Jamie has a pentagon that she thinks has two pairs of congruent angles and two pairs of congruent sides. How can she check this without using any tools?

To check if Jamie's pentagon has two pairs of congruent angles and two pairs of congruent sides without using any tools, she can follow these steps:

1. Recall that a pentagon is a polygon with five sides. Let's label the vertices of Jamie's pentagon as A, B, C, D, and E.

2. Start by checking if any two sides of the pentagon are congruent. Measure and compare the lengths of AB, BC, CD, DE, and EA. If two pairs of sides have the same length, then Jamie has found her two pairs of congruent sides.

3. Next, check Jamie's assumption about the pairs of congruent angles. Measure and compare the angles at vertices A, B, C, D, and E. Remember that the sum of the interior angles of any pentagon is equal to 540 degrees. If Jamie finds two pairs of angles that have the same measure (congruent), then she has discovered her two pairs of congruent angles.

By following these steps, Jamie can visually inspect her pentagon and verify if it has two pairs of congruent angles and two pairs of congruent sides.