SSS Criterion for Similar Triangles

https://contentstore.ple.platoweb.com/content/GeoGebra.v5.0/CCSS_GeoGebra_Activity.html

Part A

Make a random triangle, ABC. Record the lengths of its sides.

Side	Length
AB
BC
CA

Part B

Draw DEparallel to BC. You can draw DEany length and place it anywhere on the coordinate plane, but not on top of ABC. Find and record the ratio, n, of the length of DEto the length of BC. Then, multiply the lengths of ABand CAby n and record the resulting lengths.

Part C

Now you will attempt to copy your original triangle using only its sides:

• Using point D as the center, draw a circle with a radius equal to the length of nAB, which you calculated in part B.
• Using point E as the center, draw a circle with a radius equal to the length of nCA, which you calculated in part B.
• Locate and label one of the intersections of the two circles as point F.
• CompleteDEF by creating a polygon through points D, E, and F.

Take a screenshot of your results, save it, and insert the image below.

Part D

Record the measures of the angles ofABC and DEF.

Angle	Measure
ABC
BCA
CAB

Angle	Measure
EDF
FED
DFE

Part E

Using your results, draw a conclusion about the relationship between two triangles when all three sets of corresponding sides of the triangles are proportional by the same ratio.