Points to Remember
· Two triangles are similar
(i) if their corresponding angles are equal
(ii) their corresponding sides are in the same ratio or prvoportional.
· Any congruent triangles are similar but the converse is not true
· AA similarity criterion is same as the AAA similarity criterion.
· If one angle of a triangle is equal to one angle of another triangle and the sides If one angle of a triangle is equal to one angle of another triangle and the sides
· If three sides of a triangle are proportional to the corresponding sides of another triangle, then the two triangles are similar (SSS)
· If two triangles are similar then the ratio of the corresponding sides is equal to the ratio of the corresponding perimeters.
· The ratio of the area of two similar triangles are equal to the ratio of the squares of their corresponding sides.
· A tangent to a circle will be perpendicular to the radius at the point of contact.
· Two tangents can be drawn from any exterior point of a circle.
· The lengths of the two tangents drawn from an exterior point to a circle are equal.
· Two direct common tangents drawn to two circles are equal in length.