Question

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 Square Root Property of Equality
5. Triangle NRM is congruent to triangle EFD ?
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 5?
SSS Postulate
SAS Postulate
AAA Postulate
AAS Postulate

Answer 1

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

and given that ⇒ r² = m² + n²
Ben constructed a right triangle EFD with legs m and n

so, both of the triangles NRM and EFD have legs with sides m and n

beside that the third side of NRM is equal to the third side EFD, i.e ⇒ r = f

which is proved from the statement number 4

So, the sides of the triangle NRM are congruent to the sides of triangle EFD


So, the reason which best fits statement 5 is ⇒
`\framebox {SSS \ Postulate}`

Answer 2

Option "SSS postulate" is correct.

Explanation:

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

and r² = m² + n².

Now, Ben constructed a right triangle EFD with legs m and n.

and in statement 4, it is proved that f=r.

So, all the three sides of the triangles NMR and EFD are congruent.

So, the triangles are congruent bt the SSS Postulate.

⇒ option "SSS postulate" is correct.