Similar figures have the same shape: equal angles, and sides that all scale by one number. A photo enlargement is an example. It's how you can measure a tree without climbing it.
Two triangles with two matching angles are similar, since the third angle is then forced.
Work through it
Triangles are similar, with sides 3, 4, 5 and a matching side 12 for the 3. Find the side matching the 4.
Find the scale factor.
Scale the side.
A 2 m pole casts a 3 m shadow. A tree casts a 15 m shadow. How tall is it?
Sun rays make the same angle, so the triangles are similar. matches
Set up.
Solve. m
A side doubles. What happens to the area?
Both dimensions double.
Area grows by the square of the scale.4 times
Watch out for this
Matching sides by their position on the page.
Match sides by angles. The side opposite the same angle corresponds, however the triangle is turned.
The short version
Match corresponding sides. Their ratios are equal, so the scale factor links one triangle to the other.
Match corresponding sides. Their ratios are equal, so the scale factor links one triangle to the other.
Your turn
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