Showing Congruence through Sequences of Transformations

The video tutorial explains how to determine if two figures are congruent using sequences of transformations. It covers rigid transformations, including rotations, reflections, and translations, which preserve size and shape. The tutorial demonstrates congruence between figures D and B, and figures F and A, using various transformation sequences. It emphasizes that multiple sequences can achieve the same result, encouraging viewers to explore different methods.

Which of the following transformations does NOT change the size and shape of a figure?

• Translation

• Shearing

• Reflection

• Scaling

What sequence of transformations was used to show that figure D is congruent to figure B?

• A 90-degree clockwise rotation and a translation

• A reflection over the x-axis and a translation

• A reflection over the y-axis and a rotation

• A 90-degree counterclockwise rotation and a translation

Why was the initial attempt to demonstrate congruence between figure D and figure B unsuccessful?

• The figures were not the same shape

• The sequence of transformations did not align the figures

• The transformations used were not rigid

• The figures were not the same size

What was the final sequence of transformations used to demonstrate congruence between figure F and figure A?

• A reflection over the x-axis, a 180-degree rotation, and a translation

• A reflection over the y-axis, a reflection over the x-axis, and a 90-degree counterclockwise rotation

• A 90-degree clockwise rotation and a translation

• A reflection over the y-axis and a 180-degree rotation

What is a common misunderstanding about demonstrating congruence through transformations?

• That congruence requires changing the orientation of figures

• That transformations change the size of figures

• That only one sequence of transformations can demonstrate congruence

• That congruence can only be shown through reflections