Day 86: Investigating Rectangles

Today was a multi-layered activity that ties a lot of 1st semester content together to create new situations to be analyzed. 

Start by graphing a line. Create a line perpendicular through point D. Create a second perpendicular line through point C. Connect C & D (essentially, make a rectangle). 

Now: 

• Are the sides the same length? Prove with the distance formula. 
• Is the diagonal equal to sqrt(2) * side length? Prove with the distance formula.
• Are the diagonals angle bisectors? Prove using a tangent ratio. 
• Are the diagonals perpendicular bisectors? Prove using slope and midpoint. 

From this activity, we'll build into determining all of the angles and look for commonalities, leading toward the idea of parallel lines and the angle pairs that are formed.