Advertisements
Advertisements
प्रश्न
◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.
उत्तर
Given:
◻ABCD is a parallelogram.
E is a point on side BC.
Line DE intersects ray AB in point T.
To prove: DE × BE = CE × TE
Proof: In ∆BET and ∆CED
∠BET = ∠CED ...(Vertically opposite angles)
∠BTE = ∠CDE ...(Alternate interior angles, AB || CD and DT is a transversal line)
By AA test of similarity,
∆BET ∼ ∆CED
∴ `("BE")/("CE") = ("ET")/("ED")`
∴ DE × BE = CE × TE
APPEARS IN
संबंधित प्रश्न
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If `"AD"/"BD"=4/5` and EC = 2.5 cm, find AE
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = x, DB = x − 2, AE = x + 2 and EC = x − 1, find the value of x.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AB = 5.6cm, AD = 1.4cm, AC= 7.2 cm and AE = 1.8 cm.
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.
In a ΔABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4cm, AE = 3.2 cm, DE = 2cm and BC = 5 cm, find BD and CE.
M and N are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether MN || QR
PM = 4cm, QM = 4.5 cm, PN = 4 cm and NR = 4.5 cm
D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If `(AD)/(DB) = 4/7` and AC = 6.6cm, find AE.
In the given figure, ABCD is a trapezium in which AB║DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1) , BO = (7x – 5) and OD = (7x + 1), find the value of x.
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.
A guy wire attached to a vertical pole of height 18 m is 24m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
ΔABC is an isosceles triangle with AB = AC = 13cm. The length of altitude from A on BC is 5cm. Find BC.
Find the height of an equilateral triangle of side 12cm.
State the midpoint theorem
Find the value of x for which DE || AB in figure.
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.
