SOLUTION: Show that for two right angles, if the hypotenuse and leg of one are congruent to the hypotenuse and the leg of the other, then the two triangles are congruent.

Click here to see ALL problems on Triangles

Question 26341: Show that for two right angles, if the hypotenuse and leg of one are congruent to the hypotenuse and the leg of the other, then the two triangles are congruent.
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
Show that for two right angles, if the hypotenuse and leg of one are congruent to the hypotenuse and the leg of the other, then the two triangles are congruent.
YOU CAN USE PYTHOGARUS THOREM TO PROVE THAT SECOND LEGS OF THE 2 TRIANGLES ARE EQUAL.AND HENCE ALL 3 SIDES OF ONE TRIANGLE ARE EQUAL TO THE CORRESPONDING SIDES OF THE SECOND TRIANGLE HENCE BY SSS THEOREM THEY ARE CONGRUENT. NOTE THAT SAS IS ALSO HOLDING NOW AS WE HAVE PROVED THAT THE 2 LEGSF RIGHTANGLE IN ONE TRIANGLE ARE EQUAL TO 2 LEGS OF RIGHT ANGLE IN ANOTHER.
IF ABC AND DEF ARE THE 2 TRIANGLES WITH
ANGLE ABC =ANGLE DEF =90
AC = HYPOTENUSE = DF AND
ONE LEG AB = DE ,WE HAVE BY PYTHOGARUS THEOREM
BC^2=AC^2-AB^2=DF^2-DE^2=EF^2
BC=EF
SO USING SSS THE 2 TRIANGLES ARE CONGRUENT