Advertisements
Advertisements
Question
◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.
Solution
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
RELATED QUESTIONS
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 6 cm, DB = 9 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 = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x.
In a ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC
AB = 2cm, AD = 8cm, AE = 12 cm and AC = l8cm.
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.
In below Fig., state if PQ || EF.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.
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
AD = 4cm, DB = (x – 4) cm, AE = 8cm and EC = (3x – 19) cm.
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.
In the given figure, side BC of a 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 the adjoining figure, ABC is a triangle in which AB = AC. IF D and E are points on AB and AC respectively such that AD = AE, show that the points B, C, E and D are concyclic.
Find the length of a diagonal of a rectangle whose adjacent sides are 30cm and 16cm.
In ΔABC, AB = AC. Side BC is produced to D. Prove that `AD^2−AC^2`= BD.CD
An aeroplane leaves an airport and flies due north at a speed of 1000km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after` 1 1/2` hours?
State and converse of Thale’s theorem.
Each of the equal sides of an isosceles triangle is 25 cm. Find the length of its altitude if the base is 14 cm.
In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer.
ABCD is a trapezium in which AB || DC and P and Q are points on AD and BC, respectively such that PQ || DC. If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.
In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.
