Question

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

Explanation:

Step1: Analyze given sides

We know \( HG = MP \), \( GK = PN \), \( HK = 15 \) mm, \( MN = 11 \) mm. Since \( HK>MN \), by the Hinge Theorem (if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer, then the included angle of the first triangle is larger). The included angle for \( HK \) is \( \angle G \), and for \( MN \) is \( \angle P \).

Step2: Apply Hinge Theorem

So, \( m\angle G>m\angle P \) because \( HK > MN \) and \( HG = MP \), \( GK = PN \). Now check other options: \( HK
eq MN \) (15≠11), \( HG = MP \) not \( PN \), and \( m\angle P>m\angle G \) is false.

Answer:

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