similar triangles and other polygons. learning objective success criteria to understand the criteria...
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Similar Triangles and other Polygons
Learning Objective
Success Criteria
To understand the criteria that make two triangles (or two polygons) similar
• 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?
28m
6m
10m
7m
24m
40m
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.
𝑋𝑌𝐴𝐵
=𝑌𝑍𝐵𝐶
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.
Two triangles…
Finding the scale factor
18m
6m7m
4m21m
12m
×𝟑
×𝟑×𝟑
Are these two triangles similar?
12cm
3cm
5cm
3cm
12cm
20cm
Explain your answer
Problem:
6
6
510
12
11
18
18
15
Which two triangles are similar?
Explain your answer
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Two triangles…
Similar triangles are also equiangularEquiangular, meaning they share the same angles.
Problem:Which two triangles are similar?
70
50 70
60
40
70
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:
Problem:
All angles are equiangular, therefore we have similar triangles.
𝑂𝑢𝑟 𝑟𝑎𝑡𝑖𝑜𝑖𝑠
We are asked to calculate side length x.
Problem:
¿12.8𝑐𝑚∴𝑥=32×820
∴ 𝑥8=3220
𝑌𝑍𝐵𝐶
=𝑋𝑌𝐴𝐵
Calculate the height of the tree.
This is done using the shadow length, and a known height of another object.
𝑂𝑢𝑟 𝑟𝑎𝑡𝑖𝑜𝑖𝑠
Problem:
∴h=84×212
=14𝑚h2=8412
Similarity – other 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 ‘in the same position’.
PracticeFrom homework book
Page 199 Ex F: Similarity
