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Do similar shapes always have to have corresponding sides that are proportional?
Yes, similar figures always have congruent corresponding angles and proportional corresponding side lengths.
What is true about corresponding angles and corresponding sides of similar figures?
The ratio between corresponding sides or angles of similar triangles are equal
What does it mean when 2 geometric figures are similar?
It means that the sides of one are directly proportional to the corresponding sides of the other. That all the corresponding angles are equal.
When two angles are similar their corresponding angles are?
In geometry, the term "similar" refers to figures that have the same shape but potentially different sizes (length, width, height). Strictly speaking angles don't have "size" so they would not be "similar". On the other hand if we interpret the intent to be to ask about congruent angles in similar figures the corresponding angles (i.e. angles that occupy the same relative position at each intersection where a straight line crosses two others) will also be congruent. If angles are similar in that they have approximately (but not necessarily exactly) the same measure, then their corresponding angles will also be approximately the same as each other. Stated another way: If angles A and B are very close in measure, and angle C is the corresponding angle of angle A and angle D is the corresponding angle of angle B, then angles C and D will be close in measure within bounds that can be predicted based on the difference in measure between angles A and B.
Definition of Congruent Figures?
The Definition of Congruent Figures (which is a proof) says that if two figures have corresponding sides congruent and corresponding angles congruent, then the figures are to be congruent.
