One-half the product of and is the same as one-half the product of and .
Or, ignoring the one-halfs, you can simply say that the products are equal.
3 . E
The only information that’s in the question and not in the figure is that and are
parallel and that the area of ∆EFG is a. That and are parallel tells you that ∆EFG and
∆DFH are similar—they have the same angles, and their sides are in proportion. Because the
ratio of to is , the ratio of any pair of corresponding sides will also be . But
that’s not the ratio of the areas. Remember that the ratio of the areas of similar triangles is
the square of the ratio of the sides. Here the side ratio is , so the area ratio is . If
the area of the small triangle is a, then the area of the large one is .
4 . B
Drop an altitude, and you’ll reveal two hidden special right triangles:
