Question

1. in the triangle pqr, pq = 7, qr = 8, pr = 14. which is the largest angle?

∠qpr
∠prq
∠pqr
this cannot be determined.

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the largest angle is opposite the longest side. This is a fundamental property of triangles in geometry.

Step2: Identify the longest side

Given the sides of triangle \(PQR\): \(PQ = 7\), \(QR=8\), and \(PR = 14\). By comparing the lengths \(7\), \(8\), and \(14\), we can see that \(PR = 14\) is the longest side.

Step3: Find the angle opposite the longest side

The angle opposite side \(PR\) in triangle \(PQR\) is \(\angle PQR\) (because in triangle \(PQR\), side \(PR\) is opposite angle \(Q\), i.e., \(\angle PQR\)). So, according to the angle - side relationship, \(\angle PQR\) is the largest angle.

Answer:

\(\angle PQR\) (the option corresponding to \(\angle PQR\))