Question

in the figure, \\( \overline { a b } \\) is parallel to \\( \overline { d e } \\).
select from the drop - down menu to correctly complete the
statement.
triangle \\( a b c \\) and triangle \\( d e c \\) are choose...

Explanation:

Step1: Find the measure of angle \(A\)

Since the sum of angles in a triangle is \(180^{\circ}\) and \(\angle B = 72^{\circ}\), \(\angle ACB=60^{\circ}\), then \(\angle A=180^{\circ}-\angle B - \angle ACB\).

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Because \(AB\parallel DE\), \(\angle A=\angle D\) (alternate - interior angles) and \(\angle B=\angle E\) (alternate - interior angles). Also, \(\angle ACB=\angle DCE\) (vertically - opposite angles).

Step2: Use the AA (Angle - Angle) similarity criterion

Two triangles are similar if two pairs of corresponding angles are equal. In \(\triangle ABC\) and \(\triangle DEC\), \(\angle A=\angle D\), \(\angle B=\angle E\) and \(\angle ACB=\angle DCE\). By the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle DEC\).

Answer:

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