Question

7-6. the two triangles below are congruent. describe a sequence of rigid transformations that maps one onto the other. write a congruence statement relating the triangles. (there are two triangles with labeled sides and angles: one with vertices e, v, w and another with vertices x, z, y, with side lengths 110, 280, 240 and angle 110° shown.)

Explanation:

Step1: Analyze the transformation

First, observe the orientation of the triangles. Notice that a rotation is needed. Rotate \(\triangle VWZ\) \(90^{\circ}\) clockwise around the appropriate point (or you can consider the general rotation concept to align the sides and angles). Then, since the triangles may not be in the exact position after rotation, a translation (sliding) is required. Translate (slide) the rotated \(\triangle VWZ\) to map it onto \(\triangle XZY\).

Step2: Write the congruence statement

When writing the congruence statement, match the corresponding vertices. If we assume the correspondence based on side - length and angle - measure matching (since \(VW = XZ=110\), \(WZ = ZY = 240\), \(VZ=XY = 280\)), the congruence statement is \(\triangle VWZ\cong\triangle XZY\)

Answer:

A sequence of rigid transformations is a rotation (e.g., \(90^{\circ}\) clockwise) followed by a translation. The congruence statement is \(\triangle VWZ\cong\triangle XZY\)