Question

A d + b = 180

B. C + b = d + c

C. Reflect across line CE. Then, angle CBD is the image of angle EBA.

D. Rotate 180 degrees using center B. Then, angle CBD is the image of angle EBA.


E. Reflect across the angle bisector of angle ABC. Then, angle CBD is the image of angle ABE.

Answer 1

I know B is true, but i’m unsure for the other choices.

Answer 2

The best answer is C. Reflect across line CE. Then, angle CBD is the image of angle EBA.

A. d + b = 180°: This is true for any supplementary angles, but it does not tell us anything about the specific relationship between angles CBD and EBA.

B. C + b = d + c: This is true because angles CBD and EBA are alternate interior angles.

However, it does not tell us that angle CBD is the image of angle EBA under a reflection across line CE.

C. Reflect across line CE.

Then, angle CBD is the image of angle EBA.

This is true because a reflection across a line preserves the measure of angles.

D. Rotate 180 degrees using center B.

Then, angle CBD is the image of angle EBA.

This is not true because a rotation does not preserve the orientation of angles.

E. Reflect across the angle bisector of angle ABC.

Then, angle CBD is the image of angle ABE.

This is not true because a reflection across the angle bisector of an angle does not preserve the measure of angles.

Therefore, the only statement that is true is C. Reflect across line CE. Then, angle CBD is the image of angle EBA.

As you can see, the angle measures of angles EBA and CBD are the same, and they are on opposite sides of line CE.

This is what it means for an angle to be the image of another angle under a reflection.