Transformations and Reflections in Geometry

This lesson covers section 4.4 on congruence and transformations. It begins with defining congruent figures, which have the same size and shape but may be rotated or reflected. The lesson explains how transformations like rotation, reflection, and translation can map congruent figures onto each other. It introduces theorems for congruent transformations, focusing on composite reflections over parallel and intersecting lines. Examples illustrate how reflections over parallel lines result in translations, while reflections over intersecting lines result in rotations. The lesson concludes with a summary of these concepts.

What defines congruent figures?

• Same size but different shape

• Different size and shape

• Different size but same shape

• Same size and shape, possibly rotated or reflected

Which of the following is NOT a type of transformation?

• Dilation

• Rotation

• Reflection

• Translation

What is the rule for a 90-degree rotation?

• Change the sign of both x and y

• Switch x and y, change the sign of y

• Switch x and y, change the sign of x

• Keep x and y the same

What happens when you reflect over two parallel lines?

• The figure rotates

• The figure shrinks

• The figure translates

• The figure enlarges

How do you calculate the translation distance when reflecting over parallel lines?

• Three times the distance between the lines

• Twice the distance between the lines

• Half the distance between the lines

• The same as the distance between the lines

What is the result of reflecting over two intersecting lines?

• A reflection

• A translation

• A rotation

• A dilation

If a rotation of 158 degrees is achieved by two reflections, what is the angle between the intersecting lines?

• 67 degrees

• 134 degrees

• 158 degrees

• 79 degrees