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Q: What is true about the area of similar triangles when the sides are increased by a factor of two?

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

when you multiply the area of the small triangle by four it equals the area of the large triangle.

They are said to be similar but not congruent triangles.

If the angles of two triangles are equal the triangles are similar. AAA If you have three angles on both triangles these must be equal for the triangles to be similar. SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar. And SSS If you know the three sides

Yes.

Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.When two triangles have corresponding sides with identical ratios, the triangles are similar.Of course if triangles are congruent, they are also similar.

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.

Yes. You can even have two triangles with two pairs of sides that are the SAME measure without the triangles being similar.

Similar in the number of sides but not congruent

similar sides.

similar triangles have all the same angles in each of them, and their sides can be of any length

Similar triangles.

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