# Thin-Slicing a Geometry Proof

This is how I would "thin slice" this proof.

## No Constraints (Givens)

This figure below has no constraints (Givens). Grab and move the points around. There are two triangles in the figure. Are they congruent? Are they ever congruent? Under what conditions would they be congruent?

## One Constraint (Given)

This figure below has just one constraint (Given): Segment SP Segment PT. Grab and move the points around. Are the two triangles in the figure congruent now? Could they be congruent? Are they ever congruent? Under what conditions would they be congruent?

## One Constraint (Given)

This figure below has just one constraint (Given): Angle SPQ Angle TPQ. Grab and move the points around. Are the two triangles in the figure congruent now? Could they be congruent? Are they ever congruent? Under what conditions would they be congruent?

## Two Constraints (Givens)

This figure below has two constraints (Givens):
1. Angle SPQ Angle TPQ , and
2. Segment SP Segment PT
Grab and move the points around. Are the two triangles in the figure congruent now? Are they ever congruent? Under what conditions would they be congruent? Would they ever NOT be congruent?