Exploring Dilations and Angle Preservation in Geometry

What happens to a line segment when it is dilated with a scale factor greater than 1?

• It moves closer to the center of dilation.

• It remains unchanged.

• It moves farther away from the center of dilation.

• It becomes perpendicular to the original line segment.

What does a scale factor between 0 and 1 indicate in a dilation?

• The figure translates.

• The figure rotates.

• The figure expands.

• The figure contracts.

What is preserved during a dilation?

• Angle measurements

• Length of line segments

• Perimeter of shapes

• Area of shapes

Which property of dilations is crucial for preserving the shape of a geometric figure?

• Proportionality of sides

• Equality of angles

• Parallelism of lines

• Symmetry of the figure

How can the center of dilation be determined graphically?

• By measuring the distance between corresponding points

• By drawing a circle around the dilated figure

• By intersecting lines connecting corresponding vertices

• By calculating the midpoint of the dilated figure

How is the scale factor calculated using measurements from the original and the image?

• By multiplying the lengths of corresponding sides

• By dividing the length of a side in the image by its corresponding side in the original

• By adding the lengths of corresponding sides

• By subtracting the lengths of corresponding sides

What results from dilating a triangle with a center at one of its vertices?

• A larger triangle with different angles

• A smaller triangle with the same angles

• A congruent triangle

• A triangle with the same angles but different side lengths

What does it mean if two triangles are congruent as a result of dilation?

• They have the same area but different shapes.

• They have the same shape and size.

• They are mirror images of each other.

• They have the same shape but different sizes.

What is the relationship between corresponding sides in similar triangles?

• They form parallel lines.

• They are proportional.

• They have the same length.

• They are perpendicular to each other.

In the context of dilations, what does a scale factor of 1 imply?

• The figure is reduced.

• The figure is rotated.

• The figure is enlarged.

• The figure remains unchanged.