Question

hexagon stuvwz is transformed according to the rule (x,y)→(x + 8,y - 8) to form hexagon stuvwz. which statements are true? (choose two.) a hexagon stuvwz is not congruent to hexagon stuvwz. b the sum of the angle - measures of hexagon stuvwz is greater than the sum of the angle - measures of hexagon stuvwz. c hexagon stuvwz is congruent to hexagon stuvwz. d the area of hexagon stuvwz is equal to the area of hexagon stuvwz. e corresponding angles of hexagon stuvwz and hexagon stuvwz are not congruent.

Explanation:

Step1: Analyze the transformation rule

The rule $(x,y)\to(x + 8,y - 8)$ is a translation. Translation is a rigid - motion transformation. Rigid - motion transformations (translations, rotations, reflections) preserve side lengths and angle measures.

Step2: Evaluate congruence

Since translation is a rigid - motion transformation, hexagon $STUVWZ$ and hexagon $S'T'U'V'W'Z'$ are congruent. Congruent polygons have equal side lengths, equal angle measures, and equal areas.

Step3: Check each option

• Option A: Hexagon $STUVWZ$ is congruent to hexagon $S'T'U'V'W'Z'$, so this option is false.
• Option B: The sum of the interior - angle measures of a hexagon is given by $(n - 2)\times180^{\circ}=(6 - 2)\times180^{\circ}=720^{\circ}$ for any hexagon. Since the two hexagons are congruent, the sum of the angle measures is the same. This option is false.
• Option C: As mentioned, the two hexagons are congruent, so this option is true.
• Option D: Congruent polygons have equal areas, so this option is true.
• Option E: Corresponding angles of congruent polygons are congruent, so this option is false.

Answer:

C. Hexagon $S'T'U'V'W'Z'$ is congruent to hexagon $STUVWZ$
D. The area of hexagon $S'T'U'V'W'Z'$ is equal to the area of hexagon $STUVWZ$