1. Space and Shape Unit Grade 9 Math

2. Proving Similar Triangles E3 Make and apply informal deductions about the minimum sufficient condition to guarantee the similarity of two triangles

3. To review for this lesson…  Corresponding : When describing shapes, if there are 2 points that are matching, they are corresponding. (Can be lines, angles, vertices etc…)  Proportional : When measures have been increased or decreased by the same factor, they are proportional. For example: if triangle A has a side length of 6, and shape B has a length of 18, they are proportional because there is a common factor of 3  Congruent : When shapes have all of the same side and angle measures they are congruent

4. Congruent Triangles  https://www.youtube.com/watch?v=d5UCZ9hO8X4 https://www.youtube.com/watch?v=d5UCZ9hO8X4  Congruent triangles are triangles that are proven to have the same _____________  SSS : _____________  SAS : If 2 side lengths and a central angle are the same, the 3 rd side must also be the same (see SSS)  ASA : If 2 angles and a central side are the same, the 2 remaining sides must intersect at a common point  AAS : If 2 angles and the non included side are congruent, because the central side must be a fixed length to accommodate the 2 angles

5. Similar Triangles  https://www.youtube.com/watch ?v=BI-rtfZVXy0 https://www.youtube.com/watch ?v=BI-rtfZVXy0  Similar triangles are essentially triangles that can be proven _____________  _____________  Today we will try and find what are the minimum conditions for proving similarity

6. Activity #1  Discuss with your group the shape on the right  If you have the following information can you prove that the triangles are similar?  Why or why not?  AD=3 cm  BC= 5 cm  CD=4cm  AB=6cm  Note: “Because they look the same.” Is insufficient in the “court of Math”

7. Activity #2  Discuss with your group the shape on the right  If you have the following information can you prove that the triangles are similar?  Why or why not?  Angle B is congruent to Angle C  Note: “Because they look the same.” Is insufficient in the “court of Math”

8. To Prove Similarity…  To prove similarity, we need to prove that the 2 triangles are proportional  To do this we need minimum:  _____________

9. Practice Question Use the diagram on the left to answer the questions. 1.Is this enough information to prove the triangles are similar? Why/why not? Redraw the triangles (using a ruler and protractor) but with angle B and E congruent. Measure and record sides AC and DF. 2. What is the ratio of these 2 sides? 3. What is the ratio of the other 2 corresponding sides? 4. Using the triangles you have drawn, make a conclusion about their similarity. Are they similar or not? How do you know? (explain as deeply as you can)