Are the triangles below similar?
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Are the triangles below similar?
To determine whether the triangles and are similar, we shall apply the Side-Side-Side (SSS) similarity theorem, which requires that the ratios of corresponding sides of the triangles be equal.
Let's compute the ratios:
Since all the corresponding side ratios are equal (), the triangles and are similar by the SSS similarity theorem.
Therefore, the solution to the problem is Yes.
Yes
Angle B is equal to 60°
Angle C is equal to 55°
Angle E is equal to 60°
Angle F is equal to 50°
Are these triangles similar?
Look at the relative positions of the sides in each triangle. The longest side corresponds to the longest side, shortest to shortest, and middle to middle. In this problem: 8↔4, 6↔3, and 4↔2.
If any ratio is different, the triangles are NOT similar. All three ratios must be identical for SSS similarity. Even if two ratios match but the third doesn't, they're not similar.
Yes! Always put corresponding sides in the same order. If you calculate for one pair, use the same pattern for all pairs to avoid confusion.
Absolutely! Similar triangles can be different sizes - that's the whole point! As long as all corresponding angles are equal and all side ratios are the same, they're similar regardless of size.
Congruent triangles are identical in size and shape (ratio = 1). Similar triangles have the same shape but can be different sizes (any equal ratio). All congruent triangles are similar, but not all similar triangles are congruent.
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