Lecture on Similar Shapes

Introduction to Similar Shapes

• Similar shapes have the same shape but different sizes.
• Visual inspection can suggest similarity, but certainty requires comparing angles.
• Identical angles in two shapes confirm they are similar.

Exam Questions on Similar Shapes

• Exams may confirm shapes are similar and ask to find unknown side lengths.

Finding the Scale Factor

• Definition: Scale factor is how many times bigger one shape is compared to another.
• Example Calculation:
  • Compare equivalent sides.
  • If one side is 6cm and its counterpart is 3cm, scale factor is 6/3 = 2.
  • Every length on the larger shape is 2 times the size of the smaller shape.
• Application:
  • For a smaller side of 5cm, corresponding side on larger shape is 5 x 2 = 10cm.

Solving for Unknown Side Lengths

• Example Problem: Two triangles, find missing sides x and y.
  • Given base sides are 8cm and 12cm.
  • Calculate scale factor: 12/8 = 1.5.
  • Shape D is an enlargement of shape C by scale factor 1.5.

Calculating Side Lengths

• Finding x:

  • Equivalent side on smaller shape: 26cm.
  • x = 26cm x 1.5 = 39cm.

• Finding y:

  • Equivalent side is 45cm (on larger shape).
  • y = 45cm / 1.5 = 30cm.
  • Note: Divide when going from larger to smaller shape.

Tips on Working with Scale Factors

• Prefer finding scale factor from smaller shape to larger shape to avoid fractions.
• Example: Finding scale factor from D to C gives 8/12 = 2/3, which is more complex to work with.

Conclusion

• Always find scale factor from smaller to larger shape for ease of calculation.
• Encourage practice via resource website.
• End of lecture, invitation to practice questions.

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• Additional Resources: Check resource website linked in the lecture for practice questions.