Find the length of X and Y of these two right angled triangles (pictured) and prove their congruence, stating the rule.

(draws two right angled triangles, one with sides 3 and 4 units with the hypotenuse labelled 'x', one with a side labelled 4 units and 'Y' with the hypothenuse labelled 5 units).
The answer is in two parts. First, using Pythagorus' theorem find X and Y using the formula a^2 + b^2 = c^2.X = 5, Y = 3
Then, prove the triangles are congruent using the RHS rule. discuss how the SSS and SAS rules can also be easily used after the remaining sides have been discovered. Discuss how the ASA rule could also be used by calculating the angles with SOH CAH TOA.