Question

a. draw a segment in figure abcde to create a quadrilateral. draw the image of the segment when rotated 90° counter - clockwise around point a.
a. write a congruence statement for the quadrilateral you created in figure abcde and the image of the quadrilateral in figure mnpqr.

Explanation:

Step1: Draw the segment

Draw a segment in figure \(ABCDE\) to form a quadrilateral, for example, connect two non - adjacent vertices. To find its \(90^{\circ}\) counter - clockwise rotation around point \(A\), use the rule for rotation of a point \((x,y)\) counter - clockwise about the origin \((0,0)\) which is \((x,y)\to(-y,x)\). When rotating about point \(A(x_A,y_A)\), first translate the figure so that \(A\) is at the origin, perform the rotation, and then translate back.

Step2: Write the congruence statement

If the original quadrilateral is \(ABCD\) and its rotated image is \(A'B'C'D'\), the congruence statement is based on the fact that a rotation is a rigid transformation. A rigid transformation preserves side lengths and angle measures. So, if the original quadrilateral is \(Q_1\) and the rotated quadrilateral is \(Q_2\), the congruence statement is \(Q_1\cong Q_2\) since \(AB = A'B'\), \(BC=B'C'\), \(CD = C'D'\), \(DA=D'A'\) and \(\angle A=\angle A'\), \(\angle B=\angle B'\), \(\angle C=\angle C'\), \(\angle D=\angle D'\)

Answer:

a. Follow the rotation rules to draw the segment's rotated image.
b. If the original quadrilateral is \(Q_1\) and the rotated one is \(Q_2\), \(Q_1\cong Q_2\)