Similar Figures & Solids

Self-study Module (II) - Similar Figures/Solids – Length, Area and Volume

Duration of self-study: 4 weeks

Mode of Assessment: Test (Earn ACE credits)

What you need to learn:
  • Understand and describe line and rotational symmetries in 2-D figures
  • Understand and identify similarity in polygons by matching corresponding sides
  • Understand and apply relationship between the ratios of areas and corresponding sides of similar figures
  • Understand and apply relationship between the ratios of volumes and corresponding sides of similar solids

Resources:
1) Notes
2) Textbook 2A Page 101 - 115 Section 4.2, 4.3 Ex 4.2 and Ex 4.3
3) Practice questions

Instructions


This self-study is part of the entire topic on Congruency and Similarity. You do not need to learn the proofs for Congruency and SImilarity - this will be covered in class.

You will need to cover line and rotational symmetry of 2-D figures, as well as identify similar figures and use the formulas to find the area and volume of similar figures/solids.

(1) To begin, download these notes on symmetry:

(2) View these slides in conjunction with the notes on line symmetry:

(3) Move on to similar figures - usually in Math, the problems are usually similar triangles. View this short clip to have an idea of similar triangles:

(4) Download these notes on similarity:

(5) View these slides in conjunction with the notes on similarity:

(6) Download these notes on Area and Volume of similar figures/solids:


More Resources:

Video 1: This video shows you how to identify Similar Triangles and the conditions for similarity.
[URL: http://www.youtube.com/watch?v=5aOQAygTUJ8]

Video 2: The front part of this video is on Congruency, which is NOT included in your self-study. Still, no harm watching and finding out a little. The next part will talk about Conditions for Similarity, about the same as video 1.

[URL: http://www.youtube.com/watch?v=OEp7YK6WEXE]


Video 3: This video talks about Similar Triangles and Scale Factor. The last part also tells you about how the areas of similar triangles are related to the scale factor.

[URL: http://www.youtube.com/watch?v=5c6J2isloqo]

Video 4: Similar Objects - Area and Volume Relationships.

[URL: http://www.youtube.com/watch?v=XHjCbfJw4lM]

Video 5: Using Similar Triangles to Solve Problems

[URL: http://www.youtube.com/watch?v=5c6J2isloqo&feature=related]

Video 6: Scale Factor

[URL: http://www.youtube.com/watch?v=XtkU4VkWh8I]

Video 7: Area of Similar Figures

[URL: http://www.youtube.com/watch?v=4jYuWbjddU8&feature=related]

Video 8: Volume of Similar Figures

[URL: http://www.youtube.com/watch?v=EBvWL4CL4LQ]

Solutions to Exercises (amended area and Volume solutions on 4 July):




For Area Exercise Q6 (the one with the *), it involves non-similar triangles, which will be covered in class and questions like Q6 type will not be included in the self-study.

Here is a file that gives you more info regarding non-similar triangles:

More Practice Questions:
and its solutions: