Similar Triangles/Polygons

Lesson Objective

Lesson Success Criteria

To learn about similarity in triangles, and other polygons

• Can identify and solve problems involving similar triangles• Can work successfully with ratios in solving geometric problems• Can solve problems involving polygon similarity

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.

𝑋𝑌𝐴𝐵

=𝑌𝑍𝐵𝐶

Their sides will be proportion, that is, the ratio of the lengths of the same sides is the same.

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

Similar Triangles – problem 1All angles are equiangular, therefore we have similar triangles.

We are asked to calculate side length x.

Similar Triangles – problem 2

Calculate the height of the tree.

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

Similarity -polygonsThe 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.

PracticeFrom homework book

Page 199 Ex F: Similarity