Question

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

Explanation:

Step1: Recall transformation - congruence relation

Two angles are congruent if one can be mapped onto the other through a sequence of rigid - motions (translations, rotations, and reflections). Translations slide an angle without changing its size or shape. Rotations turn an angle around a point without altering its measure. Reflections flip an angle over a line, also keeping its measure the same.

Step2: Apply to given angles

If we can translate one of the angles along a line (parallel to the lines in the sketch) so that its vertex and one of its sides coincide with the corresponding parts of the other angle, and then use a rotation (if needed) to make the other sides coincide, we can show the two angles are congruent. Or, if we can find a line of reflection that maps one angle onto the other, it also proves congruence.

Answer:

We can use translations to move one angle so that its vertex and a side match with the other angle. Then, if necessary, use a rotation to align the remaining sides. If there is a line of reflection that maps one angle onto the other, that also shows the two angles are congruent.