Question

triangle fde has these angle measures:

\\(m\angle f = 60^{\circ}\\)
\\(m\angle d = 70^{\circ}\\)

order the sides of triangle fde from longest to shortest.

drag each tile to the correct box.

Explanation:

Find the third angle measure

We use the Triangle Angle Sum Theorem to find \(m\angle E\).

$$ m\angle F + m\angle D + m\angle E = 180^\circ $$

$$ 60^\circ + 70^\circ + m\angle E = 180^\circ $$

$$ m\angle E = 50^\circ $$

Order the angles from largest to smallest

We compare the three angle measures.

$$ 70^\circ > 60^\circ > 50^\circ $$

$$ m\angle D > m\angle F > m\angle E $$

Apply the side-angle relationship

Using the Side-Angle Relationship, the longest side is opposite the largest angle.

• Opposite to \(\angle D\) is side \(FE\).
• Opposite to \(\angle F\) is side \(DE\).
• Opposite to \(\angle E\) is side \(FD\).

Therefore, the sides ordered from longest to shortest are \(FE\), \(DE\), \(FD\).

Answer:

Order the sides of triangle FDE from longest to shortest:
<blank>\(FE\)</blank> , <blank>\(DE\)</blank> , <blank>\(FD\)</blank>