Geometry Regents Practice

081602geo

Which transformation would not always produce an image that would be congruent to the original figure?

• 1) translation

• 2) dilation

• 3) rotation

• 4) reflection

• 1) reflection over the y-axis

• 2) rotation of 90° clockwise about the origin

• 3) translation of 3 units right and 2 units dow

• 4) dilation with a scale factor of 2 centered at the origin

• 1) a rotation of 90 degrees counterclockwise about the origin

• 2) a translation of three units to the left and three units up

• 3) a rotation of 180 degrees about the origin

• 4) a reflection over the line y = x

In the diagram below, which single transformation was used to map triangle A onto triangle B?

081513geo

• 1) line reflection

• 2) rotation

• 3) dilation

• 4) translation

• 1) reflection over the line y = −x

• 2) reflection over the line y = −x + 2

• 3) rotation of 180° centered at (1, 1)

• 4) rotation of 180° centered at the origin

Answer explanation

Since orientation is preserved, a reflection has not occurred.

A regular pentagon is shown in the diagram below. If the pentagon is rotated clockwise around its center, the minimum number of degrees it must be rotated to carry the pentagon onto itself is

• 1) 54º

• 2) 72º

• 3) 108º

• 4) 360º

Answer explanation

Segments drawn from the center of the regular pentagon bisect each angle of the pentagon, and create five isosceles triangles as shown in the diagram below. Since each exterior angle equals the angles formed by the segments drawn from the center of the regular pentagon, the minimum degrees necessary to carry a regular polygon onto itself are equal to the measure of an exterior angle of the regular polygon.

The figure below shows a rhombus with noncongruent diagonals. Which transformation would not carry this rhombus onto itself?

011904geo

• 1) a reflection over the shorter diagonal

• 2) a reflection over the longer diagonal

• 3) a clockwise rotation of 90° about the intersection of the diagonals

• 4) a counterclockwise rotation of 180° about the intersection of the diagonals

Which polygon always has a minimum rotation of 180° about its center to carry it onto itself?

012311geo

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Answer explanation

2) 90°;

3) 360°;

4) 72°

A regular pentagon is rotated about its center. What is the minimum number of degrees needed to carry the pentagon onto itself?

062204geo

• 1) 72°

• 2) 108°

• 3) 144°

• 4) 360°

Answer explanation

Which transformation would not carry a square onto itself? 011815geo

• 1) a reflection over one of its diagonals

• 2) a 90° rotation clockwise about its center

• 3) a 180° rotation about one of its vertices

• 4) a reflection over the perpendicular bisector of one side