Transformations and Congruence: A Geometry Challenge

A triangle ABC is transformed to triangle A'B'C' using a double prime transformation. If the lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm, what are the lengths of the sides of triangle A'B'C'?

• 5 cm, 12 cm, 13 cm

• 7 cm, 12 cm, 13 cm

• 5 cm, 10 cm, 15 cm

• 6 cm, 12 cm, 14 cm

Two rectangles, one measuring 4 m by 6 m and the other measuring 8 m by 12 m, are similar. If the smaller rectangle is transformed using a double prime transformation, what will be the dimensions of the larger rectangle?

• 8 m by 12 m

• 10 m by 14 m

• 6 m by 8 m

• 4 m by 12 m

A square has a side length of 10 cm. After a double prime transformation, the new square has a side length of 15 cm. Determine if the two squares are congruent or similar and explain your reasoning.

• The squares are similar but not congruent.

• The squares are congruent and similar.

• The squares are congruent but not similar.

• The squares are neither congruent nor similar.

A triangle with vertices at (1, 2), (3, 4), and (5, 2) is reflected over the y-axis to create triangle A'B'C'. What are the coordinates of the new triangle's vertices?

• (1, -2), (3, -4), (5, -2)

• The coordinates of the new triangle's vertices are [(-1, 2), (-3, 4), (-5, 2)].

• (-1, -2), (-3, -4), (-5, -2)

• (1, 2), (3, 4), (5, 2)

A parallelogram has vertices at (2, 3), (6, 3), (5, 7), and (1, 7). If this shape undergoes a double prime transformation that enlarges it by a factor of 2, what are the new coordinates of the vertices?

• [(4, 6), (12, 6), (10, 14), (2, 14)]

• [(4, 6), (6, 3), (5, 7), (1, 7)]

• [(4, 6), (12, 6), (5, 7), (1, 7)]

• [(2, 3), (6, 3), (10, 14), (2, 14)]

Two circles have radii of 3 cm and 6 cm. If the smaller circle is transformed to the larger circle using a double prime transformation, are the circles similar or congruent? Justify your answer.

• The circles are similar but not congruent.

• The circles are congruent but not similar.

• The circles are congruent and similar.

• The circles are neither similar nor congruent.

A trapezoid has bases of lengths 10 cm and 6 cm. If the trapezoid is transformed to a new trapezoid with bases of lengths 20 cm and 12 cm, what type of transformation occurred? Are the trapezoids similar?

• The transformation is a dilation, and the trapezoids are similar.

• The transformation is a rotation, and the trapezoids are similar.

• The transformation is a reflection, and the trapezoids are not similar.

• The transformation is a translation, and the trapezoids are not similar.

A rectangle is transformed into a new rectangle that is twice as long and half as wide. If the original rectangle has dimensions of 4 m by 8 m, what are the dimensions of the new rectangle? Are they similar?

• The dimensions are 4 m by 8 m and they are similar.

• The dimensions are 1 m by 16 m and they are similar.

• The dimensions are 8 m by 4 m and they are not similar.

• The dimensions of the new rectangle are 2 m by 16 m. They are not similar to the original rectangle.

A triangle with angles measuring 30°, 60°, and 90° is transformed into a triangle with angles measuring 30°, 60°, and 90° again. What type of transformation has occurred, and are the triangles congruent?

• The transformation is reflection, and the triangles have different angles.

• The transformation is rotation, and the triangles are similar.

• The transformation is congruence, and the triangles are congruent.

• The transformation is dilation, and the triangles are not congruent.

A hexagon is transformed into a new hexagon that is rotated 90 degrees and then reflected over the x-axis. If the original hexagon has vertices at (1,1), (2,2), (3,1), (3,0), (2,-1), and (1,0), what are the coordinates of the new hexagon's vertices?

• [[0,1],[1,2],[2,1],[2,0],[1,-1],[0,0]]

• [[-1,-2],[-2,-1],[-3,-1],[0,-2],[1,-3],[0,-2]]

• [[1,1],[2,2],[3,1],[3,0],[2,-1],[1,0]]

• [[-1,-1],[-2,-2],[-1,-3],[0,-3],[1,-2],[0,-1]]