Theorem
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
If …
Then …
ABCD is a
You will prove Theorem 6-9 in Exercise 21.
Theorem
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If …
Then …
ABCD is a
You will prove Theorem 6-10 in Exercise 18.
You can use algebra together with Theorems 6-8, 6-9, and 6-10 to find segment lengths and angle measures that assume that a quadrilateral is a parallelogram.
GRIDDED RESPONSE
For what value of y must PQRS be a parallelogram?
Which theorem should you use?
The diagram gives you information about sides. Use Theorem 6-8 because it uses sides to conclude that a quadrilateral is a parallelogram.
Step 1 Find x.
Step 2 Find y.
Use the diagram below. For what values of x and y must EFGH be a parallelogram?