In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.

Which of the following statements are true (T) and which are false (F)?

(i) Sum of the three sides of a triangle is less than the sum of its three altitudes.

(ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side.

(iii) Sum of any two sides of a triangle is greater than the third side.

(iv) Difference of any two sides of a triangle is equal to the third side.

(v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.

(vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

Fill in the blanks to make the following statements true:

(i) In a right triangle the hypotenuse is the …….side.

(ii) The sum of three altitudes of a triangle is …… than its perimeter.

(iii) The sum of any two sides of a triangle is ….. than the third side.

(iv) If two angles of a triangle are unequal, then the smaller angle has the …. side opposite to it.

(v) Difference of any two sides of a triangle is ……. than the third side.

(vi) If two sides of a triangle are unequal, then the larger side has ……. angle opposite to it.

In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F. Are the two triangles necessarily congruent?

If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm, DF = 5 cm and ∠D = 75°. Are two triangles congruent?