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Two polygons with same shape not size?
The polygons are said to be similar.
Do two polygons which are similar have the same shape?
Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional. From this definition we can say they have the same shape.
When two polygons have the exact same volume are they congruent?
no
Are two regular polygons similar if and only if they have the same number of sides?
yes
Do polygons have to have the same number of sides and vertices?
Yes, polygons have the same number of sides and vertices.
Two polygons with same shape not size?
The polygons are said to be similar.
Are any two regular polygons with the same number of sides similar?
Yes, regular polygons will have all sides equal length, and all angles the same. If two polygons of the same number of sides are 'regular' then those two polygons will be similar (they may be scaled, for example).
What does it mean for two polygons to be congruent?
the two polygons are congruent if they are the same shape with the same measurements. If they can be flipped, rotated, and/or slid to look identical then they're congruent.
How can knowing two polygons are congruent help you find angle measure of the polygons?
They have the same measures.
Do two polygons which are similar have the same shape?
Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional. From this definition we can say they have the same shape.
When two polygons have the exact same volume are they congruent?
no
What has two parallel polygons that are the same size and shape?
Prism
How can you tell whether two polygons are similar?
Polygons will be similar if they have the same number of sides AND all of their angles are the same. All of their angles are the same if all but one of their angles are the same because with the same number of sides the angles must add up to the same thing. All squares are similar (4 right angles and sides of equal lenght). All rectangles are similar (4 right angles). We know two triangle are similar if two or mare angles are the same, or if one angle is the same and the two adjacent sides are the same length. Variations of this last proof may apply to some other polygons.
When two polygons have exact the same volume they are said to be congruent?
The statement is incorrect; congruence in geometry refers to two shapes being identical in form and size, meaning they have the same dimensions and can be superimposed onto one another. For polygons, congruence is determined by having the same side lengths and angles, not just the same area or volume. Volume is a property relevant to three-dimensional shapes, while polygons are two-dimensional figures. Thus, two polygons can have the same area but not necessarily be congruent.
What are the two conditions that need to be true to prove that two polygons are similar?
That the sides are of the same ratio and that the interior angles are the same.
To be considered similar two polygons must have corresponding sides that are equal?
To be considered similar, two polygons must have corresponding angles that are equal, and their corresponding sides must be in proportion, rather than equal. This means that while the shapes of the polygons are the same, their sizes may differ. Thus, similar polygons maintain the same shape but can vary in scale.
Are two regular polygons similar if and only if they have the same number of sides?
yes
