Show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B

Step-by-step explanation:

a). Let the unknown side of triangle A = x cm

And unknown side of triangle B = y cm

By applying Pythagoras theorem in triangle A,

13² = 12² + x²

x² = 169 - 144

x² = 25 ⇒ x = 5 cm

By applying Pythagoras theorem in triangle B,

y² = 5² + 12²

y² = 25 + 144

y = √169

y = 13 cm

Therefore, smaller sides of these triangles measure 5 cm and 12 cm and they are same in measure.

b). Since, corresponding sides of both the triangles are congruent,

By SSS property of congruence, both the triangles will be congruent.