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.

Assertion (A) : If two triangle have same perimeter , then they are congruent. Reason (R) : If under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent.

Consider the following statements : Two triangles are said to be congruent, if 1. Three angles of one triangle are equal to the corresponding three angles of the other triangle. 2. Three sides of one triangle are equal to the corresponding three sides of the other triangle, 3. Two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle. 4. Two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. Which of the above statements are correct ?

Two triangles are congruent if three angles of one triangle are equal to three angles of the other triangle.

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

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

If two angles of one triangle are respectively equal to two angles of another triangle; then two triangles are similar.

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.

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?