Geometry: An Interactive Journey to Mastery

Lesson 14: Exploring Special Quadrilaterals

3. Given: ABCD is a parallelogram.
   E is the midpoint of AB.
   F is the midpoint of DC.
   Prove: EBFD is a parallelogram.
   ͼ௘6HHFigure 14.5௘ͽ


4. D௘ͽ $SDUDOOHORJUDPFRQWDLQVRQHULJKWDQJOH
   ͼ௘6HHFigure 14.6௘ͽ([SODLQZK\WKDWSDUDOOHORJUDP
   must be a rectangle.
   E௘ͽ $SDUDOOHORJUDPKDVWZRFRQJUXHQWDGMDFHQWVLGHV
   ͼ௘6HHFigure 14.7௘ͽ([SODLQZK\WKDWSDUDOOHORJUDP
   must be a rhombus.


5. Two interior angles of a parallelogram come in a ratio of 11:7. What are the measures of all four interior
   angles of the parallelogram?


6. Suppose that A ͼ௘௘ͽB ͼ௘í௘ͽC ͼ௘௘ͽDQGD ͼ௘p, q௘ͽ)LQGWKHYDOXHVIRUp and q that make
   ABCD a parallelogram.


7. The perimeter of parallelogram FRED is 22 cm. The longest side of FRED is 2 cm longer than the shortest
   side. What are the four side lengths of FRED?

AB

DFC

E

Figure 14.5

Figure 14.6

Figure 14.7