Prove: two right triangles are congruent if the hypotenuse and an acute angle of one is congruent to the corresponding parts of the other

Question

Geometry

Answer 1

given right triangle ABC with angle C=90º and hypotenuse AB

given right triangle DEF with angle F=90º and hypotenuse DE

Two triangles are congruent if 2 pairs of corresponding angles and a pair of opposite sides are equal. By opposite side I mean a side opposite either one of the angles but it has to be the same in both triangles.

∠C≅∠F   right angles are congruent because they all equal 90º

let ∠B≅∠E Given  (a pair of corresponding acute angles are ≅)

__  __

AB≅DE   Given ( hypotenuse segment AB, is congruent to hypotenuse segment DE)

ΔABC≅ΔDEF by AAS (angle, angle, side)

on a side note, ∠A≅∠D because all triangle contain 180º

angle A= angle D, segment AB= segment DE, and angle B= angle E

because of this you can say the triangles are congruent by ASA (angle, side, angle)