Question

applying the converse of the hinge theorem
given ( gk = xz ) and ( gh = xy ), which statement must be true?
( hk = yz )
( hg = xz )
( mangle g>mangle x )
( mangle g<mangle x )

Explanation:

Step1: Recall the Converse of the Hinge Theorem

The Converse of the Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is shorter than the third side of the second triangle, then the included angle of the first triangle is smaller than the included angle of the second triangle.

Step2: Analyze the given side lengths

We are given \(GK = XZ\) and \(GH=XY\). The third - side lengths are \(HK = 21\) cm and \(YZ = 26\) cm. So, \(HK

Step3: Apply the Converse of the Hinge Theorem

By the Converse of the Hinge Theorem, since \(GK = XZ\), \(GH = XY\), and \(HK

Answer:

\(m\angle G < m\angle X\)