Question

in the triangles, $overline{gk}congoverline{pn}$ and $overline{hg}congoverline{mp}$. which statement correctly compares the angles? angle g is congruent to angle p. angle g is smaller than angle p. angle g is larger than angle p. angle g is congruent to angle n.

Explanation:

Step1: Recall the 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 know that $\overline{GK}\cong\overline{PN}$ and $\overline{HG}\cong\overline{MP}$, and $HK = 32$ cm, $MN=40$ cm. Since $HK

Step2: Identify the included angles

The included angle for sides $\overline{HG}$ and $\overline{GK}$ in $\triangle HGK$ is $\angle G$, and the included angle for sides $\overline{MP}$ and $\overline{PN}$ in $\triangle MPN$ is $\angle P$.
By the hinge - theorem, since $HK < MN$, angle $G$ is smaller than angle $P$.

Answer:

Angle G is smaller than angle P.