1. Similar Triangles/Polygons

2. Lesson Objective Lesson Success Criteria
To learn about similarity in triangles, and other polygons
Lesson Success Criteria
Can identify and solve problems involving similar triangles
Can work successfully with ratios in solving geometric problems
Can solve problems involving polygon similarity

3. Similar Triangles – what are they?
When two triangles are equiangular, then one triangle is an enlargement of the other – they are known as similar triangles.
Their sides will be proportion, that is, the ratio of the lengths of the same sides is the same.
𝑋𝑌 𝐴𝐵 = 𝑌𝑍 𝐵𝐶

4. 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.

5. 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.
Identify the two equiangular triangles, if possible, draw them as two separate triangles
Identify which sides are in the same relative position
Apply appropriate ratios to help calculate unknown sides
Be careful:
Some figures may overlap – identify carefully the lengths required

6. Similar Triangles – problem 1
All angles are equiangular, therefore we have similar triangles.
We are asked to calculate side length x.
𝑂𝑢𝑟 𝑟𝑎𝑡𝑖𝑜 𝑖𝑠 𝑋𝑌 𝐴𝐵 = 𝑌𝑍 𝐵𝐶 ∴ = 𝑥 ∴ 𝑥= 32×8 20 =12.8𝑐𝑚

7. Similar Triangles – problem 2
Calculate the height of the tree.
This is done using the shadow length, and a known height of another object.
𝑂𝑢𝑟 𝑟𝑎𝑡𝑖𝑜 𝑖𝑠 = ℎ ∴ ℎ= 84×2 12 =14 𝑚

8. Similarity -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 same position.

10. Practice
From homework book
Page 199 Ex F: Similarity