Question

The SSS, or side-side-side, criterion states that two triangles are similar if all three sides of one triangle are proportional to the corresponding sides of the other triangle. You'll use GeoGebra to demonstrate this condition. Open the GeoGebra activity to complete each step below. For help, watch these short videos about using GeoGebra to draw points, lines, and angles and use the measurement tools.

Part A
Create a random triangle, △ABC. Record the lengths of its sides.
Side Length
AB
BC
CA

Part B
Draw DE parallel to BC. You can draw DE any 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 DE to the length of BC. Then, multiply the lengths of AB and CA by 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 n x AB, which you calculated in part B.
Using point E as the center, draw a circle with a radius equal to the length of n x CA, which you calculated in part B.
Locate and label one of the intersections of the two circles as point F.
Complete △DEF 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 of △ABC 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.