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

The ratio of the area of two similar triangle is 4:5 , the ratio of their corresponding sides are :

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.

Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.

Theorem 7.4 (SSS congruence rule) : If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

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.

Prove that for a given correspondence, if three angles of one triangles are congruent to the corresponding three angles of the other triangle, then the two triangles are similar.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

Areas of two similar triangles are in the ratio 64:121, then the sides of these triangles are in the ratio: