Question

Based on △GHI below, which of the following inequalities is true?

Answer 1

C.
`\overline{GI} < \overline{GH} < \overline{HI}`

Explanation:

In a triangle, the longest side is opposite to the largest measure of angle. The medium side is opposite to the medium angle, while the shortest side is opposite to the smallest angle.

In ∆GHI,

✍️m<G = 95°, it is opposite to
`\overline{HI}`

<G is the largest angle, therefore,
`\overline{HI}` is the longest side.

✍️m<I = 180 - (95 + 38) = 47°.

<I is opposite to
`\overline{GH}`

<I is the medium angle, therefore,
`\overline{GH}` is the medium side.

✍️m<H = 38°, it is opposite to
`\overline{GI}`

<h is the smallest angle, therefore,
`\overline{GI}` is the shortest side.

✅This means:

`\overline{GI} < \overline{GH} < \overline{HI}`