Question

5 - 3 & 5 - 5 practice
nequalities in one triangle; triangle inequality
use the figure at the right to determine the relationship between
the measures of the given angles.

1. ( mangle qrw )__( mangle rwq ) 2. ( mangle rtw )__( mangle twr )
2. ( mangle rst )__( mangle trs ) 4. ( mangle wqr )__( mangle qrw )

use the figure at the right to determine the relationship between
the lengths of the given sides.

1. ( overline{dh} )__( overline{gh} ) 6. ( overline{de} )__( overline{dg} )
2. ( overline{eg} )__( overline{fg} ) 8. ( overline{de} )__( overline{eg} )

Explanation:

Step1: Use the triangle - angle relationship (larger side opposite larger angle)

For \(m\angle QRW\) and \(m\angle RWQ\) in \(\triangle QRW\), since \(QW = 45\) and \(QR = 47\), and in a triangle, the larger side is opposite the larger angle.

Step2: Compare the sides

In \(\triangle QRW\), \(QR>QW\). So, the angle opposite \(QR\) (\(\angle RWQ\)) and the angle opposite \(QW\) (\(\angle QRW\)).

Answer:

\(m\angle QRW