The figure below shows triangle nrm with r2 = m2 + n2:
triangle nrm has legs m and n, and r is the length of its longest side.
ben constructed a right triangle efd with legs m and n, as shown below:
triangle efd has legs m and n and hypotenuse f.
he made the following table to prove that triangle nrm is a right triangle:
statement reason
1. r2 = m2 + n2 given
2. f2 = m2 + n2 pythagorean theorem
3. f2 = r2 substitution
4. f = r ?
5. triangle nrm is congruent to triangle efd sss postulate
6. angle nrm is a right angle cpctc
7. triangle nrm is a right triangle angle nrm is a right angle
which reason best fits statement 4?
sas postulate
aas postulate
square root property of equality
triangle proportionality theorem

The correct answer is square root property of equality.

Step-by-step explanation:

Triangle NRM has legs m and n and r is the length of its longest side.

Ben constructed a right triangle EFD with legs m and n and hypotenuse f.

It means that both the triangles have legs with sides m and n beside that the third side of NRM is equal to the third side EFD, i.e ⇒ f =r(statement 4) which is proved by the square root property of equality.

Thus the correct option is  square root property of equality

Square Root Property of Equality

Step-by-step explanation:

If we have an equation with a perfect square on both sides , then Square Root Property of Equality says that we can take square root on both the sides to solve the equation and the equality remains same.

From the given proof , the statement 3. gives  

Then by applying Square Root Property of Equality, we can take square root on both sides, we get

which is the statement 4.

Hence, the correct answer is "Square Root Property of Equality".

answer: 590

step-by-step explanation: