Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B

explain why the two triangles are congruent

their congruent because they have the same length and size they would be similar if they same length and different sizes

When we have right triangles, we described its sides as one hypothenuse and two legs.

In this case, "shorter sides" refes to the legs of the right triangle, which form the right angle that defined the triangle.

On the other hand, there are several ways to demonstrate the congruence between two right triangles. Those ways are called postulates or theorems, which are

Hypothenuse-Leg theorem: if we have two right triangles with congruent hypothenuses and one congruent pair of legs, then those triangles are congruent. Leg-Leg theorem: if we have two right triangle and they have two pair of corresponding leg congruent, then those triangles are congruent. Leg-Acute Angle theore: if we have one pair of corresponding legs congruent, and one pair of corresponding acute angles congruent, then those triangles are congruent. Hypothenuse-Acute Angle theorem: if we have one pair of hypothenuse congruent, and one pair of corresponding angles congruent, then those triangles are congruent.

All these theorems are they way to demonstrate the congruence between the given triangles.

In this case, those triangles are congruent by Leg-Leg theorem.