a If you want half of something you need to divide it by 2. This is the same thing as multiplying it by a factor of 12. Note that the shape is a parallelogram, which means it has two pairs of congruent sides.
Longer sides:& 1/2(16)=8 [1em]
Shorter sides:& 1/2(11)=5.5
Now we can draw the new figure.
bCongruent shapes are identical. Therefore, the parallelogram Rakisha drew must have identical sides to the original. This means the ratio between corresponding sides equals 1.
c We will try to find a counterexample to Rakisha's claim. To do so, we should first choose an angle x between 0^(∘) and 180^(∘). Next, we should draw two line segments with lengths 16 and 11 units, which form a α degree angle between them.
Next, let's draw another 11-units long line segment from the other endpoint of the longer line segment. This time we want these segment to form an 180^(∘) - x angle between them — that way the smaller segments will be parallel.
Finally, we connect the other endpoints of the shorter segments. Since they are parallel and of the same length, the resulting quadrilateral will be a parallelogram.
Now, suppose that the angle Rakisha chose was y. As long as we chose x different from y and 180^(∘) - y, the parallelogram we got will not be congruent to the Rakisha's one. Therefore, her claim is false.
