Question

activity 2: are these parts congruent?
here is a diagram with two triangles and two polygons. use this diagram to complete problems 1 and 2.

1. triangle abd is a rotation of triangle cdb

around point e by 180°.
is angle adb congruent to angle cdb?
choose:
yes! explain your
reasoning.
no! name the angle that
is congruent to angle
adb.

Explanation:

When a figure is rotated \(180^{\circ}\) around a point, the resulting figure (image) is congruent to the original figure (pre - image). Congruent triangles have congruent corresponding parts. Since \(\triangle ABD\) is a rotation of \(\triangle CDB\) around point \(E\) by \(180^{\circ}\), \(\triangle ABD\cong\triangle CDB\). The corresponding angle to \(\angle ADB\) in \(\triangle CDB\) is \(\angle CBD\) (by the property of congruent triangles: corresponding angles of congruent triangles are congruent).

Answer:

NO. The angle that is congruent to \(\angle ADB\) is \(\angle CBD\).