Question

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

Explanation:

Step1: Recall converse of Hinge Theorem

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.
We have \(GK = XZ\), \(GH=XY\), and \(HK = 21\mathrm{cm}\), \(YZ = 26\mathrm{cm}\), so \(HK

Step2: Determine the relationship between angles

By the converse of the Hinge Theorem, the angle opposite \(HK\) in \(\triangle GHK\) (\(\angle G\)) and the angle opposite \(YZ\) in \(\triangle XYZ\) (\(\angle X\)) have the relationship \(m\angle G

Answer:

\(m\angle G