Question

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list the side lengths of δcde in order from shortest to longest.
c
67z
d
51z
62z
e
□ < □ < □

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the angle, the longer the side opposite to it. So we first need to order the angles of \(\triangle CDE\) from smallest to largest.

The angles of \(\triangle CDE\) are \(\angle C = 67z\), \(\angle D=51z\), and \(\angle E = 62z\).

Compare the angle measures: \(51z<62z < 67z\), so \(\angle D<\angle E<\angle C\).

Step2: Determine the opposite sides

• The side opposite \(\angle D\) is \(CE\).
• The side opposite \(\angle E\) is \(CD\).
• The side opposite \(\angle C\) is \(DE\).

Since \(\angle D<\angle E<\angle C\), by the side - angle relationship in a triangle (larger angle corresponds to longer opposite side), we have \(CE < CD

Answer:

\(CE < CD