It is given that QR is congruent to PQ, that RS is congruent to PQ, that QR=2x+5, and that RS=10-3x.
Statement1)& QR≅ PQ, RS≅ PQ,
& QR= 2x+5, RS= 10-3x Reason1)& Given
Since both QR and RS are congruent to PQ, by the Transitive Property of Congruence QR and RS are also congruent segments.
Statement2)& QR≅ RS Reason2)& Transitive Property of Congruence
Recall that two segments are congruent if and only if they have the same length. Therefore, since QR and RS are congruent segments, we know that they have the same length.
Statement3)& QR= RS Reason3)& Definition of Congruent Segments
Finally, the value of x can be found by using the Properties of Equality.
