SOLUTION: prove hypotenuse-leg therom
Algebra.Com
Question 698039: prove hypotenuse-leg therom
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Two ways to go about it.
1. Construct the second triangle adjacent to the first so that the two legs are coincident. This produces an isosceles triangle where the hypotenuse of the first triangle is one of the congruent sides of the isosceles triangle and the hypotenuse of the other is the other congruent side. The coincident legs are the altitude. There is a theorem (look it up) that says the altitude to the vertex of an isosceles triangle divides the triangle into two congruent triangles.
2. Use the Pythagorean theorem. If you have two right triangles with sides a, b, c (c the hypotenuse) and d, e, f (f the hypotenuse) and you know that a = d and c = f, then with Pythagoras you can show that 
and 
. But by substitution, 
. So 
which implies that 
. Therefore the triangles are congruent by SSS.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
This is a Pythagoreans Therom problem.
A right triangle has one leg that is 5cm longer (answered by checkley77)
leg a: 10cm
hypotenuse: 8cm
leg b: ? (answered by Alan3354)
leg = 6,hypotenuse = 10
leg = 30,leg =... (answered by arallie)
Prove that two right triangles are congruent if a leg and the altitude to hypotenuse of... (answered by math_helper)
In this problem I need help with finding two sides of a right triangle. One of the... (answered by KMST)
what is the answer to leg:15m hypotenuse:17m... (answered by Fombitz)
hypotenuse c =17, leg a= 8 what is leg... (answered by algebrahouse.com)
leg A 15
Leg B x
Hypotenuse... (answered by jim_thompson5910)
First leg 14
Second leg x
Hypotenuse... (answered by Fombitz,Boreal,addingup)
