Question

1. reflect pentagon c across line l.

a. in the image, write the length of each side, in grid - units, next to the side. you may need to make your own ruler with tracing paper or a blank index card.
b. in the image, write the measure of each angle in the interior.

Explanation:

Step1: Reflect the pentagon

Use the properties of reflection. The reflected pentagon will be congruent to the original pentagon. So, side - lengths and angle - measures will be the same as the original pentagon.

Step2: Measure side - lengths

To measure the side - lengths in grid units, count the number of grid squares between the endpoints of each side. For example, if a side lies exactly along the grid lines, you can simply count the number of unit squares. If it is diagonal, you can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the horizontal and vertical displacements between the endpoints and \(c\) is the length of the side.

Step3: State angle - measures

The angle - measures in the interior of the reflected pentagon are the same as in the original pentagon. Given angles are \(90^{\circ},90^{\circ},90^{\circ},120^{\circ},150^{\circ}\)

Answer:

a. Measure side - lengths by counting grid units or using Pythagorean theorem for diagonal sides.
b. Interior angles are \(90^{\circ},90^{\circ},90^{\circ},120^{\circ},150^{\circ}\)