Question

Will Give Brainlyest!

Answer 1

Answer:

The two triangles EFD and NRM are congruent by SSS Postulate.

Step-by-step explanation:

Given  a right triangle EFD with legs m and n and a right angled triangle NRM.  Triangle NRM is congruent to triangle EFD. we have to tell which best fit for the above statement.

In triangle EFD and NRM

m=m       (Given)

n=m        (Given)

r=f           (By Pythagoras theorem)

It gives all the sides equal. Hence, by SSS Postulate which states that if three sides of two triangles are congruent then these two triangles are congruent.

∴ SSS postulate best fit for the statement "Triangle NRM is congruent to triangle EFD."

Answer 2

Answer:

Step-by-step explanation:

The figure shows that $r^{2}=m^{2}+n^{2}$ in triangle NRM.

In order to make NRM a right triangle, following steps are done:

1. $r^{2}=m^{2}+n^{2}$ (Given)

2.  $f^{2}=m^{2}+n^{2}$ (By the pythagorean theorem in triangle EFD)

3. From the steps one and two, the RHS is equal, therefore $f^{2}=r^{2}$ by substitution property.

4. Now, f=r by the square root property.

5. Now, As $r^{2}=m^{2}+n^{2}$ and $f^{2}=m^{2}+n^{2}$ and f=r, therefore, by SSS postulate , ΔNRM ≅ ΔEFD.

6. By CPCTC, angle NRM is a right angle.