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It is given that two triangles are similar. So that the ratio of their corresponding sides are equal.

If you draw altitudes from the same vertex to both triangles, then they would divide the original triangles into two triangles which are similar to the originals and to each other. So the altitudes, as sides of the similar triangles, will have the same ratio as any pair of corresponding sides of the original triangles.

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Q: Will the lengths of two corresponding altitudes of similar triangles will have the same ratio as any pair of corresponding sides?

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True. With similar triangles the corresponding angles are equal.

Yes.

If two triangles are similar, then the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles

If and when two parallelograms are similar, you know that the ratio of two side lengths within one parallelogram will describe the relationship between the corresponding side lengths in a similar parallelogram. If and when two parallelograms are similar, you know that the ratio of corresponding side lengths in the other parallelogram will give you the scale factor that relates each side length in one parallelogram to the corresponding side length in a similar parallelogram.

Yes. The triangles have the same angle measures but different, similar side lengths. Think of two different sized equilateral triangles. One can have side lengths of 6 inches while the other has side lengths of 20 inches, but they still have congruent angles of 60 degrees. Each ratio of side lengths is equal [6/20=6/20=6/20].

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Similar triangles means they have the same lengths OR the corresponding lengths have equal ratios.

ratio

ratio

Their corresponding angles are equal, or the ratio of the lengths of their corresponding sides is the same.

You either show that the corresponding angles are equal or that the lengths of corresponding sides are in the same ratio.

Trigonometric ratios are characteristics of angles, not of lengths. And, by definition, the corresponding angles an similar triangles have the same measures.

It is true.

Yes. Corresponding angles of the two triangles are always equal, and lengths of corresponding sides are always in the same ratio.

The corresponding angles in both cases are the same. With congruent triangles, the lengths of the corresponding sides are also equal.

Similar triangles.

Yes, similar triangles are congruent because in order to be congruent they must first be equal. Which in turn is the definition of a similar triangle. A triangle equal in angle measurements and/or side lengths. So, yes.

They are similar triangles.

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