Question

1. when triangle abc is reflected across line ab, the image is triangle abd. why is angle acd congruent to angle adb?

a. corresponding parts of congruent figures are congruent.
b. congruent parts of congruent figures are corresponding.
c. segment ab is a perpendicular bisector of segment dc.
d. an isosceles triangle has a pair of congruent angles.
(from unit 2, lesson 1.)

Explanation:

When a figure is reflected, the original figure and its image are congruent. In this case, triangle \(ABC\) and triangle \(ABD\) are congruent (since reflection is a rigid - motion transformation that preserves shape and size). For congruent triangles, corresponding parts (angles and sides) are congruent. Angle \(ACD\) in triangle \(ABC\) and angle \(ADB\) in triangle \(ABD\) are corresponding angles.

Answer:

A. Corresponding parts of congruent figures are congruent.