Geometry, Semester A

With regard to mathematics, what is an accepted statement of fact that is used to prove other statements?

• A. theorem

• B. axiom

• C. definition

• D. undefined term

Which Greek mathematician is known as the Father of Geometry?

• A. Pythagoras

• B. Thales

• C. Euclid

• D. Hippocrates

Which statement is NOT one of the axioms of Euclidean geometry?

• A. Given any two distinct points, there is exactly one line that contains them.

• B. Every plane contains at least three points that do not lie on the same line.

• C. If two points lie in a plane, the line containing these points also lies in the plane.

• D. If two planes intersect, their intersection is a point.

By which angle must  $\overline{AB}$    turn about point A in the clockwise direction so that it coincides with  $\overline{AE}$   ?

• A. 90°

• B. 180°

• C. 270°

• D. 360°

Jonathan is standing near a fountain (F) that is located at the center of a circular garden. The pizza shop (P), the book store (B), and the gift shop (G) are located as shown. Which statement must be true with respect to Jonathan’s position?

• A. The distance from G to P is less than the distance from F to B.

• B. The distance from F to G is greater than the distance from F to B.

• C. The distance from B to P is equal to the distance from G to P.

• D. The distance from F to G is equal to the distance from F to B.

∆ABC transforms to produce ∆A'B'C'. Which transformation did NOT take place?

• A. rotation 180° counterclockwise about the origin

• B. reflection across the origin

• C. rotation 180° clockwise about the origin

• D. reflection across the line y = -x

The figure above the x-axis is the preimage. The figure below the x-axis is the image. Which transformation produced the image?

• A. reflection across the x-axis

• B. reflection about the origin

• C. rotation 90° clockwise about the origin

• D. rotation 90° counterclockwise about the origin

Which transformation will map an isosceles trapezoid onto itself?

• A. rotation by 180° about its center

• B. reflection across a diagonal

• C. reflection across a line joining the midpoints of the nonparallel sides

• D. rotation by 360° about its center

A regular polygon has an odd number of sides. Which statement is true about the lines of reflection for the polygon that will map the shape onto itself?

• A. Lines that connect pairs of opposite vertices are lines of reflection.

• B. The perpendicular bisectors for each side are the only lines of reflection.

• C. The lines of reflection are parallel to the sides of the polygon.

• D. There are no lines of reflection.

Regular hexagon FGHIJK shares a common center with square ABCD on a coordinate plane.  $\overline{AB}$ || $\overline{FG}$  . Across which lines can the combined figure reflect onto itself?

• A. any of the perpendicular bisectors of the sides of the hexagon

• B. either diagonal of the square

• C. any of the perpendicular bisectors of the sides of the square

• D. there are no lines across which this figure can reflect onto itself