Options:
A. Segment EF is twice as long as segment AB.
B. Segment CD is twice as long as segment FG.
C. The measure of angle HEF is twice the measure of angle DAB.
D. The length of segment EH is 16 units.
E. The measure of angle BCD is the same as the measure of angle GFE.
Answer:
A. Segment EF is twice as long as segment AB.
D. The length of segment EH is 16 units.
Explanation:
First, let's find out the scale factor that was used in creating quadrilateral EFGH.
Scale factor = ratio of their corresponding segment length.
Segment GH corresponds with segment CD.
Scale factor = GH/CD = 12/6 = 2.
This means all segments that make up quadrilateral ABCD were increased proportionally to give corresponding segment lengths that make up quadrilateral EFGH.
The size of ABCD would increase, while the shape remains the same. This implies that, the measures of corresponding angles are the same, i.e. m<C = m<G.
The following statements are therefore true:
A. Segment EF is twice as long as segment AB.
AB corresponds to EF. Therefore, AB*scale factor = length of EF
AB*2 = EF
EF is twice the length of AB.
D. The length of segment EH is 16 units.
AD corresponds to EH.
AD*scale factor = length of EH
AD*2 = EH
Given that AD = 8, therefore:
8*2 = EH
16 = EH
EH = 16 units