Given that m∠ABH > m∠GHB, the inequality that relates AH and GB based on the relationship between the angles and sides of a triangle is: AH > BG.
Recall:
- The relationship between the sides and angles of a triangle is such that the size of an angle is relative to the length of the side it is directly opposite to.
- This means, the biggest angle measure will be opposite to the longest side, and vice versa in the triangle.
Given the image attached below where,
m∠ABH > m∠GHB
∠ABH is directly opposite side AH
∠GHB is directly opposite to side GB
- Since m∠ABH > m∠GHB, the inequality that relates AH and GB based on the relationship between the angles and sides of a triangle is: AH > BG.
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