1. For a triangle XYZ, we use [XYZ] to denote its area.

Let ABCD be a square with side length 1. Points E and F lie on line BC and line CD, respectively, in such a way that angle EAF=45 degrees If [CEF]=1/9, what is the value of [AEF]?

2. A triangle T is separated into two congruent triangles by a straight cut. Which of the following statements are true?

A) T must have two sides with equal length.

B) The cut must be perpendicular to one side of T.

C) T must have two interior angles with the same measure.

D) The cut must go through the midpoint of one side of T.

Type your answer as a list of letters separated by commas. For instance, if you believe that conditions A, B, and C are enough, then type "A,B,C" into the answer box. If you believe none of the options are correct, enter "none."

3. Line PS bisects angle QPR . We can ensure that triangle PQS is congruent to triangle PRS by adding just one more condition. Which of the following statements could be that condition?

A) PQ=PR

B) SQ=SR

C) Angle PQS=Angle PRS

D) Angle PSQ=Angle PSR

Hint: The figure is a kite bisected into two parts from P to S

Type your answer as a list of letters separated by commas. For instance, if you believe that any of the conditions A, B, or C would be enough, then type "A,B,C" into the answer box. If you believe none of the options are correct, enter "none."