which of the following transformations does not result in a congruent figure? (2024)

FAQs

Which of the following transformations does not result in a congruent figure? ›

2 Answers By Expert Tutors

Dilation is a non-rigid transformation, which means that the original and the image are not congruent.

A transformation that will produce a similar, but not congruent figure is a dilation. When a figure is dilated, its shape changes, but the angles remain the same. The resulting figure will be similar to the original one, but not congruent.

There are three congruent transformations: reflections, rotations, and translations. Resizing is not a congruence transformation.

Congruence transformations

Using three forms of transformations, Rotations, Reflections and Translations, we can create congruent shapes. In fact all pairs of congruent shapes can be matched to each other using a series or one or more of these three transformations.

Non-congruent rectangles. These two polygons have matching sides equal but their matching angles are not equal and so they are not congruent. They are different shapes even though the sides are the same size.

non-congruent adjective (NOT AGREEING)

different from something, so that the two things cannot exist together or be easily combined: Our values and beliefs were jarringly non-congruent. Idiomatic expressions that are non-congruent with the learner's first language will be most difficult to learn.

If we can map one figure onto another using rigid transformations, they are congruent. They are still congruent if we need to use more than one transformation to map it. They aren't if we use a transformation that changes the size of the shape.

Hence, two equilateral are not always congruent.

Transformations include rotations, reflections, translations, and dilations. Students must understand that rotations, reflections, and translations preserve congruence but dilations do not unless the scale factor is one.

What is the symbol for not congruent? ›

The symbol for "not congruent" is ≁. It is also sometimes represented as ≠ with a congruence symbol, or as the negation of the congruence symbol, which looks like an equals sign with a tilde above it (≅), resulting in a crossed out or slashed equals sign (≆).

Hence, one rotation followed by a dilation will result in triangles that are similar (same shape) but not congruent (different sizes).

Rigid transformations, like translations, keep shapes congruent, but dilations are not rigid transformations because they change the size. So, if we use a dilation to map one shape onto another, they are not congruent.

Congruent shapes or congruent figures are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same. To do this, we need to check all the angles and all the sides of the shapes. If two shapes are congruent, they will fit exactly on top of one another.

Dilation is a non-rigid transformation, which means that the original and the image are not congruent.

A dilation is the only transformation that does not preserve congruency but preserves orientation.

Expert-Verified Answer

Translation and reflection are "rigid" motions. They do not change the size or shape of the figure, so the resulting figure will be congruent with the original. Dilation by a factor of 2/3 changes the size, so will not result in a congruent figure.

Two triangles can never be congruent if the size of the other triangle is larger than the first even if the sides of both the triangles are in proportion. Therefore, the transformation that includes the dilation with a scale factor of 2 centered at the origin, the triangles will not be congruent.