congruence and similarity real world examples grade 8

📚 Quick Study Guide

• 📐 Congruent Figures: Figures that have the same size and shape. All corresponding sides and angles are equal. Think of identical twins!
• 📏 Similar Figures: Figures that have the same shape but may have different sizes. Corresponding angles are equal, and corresponding sides are proportional. Imagine a photo and its smaller print.
• 比例 Proportionality: The relationship between two ratios that are equal. For example, if two triangles are similar, the ratio of their corresponding sides will be the same.
• 🔍 Scale Factor: The ratio used to enlarge or reduce a figure to create a similar figure. If the scale factor is 1, the figures are congruent!
• 💡 Symbol for Congruence: $\cong$ (equal sign with a tilde above).
• 📝 Symbol for Similarity: $\sim$ (a tilde).

🧪 Practice Quiz

1. Which of the following is an example of congruent figures in the real world?
   1. A map and the actual area it represents.
   2. A photograph and a smaller copy of the same photograph.
   3. Two identical stamps from the same sheet.
   4. A globe and a basketball.
2. Two triangles are similar. The sides of the smaller triangle are 3, 4, and 5. The longest side of the larger triangle is 10. What is the length of the shortest side of the larger triangle?
   1. 5
   2. 6
   3. 8
   4. 10
3. Which statement is true about similar figures?
   1. Corresponding angles are always different.
   2. Corresponding sides are always congruent.
   3. Corresponding sides are proportional.
   4. They must be the same size.
4. A building is 50 feet tall and casts a shadow of 20 feet. A nearby tree casts a shadow of 8 feet. Assuming the angle of the sun is the same, how tall is the tree?
   1. 10 feet
   2. 20 feet
   3. 25 feet
   4. 40 feet
5. Which of the following transformations always produces a congruent figure?
   1. Dilation
   2. Reduction
   3. Enlargement
   4. Translation
6. If two rectangles are similar, and the first rectangle has dimensions 4x6, which of the following could be the dimensions of the second rectangle?
   1. 6x8
   2. 8x10
   3. 8x12
   4. 10x14
7. Two circles are always:
   1. Congruent
   2. Similar
   3. Equal
   4. The same