Question

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Answer 1

The smaller triangle is DEF which has sides

• DF = 1
• DE = 2
• EF = 3

The larger triangle ABC has side lengths of

• AC = 2
• AB = 4
• BC = 6

Note how the sequence 2,4,6 is exactly double that of 1,2,3. Therefore, the sides of triangle ABC are twice as large as the corresponding sides of triangle DEF.

Put another way, computing the ratios of the corresponding sides all lead to the same value, so we have BC/EF = 6/3 = 2, and we have  AB/DE = 4/2 = 2, and finally AC/DF = 2/1 = 2. These three equations all confirm ABC is twice as large as DEF.

By the SSS (side side side) similarity theorem, we can conclude the triangles are similar. They have the same shape, but different size.