Chapter 8: Similar Triangles

Critieria for similarities of two triangles.

1. If in two triangles, the corresponding angles are equal, then their corresponading sides are proportional (i.e. in the same ratio) and hence the triangles are similar.

This property is referred to as the AAA similarily criterian

In the above property if only two angles are equal, then the third angle will be automatically equal

Hence AAA criteria is same as AA criteria.

2. If the coreponding sides of two trianlgles are proportional (i.e.in the same ratio), their corresponding angles are equal and hence the triabgles are similar.

This property is referredd to as SSS similarily criteria.

3. If one angles of a triangle is equal to one angle of the other and the sides including these angles are proportional, the triagngle are similar.

This proprerty is referred to as SAS critreria.

Example 6. P and Q are pointes on AB and AC respectively of If AP = 1cm, PB = 2cm, AQ = 3cm and QC = 6cm. Show that BC = 3PQ.

Solution:-

Given:- in which P and Q are points on AB and AC such that AP = 1cm, AQ = 3cm, PB = 2cm, QC = 6cm.

To Prove:- BC = 3PQ

Proof:-

Hence PQ || BC

and

But AB = AP + PB = 1 + 2 = 3cm

Hence BC = 3PQ.