In \(\triangle\)ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm.

In figure if PQ || RS Prove that \(\Delta POQ\sim \Delta SOQ\)

In figure the line segment XY is parallel to side AC of \(\Delta ABC\) and it divides the triangle into two parts of equal areas. Find the ratio \(\cfrac { AX }{ AB } \)

The areas of two similar triangles \(\Delta\)ABC and \(\Delta\)DEF are 81 cm² and 100 cm² respectively. If EF = 5 cm, then find BC.

\(\text { The area of } \triangle P Q R=64 \mathrm{~m}^{2} \text {. Find the area of }\Delta L M N \text { if } \frac{P Q}{L M}=\frac{4}{5} \text { and } \Delta P Q R \sim \Delta L M N\)

Check whether the given pair of triangles are similar or not

Check the similarity of the given triangles.

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles show that \(\frac{O A}{O C}=\frac{O B}{O D}\)

In the figure AD is the bisector of \(\angle\)A. If BD = 6 cm, DC = 4.5 cm and AB = 9 cm, Find AC

ln the figure AD is the bisector of \(\angle\)BAC If AB = 20 cm, AC = 28 cm and BC = 12 cm, find BD and DC.

In \(\Delta\)ABC AD is the bisector of \(\angle\)A meeting BC at D If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

In a \(\Delta\)ABC If AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm. Check whether AD is the bisector of \(\angle A \text { of } \triangle A B C\)

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle ls isosceles.

Check the given sides are the sides of a right angled triangle.
(i) a = 6 cm, b = 5 cm and c = 10 cm
(ii) a = 5 cm, b = 5 cm and c = 11 cm

A ladder is placed in such a way that its foot is at a distance of 5 m from a wall and its tip reaches a window 12 m above the ground. Determine the length of the ladder.