Answer:
10. It is a parallelogram.
11. The parallelogram is a rhombus.
Step-by-step explanation:
10. Use the given sets of congruent segments with congruent vertical angles XNY and WNZ to prove that triangles XNY and ZNW are congruent. Now use CPCTC to show that angles XYN and ZWN are congruent. They are alternate interior angles making sides XY and WZ parallel. Now use CPCTC to show that sides XY and WZ are congruent. Since a quadrilateral has two opposite sides that are both parallel and congruent, the quadrilateral is a parallelogram.
11. A rectangle and a square have 4 right angles. If you add 72 deg and 72 deg, you get 144 deg which is not a right angle. Since one angle of the parallelogram is not a right angle, the parallelogram is not a square or a rectangle.
There are two triangles. Let's look at the upper triangle. The triangle has 2 angles measuring 72 deg each. That means the opposite sides are congruent, and the triangle is isosceles. Since the quadrilateral is a parallelogram, opposite sides are congruent, so all 4 sides are congruent, and the parallelogram is a rhombus.
