AD = 4 cm, DB = (x - 4) cm, AE = 8 cm and EC = (3x - 19) cm.
(iii) AD = (7x - 4) cm, AE = (5x - 2) cm, DB = (3x + 4 ) cm and EC = 3x cm.
In the following figure, DE||OQ and DF||OR, show that EF||QR.
The minimum value of is
In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —
BD/DC = AB/AC =34
So, BD : DC = 3 : 4.
In did not understand how we proved the similarity and how we are taking the sides proportionality. Plz explain. Thank you.
ΔABC and ΔDBC lie on the same side of BC, as shown in the figure. From a point P on BC, PQ || AB and PR || BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR || AD.