State, true or false, for each of the following statements.

(i) If three angles of two triangles are equal, the triangles are congruent.

(ii) If two sides of a right triangle, containing right angle, are equal to corresponding sides of another right triangle, the triangle are congruent.

(iii) If two triangles are congruent, then the corresponding angles are equal.

(iv) If two angles and a side of one triangle are equal to two angles and a side of another triangle, the triangles are congruent.

(i) False

Reason

Congruence means that two triangles are identical in both shape and size, requiring all corresponding sides to be equal. However, if only the angles are known to be equal, the triangles may have different sizes (i.e., they are similar but not necessarily congruent).

Thus, if three angles of two triangles are equal, the triangles are similar, not necessarily congruent.

(ii) True

Reason

According to the RHS (Right-Angle-Hypotenuse-Side) Congruence Theorem, if the hypotenuse and one other side of a right-angled triangle are equal to the corresponding hypotenuse and side of another right-angled triangle, then the two triangles are congruent.

(iii) True

Reason

If two triangles are congruent, it means they are identical in both shape and size. This implies that their corresponding sides are equal, and as a result, their corresponding angles are also equal.

(iv) True

Reason

If two angles and a corresponding side of one triangle are equal to two angles and a corresponding side of another triangle, the triangles are congruent.

This follows from the ASA (Angle-Side-Angle) Congruence Criterion or the AAS (Angle-Angle-Side) Congruence Criterion, both of which confirm that the triangles are identical in shape and size.