Congruent vs. similar figures after transformations: Grade 8 explanation.

📚 Understanding Congruent vs. Similar Figures After Transformations

Transformations in geometry change the position or size of a figure. The key difference between congruent and similar figures lies in whether the size changes during the transformation.

📐 Congruent Figures

Congruent figures are exactly the same – same size and shape. Transformations that produce congruent figures are called rigid transformations. These include translations, rotations, and reflections.

• ➡️ Translation: Sliding a figure without changing its size or shape. Imagine moving a puzzle piece across the table.
• 🔄 Rotation: Turning a figure around a fixed point. Think of spinning a wheel.
• mirror Reflection: Flipping a figure over a line. Like seeing your image in a mirror.

If figure A is transformed into figure B using only translations, rotations, and reflections, then figure A and figure B are congruent. We write this as $A \cong B$.

✨ Similar Figures

Similar figures have the same shape but can be different sizes. Transformations that produce similar figures include rigid transformations (translations, rotations, reflections) and dilations.

• 🔍 Dilation: Enlarging or reducing a figure by a scale factor. Imagine zooming in or out on a picture on your phone.

If figure A is transformed into figure B using translations, rotations, reflections, and dilations, then figure A and figure B are similar. We write this as $A \sim B$.

📝 Key Differences Summarized

Here's a table to help you remember:

✍️ Examples

• 🌍 A square with side length 5 cm is translated 3 cm to the right. The new square is congruent to the original.
• 📈 A triangle is rotated 90 degrees clockwise and then dilated by a scale factor of 2. The new triangle is similar to the original.