Proving Triangles Congruent

[vampirewitchreine]

Name a pair of overlapping congruent triangles. Tell which method you can use to prove the triangles congruent.

(Blue is everything that I worked out by the given)

Given: line AD is congruent to line BC
line AB is perpendicular to line BC
line AB is perpendicular to line DA


I know that the 2 triangle must be right triangles and that my 2 triangles are ▲DAB and ▲CBA. This means that because AB and BA are overlapping that they must be the same length due to the reflexive property. What I'd need help with is what theorem I can use for proving the triangles congruent when the hypotenuses are not proven to be congruent.

 

[tkhunny]

Two ways come immediately to mind.

1) Since you seem to like the hypotenuse, calculate it using the Pythagorean Theorem and see that they are congruent.

2) Why bother with the hypotenuse? Don't you have a Side-Angle-Side Theorem? This gives congruent triangles and establishes congruent hypotenuses.