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If STU is similar to XYZ the sides of STU must be congruent to the corresponding sides of XYZ.?
False
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Why do corresponding angles of similar figures have to be congruent?
Corresponding angles of similar figures are congruent because similarity in geometry implies that the shapes have the same shape but may differ in size. When two figures are similar, their corresponding sides are in proportion, which leads to their angles being equal. This relationship ensures that the angles maintain their measures regardless of the scale of the figures, thus confirming that corresponding angles must be congruent.
Similar triangles must have congruent angles and congruent sides?
False dood
If two triangles have three pairs of congruent angles the the triangles are not guarenteed to be congruent?
If two triangles have three pairs of congruent angles, they are said to be similar but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are in proportion but not equal. For triangles to be congruent, both their angles and corresponding sides must be equal, which is not guaranteed if only angle congruence is established. Therefore, while angle congruence indicates similarity, it does not ensure congruence.
Can two similar polygons be congruent polygons?
Yes. The polygons must be congruent. They must have an even number of sides and angles. -alessandra
What are the 3 requirements to be similar figures?
The three requirements to be similar figures are: Corresponding angles must be congruent (equal in measure). Corresponding sides are in proportion; this means that the ratio of corresponding side lengths is the same for all sides. The figures have the same shape, but can be of different sizes.
Are all pentagons similar?
No, similar pentagons (or any polygon for that matter) must have corresponding congruent angles and all sides must be proportional to its corresponding sides. For example, if a square with a triangle on it is a pentagon, then a regular pentagon would not be similar to it (because corresponding angles are not congruent).
What are two parallegrams that are congruent?
They are simply two congruent parallelograms.
If two rectangles are similar then the corresponding sides are?
If two rectangles are similar, they have corresponding sides and corresponding angles. Corresponding sides must have the same ratio.
Two polygons are similar then the corresponding angles must be?
congruent
Similar triangles must have congruent angles and congruent sides?
False dood
Is is true if two parallelograms have corresponding sides that are equal they must be congruent?
yes it is ture
Are two rhombuses always-sometimes or never similar?
Sometimes. Remember, in order for two polygons to be similar, their angles must be congruent, and their corresponding sides must be proportional. In a rhombus, it is always possible for the angles to differ.
If two polygons are similar then the corresponding sides must be?
Similar
Can two similar polygons be congruent polygons?
Yes. The polygons must be congruent. They must have an even number of sides and angles. -alessandra
What are the 3 requirements to be similar figures?
The three requirements to be similar figures are: Corresponding angles must be congruent (equal in measure). Corresponding sides are in proportion; this means that the ratio of corresponding side lengths is the same for all sides. The figures have the same shape, but can be of different sizes.
If two triangles are congruent statements must be true?
It means they have the same size and shape, corresponding sides have the same length and corresponding angles are the same.
Is there an SAS postulate for similarity of two triangles also just as you have one for congruency of triangles?
YesFor two triangles to be congruent, their corresponding sides must be of equal length. But for triangles to be similar, they must only have equal angles. For there to be a SAS postulate for similarity, the two corresponding sides would have to be proportionate, not equal. If they were equal, the triangles would be congruent.So, an SAS postulate for similar triangles would mean that two of the sides of the smaller triangle are, for example, half the two corresponding sides of the other triangle. If also the corresponding included angles are equal, then the two triangles would be similar triangles.APEX: similar
