Answer:
GF = 11
DF = 28
HF = 14
DG = 25.75
Explanation:
GF: Both pairs of parallel lines are congruent, and all angles are 90°. With that said, since DE is 11, and it is parallel to GF, they are equivalent, so GF is 11.
DF: Since the quadrilateral is a rectangle, the intersecting lines are equivalent. This is because both pairs of parallel lines are congruent, and all angles are 90°. So, since GE is 28, and DF is congruent to GE, DF is 28.
HF: As with DF, both the intersecting lines are congruent, so that means the halves that they create are also congruent to one another. With that said, since GH is 14, that means HD, HE, and HF are all 14 as well.
DG: Since rectangle DEFG is a rectangle with a line diagonally crossing from one corner to another, this creates a right triangle with exactly half of the rectangle. The Pythagorean Theorem works to find an unknown side of a right triangle, so it can be used to find side DG. Since the formula is (a^2 + b^2 = c^2), with c being the hypotenuse (line DF), and a & b are the two sides (a can be side GF, and b is what is being solved for), the formula can be turned into this: (11^2 + b^2 = 28^2). This simplifies to (121 + b^2 = 784). Subtract 121 from both sides to get (b^2 = 663). Square root to get b. b is about 25.75 (rounding). This means, the other side of the triangle, or DG, is 25.75 units. Hope this helps! Have a great day! :)