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if B=90 degrees, prove the congruence of the 2 triangles using any of the three different congruities

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GEOMETRY TRIANGLES

Nelly S. asked • 03/14/15

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

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Arthur D. answered • 03/14/15

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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)