Exploring Similarity and Transformations in Geometry

What is the key concept to determine if two figures are similar?

• The figures must be identical.

• The figures must have the same color.

• The figures must be in the same position.

• The figures must have the same ratio between their sides.

In the first example, what is the ratio of side EF to side VW?

• 1/2

• 2/3

• 3/2

• 3/4

Why is it important to compare different sets of sides when determining similarity?

• To confirm the figures have the same color.

• To check if the figures are in the same orientation.

• To verify that the ratios are consistent across all corresponding sides.

• To ensure the figures are the same size.

What is the scale factor used to map figure EF to VW if the figures are similar?

• 2/1

• 1/2

• 2/3

• 3/2

When mapping a larger figure onto a smaller one, what should the scale factor be?

• Zero

• Equal to one

• Greater than one

• Less than one

In the example involving rotation and reflection, what additional transformations are needed besides dilation and translation?

• Scaling

• Shearing

• Rotation and reflection

• Translation only

What is the ratio of side EF to side XY in the example involving rotation and reflection?

• 1/2

• 2/3

• 3/4

• 1/1

Why are the figures in the rotation and reflection example not similar?

• They are not the same size.

• They are not in the same position.

• Their corresponding sides do not have the same ratio.

• They have different colors.

In the final example, what is the ratio of side RS to side OP?

• 2/1

• 1/1

• 2/3

• 1/2

What transformations were used to map triangle HJ onto triangle PQ in the final example?

• Scaling and shearing

• Dilation and rotation

• Rotation and reflection

• Dilation and translation