Similar Figures and Scale Factor Test Prep

Identify two figures that are similar and explain how you know.

• A square and a rectangle are similar because they both have four sides.

• Two triangles with angles measuring 30°, 60°, and 90° are similar. We know this because their corresponding angles are equal, and their side lengths are in proportion to each other.

• A triangle and a hexagon are similar because they both have straight sides.

• Two circles with different radii are similar because they both have a curved shape.

If the scale factor between two similar figures is 3, and the length of one side of the smaller figure is 5 cm, what is the length of the corresponding side in the larger figure?

• 8 cm

• 20 cm

• 10 cm

• 15 cm

Determine if the following pairs of figures are similar: (a) Triangle ABC and Triangle DEF with corresponding angles: ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F. (b) Rectangle PQRS and Rectangle WXYZ with corresponding angles: ∠P ≅ ∠W, ∠Q ≅ ∠X, and ∠R ≅ ∠Y.

• Maybe

• Yes

• No

• Not sure

Explain the meaning of the term 'corresponding sides' in the context of similar figures.

• Corresponding sides are the sides that are opposite to each other.

• Corresponding sides are the sides that are in the same relative position to each other and have the same proportional lengths.

• Corresponding sides are the sides that are not related to each other.

• Corresponding sides are the sides that have different proportional lengths.

Calculate the scale factor between two similar rectangles if one rectangle has a length of 8 cm and the other has a length of 12 cm.

• 1.5

• 10

• 0.75

• 2.5

Identify the similar figures in the following set of shapes: (a) Triangle LMN and Triangle PQR with corresponding angles: ∠L ≅ ∠P, ∠M ≅ ∠Q, and ∠N ≅ ∠R. (b) Square ABCD and Square WXYZ with corresponding angles: ∠A ≅ ∠W, ∠B ≅ ∠X, ∠C ≅ ∠Y, and ∠D ≅ ∠Z.

• Triangle PQR and Square WXYZ

• Triangle LMN and Triangle PQR, Square ABCD and Square WXYZ

• Triangle LMN and Square WXYZ

• Triangle LMN and Square ABCD

Explain the concept of 'scale factor' in the context of similar figures.

• The scale factor is the difference of the lengths of corresponding sides of two similar figures.

• The scale factor is the sum of the lengths of corresponding sides of two similar figures.

• The scale factor is the ratio of the lengths of corresponding sides of two similar figures.

• The scale factor is the product of the lengths of corresponding sides of two similar figures.

If two similar triangles have a scale factor of 2, and the length of one side of the smaller triangle is 6 cm, what is the length of the corresponding side in the larger triangle?

• 10 cm

• 8 cm

• 12 cm

• 4 cm

Determine if the following pairs of figures are similar: (a) Pentagon UVWXY and Pentagon LMNOP with corresponding angles: ∠U ≅ ∠L, ∠V ≅ ∠M, ∠W ≅ ∠N, ∠X ≅ ∠O, and ∠Y ≅ ∠P. (b) Circle A and Circle B with radii of 5 cm and 7 cm, respectively.

• Yes, both pairs of figures are similar.

• No, the pairs of figures are not similar

• Yes, only the first pair of figures is similar

• No, only the second pair of figures is similar

Explain the meaning of the term 'similar figures' and provide an example.

• Similar figures are figures that have different shapes and sizes.

• Similar figures are figures that have the same size but not necessarily the same shape.

• Similar figures are figures that have the same shape but not necessarily the same size. They have proportional sides and angles. For example, a small triangle and a larger triangle with the same angles are similar figures.

• Similar figures are figures that have no proportional sides or angles.