Quiz on Congruent and Similar Shapes

📚 Quick Study Guide

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• Congruent Shapes: Two shapes are congruent if they have the same size and shape. This means all corresponding sides and angles are equal.
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• Similar Shapes: Two shapes are similar if they have the same shape but can be different sizes. Corresponding angles are equal, and corresponding sides are in proportion.
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• Scale Factor: The ratio of the lengths of corresponding sides in similar figures is called the scale factor. If the scale factor is 1, the shapes are congruent.
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• Symbol for Congruence: The symbol $\cong$ means 'is congruent to'. For example, $\triangle ABC \cong \triangle XYZ$ means triangle ABC is congruent to triangle XYZ.
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• Symbol for Similarity: The symbol $\sim$ means 'is similar to'. For example, $\triangle ABC \sim \triangle XYZ$ means triangle ABC is similar to triangle XYZ.
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• Area and Similarity: If two figures are similar with a scale factor of $k$, then the ratio of their areas is $k^2$.
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• Volume and Similarity: If two solids are similar with a scale factor of $k$, then the ratio of their volumes is $k^3$.

🤔 Practice Quiz

1. What does it mean for two shapes to be congruent?
   1. They have the same shape.
   2. They have the same size.
   3. They have the same shape and size.
   4. They have different shapes but the same size.
2. If two triangles are similar, which of the following statements must be true?
   1. Their corresponding sides are equal.
   2. Their corresponding angles are equal.
   3. Their areas are equal.
   4. Their perimeters are equal.
3. What is the scale factor in similar figures?
   1. The ratio of their areas.
   2. The ratio of their volumes.
   3. The ratio of the lengths of corresponding sides.
   4. The sum of the lengths of their sides.
4. If two squares are similar, and the side length of the first square is 4 and the side length of the second square is 8, what is the scale factor?
   1. 1/2
   2. 2
   3. 4
   4. 8
5. If two cubes are similar with a scale factor of 3, what is the ratio of their volumes?
   1. 3
   2. 6
   3. 9
   4. 27
6. Triangle ABC has sides 3, 4, and 5. Triangle XYZ has sides 6, 8, and 10. Are they similar?
   1. No, because the sides are not equal.
   2. Yes, because the angles are the same.
   3. Yes, because the sides are in proportion.
   4. No, because they do not have the same area.
7. Which of the following transformations preserves congruence?
   1. Dilation
   2. Enlargement
   3. Reduction
   4. Rotation