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Nikki is going to use SSS to prove that triangle PQR is congruent to triangle SQR.

Which of these is a necessary step in Nikki's proof?

A. Prove that \(\angle PQR \cong \angle SQR\) by vertical angles.

B. Prove that \(\overline{PQ} \cong \overline{QR}\) by CPCTC.

C. Prove that \(\overline{QR} \cong \overline{QR}\) by the reflexive property.

D. Prove that \(\angle QPR \cong \angle QSR\) by the transitive property.

Answer :

Prove that QR QR by the reflexive property.

The triangles are congruent by reflexive property of SSS

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be ΔPQR

Let the second triangle be ΔQRS

And , the side QR is the common side

Now , measure of side PQ = measure of side QS

And , measure of side PR = measure of side RS

So , the three sides are equal (SSS: side, side, side) and they are congruent triangles

And , QR ≈ QR by the reflexive property.

Hence , the triangles are congruent by SSS

To learn more about congruent triangles click :

https://brainly.com/question/26131452

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The complete question is attached below :

Nikki is going to use SSS to prove that PQR SQR.

Which of these is a necessary step in Nikki's proof?

A.

Prove that PQR SQR by vertical angles.

B.

Prove that PQ QR by CPCTC.

C.

Prove that QR QR by the reflexive property.

D.

Prove that QPR QSR by the transitive property.

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