Are the triangles below similar?
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Are the triangles below similar?
To determine if the triangles ABC and DEF are similar, we need to examine the ratios of corresponding sides.
We calculate the ratios of corresponding sides:
All the corresponding side ratios are equal to 2, indicating that the sides of triangle ABC are proportional to the sides of triangle DEF by a common ratio. According to the Side-Side-Side (SSS) similarity criterion, this means the triangles are similar.
Therefore, the triangles are indeed similar. The correct answer is Yes.
Yes
The two parallelograms above are similar. The ratio between their sides is 3:4.
What is the ratio between the the areas of the parallelograms?
Look at the vertex labels and side lengths! The longest side in one triangle corresponds to the longest side in the other. In this problem: AC (6) ↔ DF (3), BC (4) ↔ EF (2), AB (2) ↔ DE (1).
All three ratios must be equal for similarity! If only two match, the triangles are not similar. This is the SSS similarity criterion - all sides must be proportional.
Yes! Always write ratios consistently. Either Triangle 1 : Triangle 2 for all pairs, or Triangle 2 : Triangle 1 for all pairs. Mixing orders will give wrong conclusions.
Absolutely! Similar triangles can be rotated, flipped, or scaled. Focus on the side lengths and their ratios, not the visual position of the triangles.
The common ratio is the scale factor! In this problem, triangle ABC is exactly 2 times larger than triangle DEF in all dimensions.
No! If all three pairs of corresponding sides are proportional (SSS), the triangles are automatically similar and their corresponding angles are equal.
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