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What effects do rigid transformations have on geometric figures?
They can alter the location or orientation of the figures but do not affect their shape or size.
When the preimage and image are congruent the transformation is called an isometry true or false?
True. An isometry is a transformation that preserves distances and angles, meaning that the preimage and image are congruent. Examples of isometries include translations, rotations, and reflections, all of which maintain the shape and size of geometric figures.
What does congruent and similar figures both have in common?
Both congruent and similar figures are types of geometric figures that share specific relationships. Congruent figures have the same shape and size, meaning all corresponding sides and angles are equal. In contrast, similar figures have the same shape but may differ in size; their corresponding angles are equal, and their sides are proportional. Ultimately, both types of figures maintain certain geometric properties that define their relationships.
What is topolgies?
The official definition for topology is "the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures."
What is is called if something has the same she and size?
If something has the same shape and size, it is referred to as "congruent." In geometry, two figures are congruent if they can be transformed into each other through rotations, translations, or reflections without altering their size or shape. This concept applies to various geometric figures such as triangles, circles, and other polygons.
1What is the difference between congruent and similar?
Two congruent geometric figures have the same shape and the same size, whereas two similar geometric figures have the same shape but they differ in size.
What effects do rigid transformations have on geometric figures?
They can alter the location or orientation of the figures but do not affect their shape or size.
What is the term for two figures that have the same shape and size?
Geometric shapes that are identical in size and shape are congruent.
Definition of topology?
the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
What map preserves shape and what map preserves size?
A conformal map preserves shape, meaning angles are maintained. A equal-area map preserves size, meaning areas are accurately represented.
When the preimage and image are congruent the transformation is called an isometry true or false?
True. An isometry is a transformation that preserves distances and angles, meaning that the preimage and image are congruent. Examples of isometries include translations, rotations, and reflections, all of which maintain the shape and size of geometric figures.
What does congruent and similar figures both have in common?
Both congruent and similar figures are types of geometric figures that share specific relationships. Congruent figures have the same shape and size, meaning all corresponding sides and angles are equal. In contrast, similar figures have the same shape but may differ in size; their corresponding angles are equal, and their sides are proportional. Ultimately, both types of figures maintain certain geometric properties that define their relationships.
What is topolgies?
The official definition for topology is "the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures."
What type of map preserves shape and preserves size?
A conformal map is a type of map that preserves shape (angles) and a equal-area map preserves size (area). However, no single map projection can perfectly preserve both shape and size simultaneously across an entire map.
What transformation preserves the shape and size?
Rigid motion
What is it called when figures have the same shape but not the same size?
Figures that have the same shape but not size are similar. Figures that have the same size are congruent.
What are pairs of figures of congruent?
Any two figures, polygonal or not, that are the same shape and size. Any two figures, polygonal or not, that are the same shape and size. Any two figures, polygonal or not, that are the same shape and size. Any two figures, polygonal or not, that are the same shape and size.
