Theorem 6.3 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Theorem 6.5 : If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

If two triangles are congrent , then the corresponding angles are equal

If the ex-radii of a triangle are in H.P.,then the corresponding sides are in

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

If in a triangle the angles are in the ratio as 1:2:3 , prove that the corresponding sides are 1:sqrt(3): 2.

If in triangle the angles are in the ratio as 1:2:3 , prove that the corresponding sides are 1:sqrt(3): 2.

Theorem 6.4 : If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar

If two sides and a median bisecting the third side of a triangle ar respectively proportional to the corresponding sides and median of the other triangle; then the two triangles are similar.

Theorem 7.6 : If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater)

If two triangles are similar; prove that the ratio of the corresponding sides is same as the corresponding angle bisector segments.