Hexagon STUVWZ is transformed according to the rule (x, y) →.(x + 8, y – 8) to form hexagon S'T'U'V'W'Z'.
Which statements are true?
(choose two)
Responses
A Hexagon STUVWZ is not congruent to hexagon S'T'U'V'W'Z'.Hexagon STUVWZ is not congruent to hexagon S'T'U'V'W'Z'.
B The sum of the angle measures of hexagon S'T'U'V'W'Z' is greater than the sum of the angle measures of hexagon STUVWZ.The sum of the angle measures of hexagon S'T'U'V'W'Z' is greater than the sum of the angle measures of hexagon STUVWZ .
C Hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ.Hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ .
D The area of hexagon STUVWZ is equal to the area of hexagon S'T'U'V'W'Z'.The area of hexagon STUVWZ is equal to the area of hexagon S'T'U'V'W'Z'.
E Corresponding angles of hexagon S'T'U'V'W'Z' and hexagon STUVWZ are not congruent.
A. Hexagon STUVWZ is not congruent to hexagon S'T'U'V'W'Z'.
B. The sum of the angle measures of hexagon S'T'U'V'W'Z' is greater than the sum of the angle measures of hexagon STUVWZ.
C. Hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ.
D. The area of hexagon STUVWZ is equal to the area of hexagon S'T'U'V'W'Z'.
E. Corresponding angles of hexagon S'T'U'V'W'Z' and hexagon STUVWZ are not congruent.
The correct statements are:
A. Hexagon STUVWZ is not congruent to hexagon S'T'U'V'W'Z'.
E. Corresponding angles of hexagon S'T'U'V'W'Z' and hexagon STUVWZ are not congruent.
The correct statements are:
B. The sum of the angle measures of hexagon S'T'U'V'W'Z' is greater than the sum of the angle measures of hexagon STUVWZ.
E. Corresponding angles of hexagon S'T'U'V'W'Z' and hexagon STUVWZ are not congruent.
To determine which statements are true, we need to analyze the given transformation and its effect on the properties of the hexagon.
The rule (x, y) → (x + 8, y – 8) involves adding 8 to the x-coordinate and subtracting 8 from the y-coordinate. This means that each point of the original hexagon is shifted 8 units to the right and 8 units downward to form the new hexagon.
Now let's evaluate each statement:
A. Hexagon STUVWZ is not congruent to hexagon S'T'U'V'W'Z'.
Since each point in hexagon STUVWZ has been shifted by the same amount, the shape and size of the two hexagons remain the same. Thus, they are congruent. Therefore, this statement is false.
B. The sum of the angle measures of hexagon S'T'U'V'W'Z' is greater than the sum of the angle measures of hexagon STUVWZ.
The sum of angle measures in a hexagon is always 720 degrees, regardless of its position or orientation. Since the transformation does not affect the internal angles of the hexagon, the sum of angle measures in hexagon S'T'U'V'W'Z' remains 720 degrees, just like in hexagon STUVWZ. Therefore, this statement is false.
C. Hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ.
As mentioned earlier, the shape and size of the hexagons remain the same after the transformation. So, hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ. Therefore, this statement is true.
D. The area of hexagon STUVWZ is equal to the area of hexagon S'T'U'V'W'Z'.
Since the transformation involves a horizontal and vertical shift, it does not change the shape or size of the hexagon. Therefore, hexagon STUVWZ and hexagon S'T'U'V'W'Z' have the same area. Thus, this statement is true.
E. Corresponding angles of hexagon S'T'U'V'W'Z' and hexagon STUVWZ are not congruent.
Because the transformation does not affect the internal angles of the hexagon, the corresponding angles in the original and transformed hexagons remain congruent. Therefore, this statement is false.
Based on our analysis, the true statements are:
C. Hexagon S'T'U'V'W'Z' is congruent to hexagon STUVWZ.
D. The area of hexagon STUVWZ is equal to the area of hexagon S'T'U'V'W'Z'.
Thus, the correct options are C and D.