Congruence Through Transformations

Congruence Through Transformations

Congruent figures have the same size and shape. In transformation problems, you often prove congruence by showing that one figure can be moved onto the other using rigid transformations. Rigid transformations preserve distances and angle measures, so the image stays congruent to the original.

1) Identify the transformation(s)

Look for a translation, rotation, reflection, or a combination of these. Read the directions carefully:

• Translation: slide a figure.
• Rotation: turn a figure around a point.
• Reflection: flip across a line.

2) Track corresponding points

Match each vertex of the original figure with the correct vertex of the image. Keep the order consistent so side lengths and angles line up correctly.

3) Apply the transformation step by step

If more than one move is needed, do them in the given order. A common mistake is reversing the order or using the wrong center, line, or direction.

4) Simplify the final answer

Write the final coordinates, expression, or congruence statement in simplest form. If asked for a description, name each transformation clearly.

Check your work

Verify that corresponding side lengths and angles match after the transformation. If the image can be placed exactly on top of the original without stretching or resizing, the figures are congruent.