PLZ HELP 40 POINTS!! GEOMETRY SAS Criterion for Similar Triangles The SAS criterion states that two triangles are similar if two pairs of corresponding sides are in the same ratio and the angles included by the pairs of sides in the two triangles are congruent. You’ll use GeoGebra to demonstrate this. Go to GeoGebra, and complete each step below.

Part A
Create a random triangle, ∆ABC. Record the lengths of two of the sides of the triangle and the measure of the included angle.

Part B
In this step, you’ll attempt to copy your original triangle using only two of its sides and the included angle. Follow these steps to construct the triangle: Draw a new line segment, DE, of any length, and place it anywhere on the coordinate plane, but not on top of ∆ABC. Find and record the ratio of the length of this line segment to one of the corresponding line segments on ∆ABC that you recorded in part A. Now multiply the ratio you calculated by the length of the other side of ∆ABC that you selected in part A. Record the resulting length. Locate the endpoint on DE that corresponds with the vertex of the angle you chose in part A. Using that point as the center, draw a circle with a radius equal to the length you calculated in the previous step. From the center of the circle, draw a ray at an angle to DE. Make the angle congruent to the angle of ∆ABC that you measured in part A. Mark the point of intersection of the ray and the circle, and label it point F. Complete ∆DEF by drawing a segment from F to the free endpoint of DE. Create a polygon through points D, E, and F. Take a screenshot of your results, save it, and insert the image below the measurements you record.

Part C
Measure all the angles of ∆ABC and ∆DEF, and enter the measurements in the table. ANGLE | MEASURE | | ANGLE | MEASURE | | |

Part D
Does a relationship exist between the measures of the angles of ∆ABC and ∆DEF? If so, explain how the triangles are related by these measurements. Use information that you discovered earlier in these Lesson Activities.

Part E
Your constructions for ∆ABC and ∆DEF were unique. Based on the random nature of this activity, what conclusion can you draw about the similarity of two triangles when two side lengths are proportional by the same ratio and the included angle is congruent?