Question

essay 14 points. explain why pentagon abcde is congruent to fghij.

Explanation:

Step1: Check side - length equality

By counting the grid units, we find that \(AB = 4.1\), \(BC=2.8\), \(CD = 2.2\), \(DE=1.4\), \(EA = 3.2\) in pentagon \(ABCDE\) and \(FG = 4.1\), \(GH=3.2\), \(HI = 1.4\), \(IJ=2.2\), \(JF = 2.8\) in pentagon \(FGHIJ\). So, corresponding sides are equal.

Step2: Check angle - measure equality

We see that \(\angle A=162^{\circ}\), \(\angle B = 108^{\circ}\), \(\angle C=117^{\circ}\), \(\angle D = 94^{\circ}\), \(\angle E=59^{\circ}\) in pentagon \(ABCDE\) and the corresponding angles in pentagon \(FGHIJ\) (by matching the vertices of congruent - side pairs) have the same measures.

Answer:

Pentagon \(ABCDE\) is congruent to pentagon \(FGHIJ\) because all corresponding sides are equal in length and all corresponding angles are equal in measure.