Similar Triangles and other Polygons Learning Objective To

Similar Triangles and other Polygons

Learning Objective To understand the criteria that make two triangles (or two polygons) similar Success Criteria • I can identify similar triangles and explain why they are similar • I can work successfully with ratios in solving geometric problems • I can solve problems involving polygon similarity

Are these two triangles similar? 28 m 7 m 10 m 40 m 6 m 24 m Explain your answer

An object is similar to another object if they are the same shape One object is larger than the other by a scale factor

Bigger versions can exist…

Two triangles are similar if one of them is larger than the other by a scale factor.

Two triangles… If similar will mean that their sides will be in proportion, that is, the ratio of the lengths of the same sides is the same. Largest divided by smallest provides the scale factor.

Finding the scale factor 7 m 6 m 21 m 4 m 12 m 18 m

Are these two triangles similar? 12 cm 3 cm 5 cm 20 cm 3 cm 12 cm Explain your answer

Problem: Which two triangles are similar? 5 6 12 10 6 11 18 18 15 Explain your answer

Two triangles…

Similar triangles are also equiangular Equiangular, meaning they share the same angles.

Problem: Which two triangles are similar? Hint: What do the angles in a triangle add up to?

Similar Triangles - examples Here are some common examples of similar triangles. Note the parallel sides in the first two examples. Remember: Equiangular means equal angles.

Similar Triangles - calculation Identifying similar triangles is a skill, as you are not normally told this. You may need to use geometric reasons to prove similarity first. 1. Identify the two equiangular triangles, if possible, draw them as two separate triangles 2. Identify which sides are in the same relative position 3. Apply appropriate ratios to help calculate unknown sides Be careful: Some figures may overlap – identify carefully the lengths required

Problem:

Problem: We are asked to calculate side length x. All angles are equiangular, therefore we have similar triangles.

Problem: Calculate the height of the tree. This is done using the shadow length, and a known height of another object.

Similarity – other polygons The same principles can be applied to any polygons that are similar: • Corresponding angles are equal • Corresponding sides are in proportion Following the same process as with triangles, you can through geometric reasoning solve for unknown sides. Remember: Corresponding means ‘in the same position’.

Practice From homework book Page 199 Ex F: Similarity