Geometry Symmetry of Polygons and Rigid Motions Quiz: 10 Questions with Explanations

A 5B 1C 10D 0

A regular n-gon has n lines of symmetry, so a pentagon has 5. Doubling the count (10) counts each line twice.

A 18 degreesB 36 degreesC 10 degreesD 72 degrees

360 divided by 10 sides is 36 degrees. The angle 72 degrees is two steps, not the smallest.

A A parallelogram with no right anglesB A rectangleC An isosceles trapezoidD A kite

A parallelogram maps onto itself under a 180 degree rotation, but no reflection works. A rectangle also has two lines of symmetry.

A 4B 1C 2D 0

Each diagonal of a rhombus is a line of symmetry, so there are 2. A square has 4 because its midlines also work.

A DE = 16 and angle D = 70 degreesB DE = 8 and angle D = 35 degreesC DE = 8 and angle D = 55 degreesD DE = 4 and angle D = 35 degrees

Rigid motions preserve both distance and angle measure. Doubling or halving would be a dilation.

A Two lines of symmetryB A 180 degree rotationC One line of symmetry and no rotational symmetryD No symmetry at all

The perpendicular bisector of the bases is its only symmetry. Different base lengths rule out a 180 degree rotation.

A 24B 12C 16D 15

The number of sides is 360 divided by 24, which is 15. Using 24 itself confuses the angle with the side count.

A ZB HC AD T

Z looks the same upside down, but no reflection maps it to itself. H has line symmetry, and A and T have vertical lines of symmetry.

A AB BC CD D

Rule (x, y) to (-y, x) sends (-4, 0) to (0, -4), which is B. A clockwise turn would give D.

A 20 degreesB 40 degreesC 50 degreesD 90 degrees

The spokes are 30 degrees apart, so rotations must be multiples of 30. Of the choices only 90 degrees is a multiple of 30.