Let's analyze the given quadrilaterals and the statements:

Quadrilateral Information:

• The quadrilateral $EFGH$ is a scaled copy of quadrilateral $ABCD$.
• Dimensions:
  • $ABCD$: $AB = 3$, $BC = 4$, $CD = 6$, and $DA = 8$.
  • $EFGH$: $FG = 6$, $GH = 12$, and we need to determine other values.

Scale Factor:

Since $FG = 6$ and $AB = 3$, the scale factor between $ABCD$ and $EFGH$ is $2$ (i.e., $6 / 3 = 2$).

Analyzing the Statements:

1. Segment $EF$ is twice as long as segment $AB$:

   • $EFGH$ is a scaled copy, and the scale factor is $2$.
   • Since $AB = 3$, the length of $EF$ should be $2 \times 3 = 6$.
   • True.

2. Segment $CD$ is twice as long as segment $FG$:

   • $CD = 6$ and $FG = 6$. They are equal, not double.
   • False.

3. The measure of angle $HEF$ is twice the measure of angle $DAB$:

   • Since the quadrilaterals are similar, corresponding angles remain the same.
   • $\angle HEF = \angle DAB$, not twice.
   • False.

4. The length of segment $EH$ is 16 units:

   • Using the scale factor, $DA = 8$, so $EH = 2 \times 8 = 16$.
   • True.

5. The area of $EFGH$ is twice the area of $ABCD$:

   • The area scales by the square of the linear scale factor. Since the scale factor is 2, the area of $EFGH$ is $4$ times the area of $ABCD$, not twice.
   • False.

Correct Answers:

• The true statements are:
  1. Segment $EF$ is twice as long as segment $AB$.
  2. The length of segment $EH$ is 16 units.

Would you like further clarification on any of these points?

Related Questions:

1. How do you find the scale factor between similar quadrilaterals?
2. How does the area of a shape change when scaled by a factor?
3. What is the relationship between corresponding angles in similar figures?
4. How do you calculate the length of sides in a scaled figure?
5. How do linear scaling and area scaling differ in geometry?

Tip:

For similar figures, the ratio of areas is the square of the ratio of corresponding side lengths.