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Why are congruent figures also similar?
They are similar, with a scale factor of 1.
Can congruent figures also be similar?
They must be similar, with scale factor = 1.
The transitive property holds for similar figures?
The transitive property states that if A is equal to B, and B is equal to C, then A is equal to C. In the context of similar figures, this property holds true. If two figures are similar, and one figure is congruent to a third figure, then the second figure is also congruent to the third figure.
What term is used for having the same measure?
The term used for having the same measure is "congruent." In geometry, congruent figures have the same size and shape, meaning their corresponding sides and angles are equal. This concept applies not only to geometric figures but also to various contexts where measurements or values are identical.
What does symmetric property of congruence mean?
The symmetric property of congruence states that if one geometric figure is congruent to another, then the second figure is also congruent to the first. In other words, if shape A is congruent to shape B, then shape B is congruent to shape A. This property emphasizes the mutual relationship of congruence between two figures, ensuring that the congruence can be expressed in either direction.
Are similar figures also congruent figures?
no
Why are congruent figures also similar?
They are similar, with a scale factor of 1.
Can congruent figures also be similar?
They must be similar, with scale factor = 1.
If two figures are similar then are they also congruent?
No. Two figures are similar if they have same shape, and all the angles are equal; but they can have the sides of different sizes. I mean, similar figures may have different sizes, but must have the same shape.
The transitive property holds for similar figures?
The transitive property states that if A is equal to B, and B is equal to C, then A is equal to C. In the context of similar figures, this property holds true. If two figures are similar, and one figure is congruent to a third figure, then the second figure is also congruent to the third figure.
When are two similar figures also congruent?
If the scale factor is 1. That is, if a pair of corresponding sides are the same length.
Why is it important to keep track of corresponding parts in congruent figures?
It is important so you can later prove that the figure is congruent using a geometric proof or other method. It is also useful for finding side lengths and the measures of angles.
What are similarities of congruent shapes and similar shapes?
The angles for congruent shapes and the angles in similar shapes are all the same. All the sides are also proportional in both. Basically, all congruent shapes are similar but not all similar shapes are congruent.
Are all similar triangles also congruent?
No.
What is a figure that has two congruent faces?
Prisms are three dimensional figures that always have two congruent faces. The congruent faces are also parallel to one another.
What geometric concept does the duplication of keys represent?
The duplication of keys represents the geometric concept of symmetry, particularly in terms of congruence and transformation. When keys are duplicated, each new key is a congruent copy of the original, maintaining the same shape and size. This process can also be viewed as a reflection or translation in geometric terms, as the new key mirrors the properties of the original. Thus, the duplication illustrates how geometric figures can maintain their identity through specific transformations.
Why congruent figures have the same surface area?
Geometrical figures are said to be congruent if they are the same in every respect; all lengths and angles are exactly the same. That being the case, the surface area must also be the same; the calculation will be the same for both figures.
