If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

Is \(\triangle\)ABC ~ \(\triangle\)PQR?

A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

An Aeroplane after take off from an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?

Show that \(\triangle\)PST~\(\triangle\)PQR 

In figure OA· OB = OC·OD
Show that \(\angle A=\angle C\ and\ \angle B=\angle D\)

D and E are respectively the points on the sides AB and AC of a \(\triangle\)ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, show that DE || BC

In the figure DE||AC and DC||AP. Prove that \(\frac { BE }{ CE } =\frac { BC }{ CP } \)

In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

Prove that in a right triangle, the square of 8. the hypotenuse is equal to the sum of the squares of the others two sides.

Check whether the which triangles are similar and find the value of x.
(i)

(ii)

In fig. if PQ || BC and PR ||CD prove that

 \(\frac { AB }{ AD } =\frac { AQ }{ AB } \)