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Will Give Brainlyest!



The figure below shows triangle NRM with r2 = m2 + n2:


Ben constructed a right triangle EFD with legs m and n, as shown below:





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? (6 points)
Select one:
a. SSS Postulate
b. SAS Postulate
c. AAA Postulate
d. AAS Postulate

Will Give Brainlyest The figure below shows triangle NRM with r2 m2 n2 Ben constructed a right triangle EFD with legs m and n as shown below He made the followi class=
Will Give Brainlyest The figure below shows triangle NRM with r2 m2 n2 Ben constructed a right triangle EFD with legs m and n as shown below He made the followi class=

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Answer:


Step-by-step explanation:

The figure shows that [tex]r^{2}=m^{2}+n^{2}[/tex] in triangle NRM.

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

1. [tex]r^{2}=m^{2}+n^{2}[/tex] (Given)

2.  [tex]f^{2}=m^{2}+n^{2}[/tex] (By the pythagorean theorem in triangle EFD)

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

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

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

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

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."




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