Question

Suppose m∠ABH>m∠GHB in the figure below. What is an inequality that relates AH and GB?

Answer 1

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.

 

Learn more about sides and angles of a triangle on:

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