Question

Determine the shortest segment in △ PQS and △ QRS. Remember that a segment is named by its endpoints (two letters).

Answer 1

Answer: QS and QR are the shortest segment of the triangle ΔPQS, and ΔSQR respectively.

Step-by-step explanation:

Since we have given that

ΔPQS, and ΔSQR,

Consider, ΔPQS,

As we know that " the length opposite to the largest angle is the shortest segment."

So, According to the above statement.

$\angle QPS=63\textdegree\\\\\text{So, QS is the shortest segment of this triangle}$

Similarly,

Consider, ΔSQR,

Again applying the above statement, we get that,

$\angle QSR=75\textdegree\\\\\text{ So, QR is the shortest segment of this triangle}$

Hence, QS and QR are the shortest segment of the triangle ΔPQS, and ΔSQR respectively.