M4.4.5 For the adult
Similar shapes
A 3 m pole has a 2 m shadow. At the same time a tree has a 6 m shadow. How tall is the tree?
What this chapter teaches
Similar shapes have equal angles and sides in the same ratio, as if one were an enlargement of the other. Two triangles with two equal angles are similar. A missing side comes from the scale factor, the ratio of two matching sides.
Three questions to ask
There is no one right wording. Listen for the idea.
- How can you tell that two triangles are similar from their angles?
- How do you find the scale factor between two similar triangles?
- Why do the pole and the tree make similar triangles with their shadows?
After the chapter, the learner can
- Show two triangles are similar from their angles
- Find a missing side using a scale factor
What they copy into their notebook
Similar shapes have equal angles and matching sides in the same ratio. Two equal angles make triangles similar. Scale factor = a side of one ÷ the matching side of the other. Multiply.