Question

In correspondence of two right triangles, if their hypotenuses are congruent and one more side of one Triangle is congruent to the corresponding side of the Other the two triangles are congruent prove it.

Answer 1

the triangle have hypotenuse called as right angle triangle . so one angle is 90.Hence they are congruent by SAS rule

Answer 2

Answer:

Given: Two Right angled Triangles say ΔABC & ΔXYZ

           Hypotenuses are congruent.i.e, AC = XZ

           Corresponding pair of one side are congruent, say AB = XY

To Prove: ΔABC congruent to ΔXYZ

Figure is attached.

Let say ΔABC is right angled at ∠B and ΔXYZ is right angled at ∠Y

then,

In ΔABC  &  ΔXYZ

        AB   =   XY         (Given)

        AC   =   XZ         (Given)

        ∠B   =   ∠Y    =  90°          (Given)

⇒ΔABC ≅ ΔXYZ  by RHS Congruence criteria

because A Pair of corresponding sides are equal, Both hypotenuse are equal, And both has one right angle.

Hence Proved.