Question

i can verify by measuring and comparing the properties of rotated, reflected or translated geometric figures. (8.g.a.1a, 8.g.a.1b) 4.a figure efgh an image of figure abcd after a rotation using center p. explain your reasoning with math vocabulary.

Explanation:

Step1: Recall rotation property

In a rotation, the pre - image and image are congruent. This means corresponding sides are equal in length and corresponding angles are equal in measure. For figure \(ABCD\) rotated about point \(P\) to get figure \(EFGH\), we know that \(AB = EF\), \(BC=FG\), \(CD = GH\), \(DA=HE\) and \(\angle A=\angle E\), \(\angle B=\angle F\), \(\angle C=\angle G\), \(\angle D=\angle H\).

Step2: Use congruence vocabulary

We can say that figure \(EFGH\) is congruent to figure \(ABCD\) because a rotation is a rigid transformation. Rigid transformations preserve the size and shape of the figure. The distance from the center of rotation \(P\) to each corresponding point on the pre - image and image is the same. For example, the distance from \(P\) to \(A\) is equal to the distance from \(P\) to \(E\), the distance from \(P\) to \(B\) is equal to the distance from \(P\) to \(F\), and so on.

Answer:

Figure \(EFGH\) is congruent to figure \(ABCD\) because a rotation is a rigid transformation which preserves side - lengths and angle - measures. The distances from the center of rotation \(P\) to corresponding points on \(ABCD\) and \(EFGH\) are equal.