Question

synthesis
how can you use transformations to show that two angles are congruent?
use the sketch tool if it helps with your thinking.

Explanation:

Step1: Define congruent angles

Two angles are congruent if they have the same measure.

Step2: Recall transformation types

Transformations include translations, rotations, and reflections.

Step3: Explain translation

A translation moves an angle without changing its orientation or measure. If one angle can be translated to coincide with another, they are congruent.

Step4: Explain rotation

A rotation turns an angle around a point. If an angle can be rotated to match another angle exactly, they are congruent.

Step5: Explain reflection

A reflection flips an angle over a line. If an angle can be reflected to fit exactly over another angle, they are congruent. In all these cases, the measure of the angle is preserved, showing congruence.

Answer:

You can use translations, rotations, or reflections. If one angle can be translated, rotated, or reflected to coincide exactly with another angle, then the two angles are congruent because these transformations preserve angle - measure.