Lori has written the conjectures below. For each one, decide if it is true or not. If you believe it is not true, find a counterexample (an example that proves that the statement is false).  

1. If a shape has four equal sides, it cannot be a parallelogram.

   Answer (a):

   False. A rhombus and a square are counterexamples because both have $4$ equal sides and opposite sides are parallel like in all parallelograms.

2. If tan $θ$ is more than $1$, then $θ$ must be more than $45^\circ$.

   Hint (b):

   Look at the Math Notes box for Lesson 4.1.4 for extra help.

   What happens when $\large\frac{\text{opp}}{\text{adj}}$ is more than $1$?

3. If two angles formed when two lines are cut by a transversal are corresponding, then the angles are congruent.

   Hint (c):

   What if the lines are not parallel? Draw a diagram.