Question

triangles
in the triangles, ( hg = mp ) and ( gk = pn ).
which statement about the sides and angles is true?
( hk = mn )
( hg = pn )
( mangle p>mangle g )
( mangle g>mangle p )

Explanation:

Step1: Apply the Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
In \(\triangle HGK\) and \(\triangle MPN\), \(HG = MP\), \(GK=PN\), and \(HK = 15\space mm\), \(MN=11\space mm\). So \(HK>MN\).

Step2: Compare the angles

Since \(HK>MN\), by the Hinge Theorem, \(m\angle G>m\angle P\).

Answer:

\(m\angle G > m\angle P\)