Lecture on Determining Similarity of Shapes

Introduction

• Explanation of how to determine if two shapes are similar.
• Focus on comparing a pair of triangles and rectangles.

Example 1: Triangles

1. Given: Two Triangles
   • Triangle 1: Base = 8, Height = 12
   • Triangle 2: Base = 6, Height = 9
2. Method 1: Ratio of Corresponding Sides
   • Compare heights:
     • Ratio: 12 (larger triangle height) to 9 (smaller triangle height)
     • Simplify ratio: 12/9 = 4/3 (scaling up) or 3/4 (scaling down)
   • Compare bases:
     • Ratio: 8 (base of larger triangle) to 6 (base of smaller triangle)
     • Simplify: 8/6 = 4/3
   • Conclusion: Both heights and bases have the same ratio, hence similar triangles.
3. Method 2: Proportion
   • Set up proportion with heights and bases:
     • 12/9 = 8/6
   • Cross-multiply to confirm similarity:
     • 9 * 8 = 72, 6 * 12 = 72
   • Conclusion: Similar triangles.
4. Method 3: Mental Math
   • Simplify in mind: 9/12 = 3/4 and 6/8 = 3/4
   • Conclusion: Similar triangles.
5. Method 4: Base to Height Ratio
   • Compare within each triangle:
     • 8/12 = 6/9
   • Cross-multiply:
     • 12 * 6 = 72, 8 * 9 = 72
   • Conclusion: Similar triangles.

Example 2: Rectangles

1. Given: Two Rectangles
   • Rectangle 1: Side = 8 cm, Corresponding side = 12 cm
   • Rectangle 2: Side = 7 cm, Corresponding side = 10 cm
2. Checking Similarity
   • Initial ratio: 8/7
   • Check against ratio: 12/10
   • Cross-multiply:
     • 8 * 10 = 80, 7 * 12 = 84
   • Conclusion: Rectangles are not similar.
3. Verification: Base to Height Comparison
   • Compare within rectangles:
     • 8/12 vs 7/10
   • Cross-multiply:
     • 8 * 10 = 80, 7 * 12 = 84
   • Conclusion: Not similar.

Conclusion

• Summary of methods to determine similarity between shapes.
• Understanding of ratios and proportions is key.
• Call to action: Subscribe for more math tutorials.

Presenter: Shane Masonette Channel: Masonette Math