Symmetry and Similarity in Transformation Geometry

A butterfly has wings that are symmetrical. If one wing is folded over the other, what type of symmetry does the butterfly exhibit?

• Reflective symmetry

• Bilateral symmetry

• Radial symmetry

• Asymmetrical symmetry

A square is transformed into a rectangle by stretching it. If the original square has a side length of 4 cm, what are the dimensions of the rectangle if it maintains the same area?

• Length: 5 cm, Width: 3.2 cm

• Length: 10 cm, Width: 1.6 cm

• Length: 8 cm, Width: 2 cm

• Length: 6 cm, Width: 4 cm

Two triangles are similar. If the first triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what are the possible lengths of the sides of the second triangle if its longest side is 10 cm?

• 4 cm, 6 cm, 12 cm

• 6 cm, 8 cm, 10 cm

• 3 cm, 5 cm, 11 cm

• 5 cm, 7 cm, 9 cm

A park has a circular fountain that is reflected in a rectangular pond. If the radius of the fountain is 5 m, what is the diameter of the reflection in the pond?

• 10 m

• 20 m

• 15 m

• 5 m

A piece of art is rotated 90 degrees clockwise. If the original coordinates of a point on the art are (2, 3), what are the new coordinates after the rotation?

• (3, -2)

• (2, 3)

• (0, 5)

• (5, 2)

Two rectangles are congruent. If one rectangle has a length of 8 cm and a width of 5 cm, what is the perimeter of the other rectangle?

• 24 cm

• 20 cm

• 30 cm

• 26 cm

A triangle is dilated by a scale factor of 2. If the original triangle has a perimeter of 18 cm, what is the perimeter of the dilated triangle?

• 18 cm

• 24 cm

• 30 cm

• 36 cm

A logo is designed with rotational symmetry. If it looks the same after a 120-degree rotation, how many times will it look the same in a full 360-degree rotation?

• 3

• 2

• 4

• 5

A garden is shaped like a parallelogram. If the base is 10 m and the height is 6 m, what is the area of the garden?

• 60 m²

• 30 m²

• 50 m²

• 70 m²

A rectangular table is reflected in a mirror. If the table has dimensions of 2 m by 1 m, what are the dimensions of the reflected image?

• 1 m by 2 m

• 2 m by 2 m

• 1 m by 1 m

• 2 m by 1 m