given line segment PQ , PQ=3QR, and QR= 1/3 RS Prove: line segment PQ is congruent to line segment RS

QR = 1/3 RS

so
RS = 3 QR
but
PQ = 3 QR

so,
PQ = RS
and the line segments are congruent

Rs

To prove that line segment PQ is congruent to line segment RS, we will use the given information and the properties of congruent line segments.

First, we are given that PQ = 3QR. Let's substitute this value into the expression for QR:

QR = (1/3)RS

Since PQ = 3QR, we can substitute PQ with 3QR:

PQ = 3(1/3)RS

Simplifying this expression, we get:

PQ = RS

Therefore, we have shown that line segment PQ is congruent to line segment RS based on the given information and substitution.