Step {{currentStep}} of 4
Drag to grid

Build a Parallelogram

Drag vertex D so that quadrilateral ABCD forms a parallelogram.

A B C D
Opposite sides must be parallel and equal length.
Tap congruent parts

Prove the Diagonals

To prove , we first prove by SAS.
Tap the 3 pairs of congruent parts on the rectangle.

SAS Checklist

  • Opposite Sides ()
  • Right Angles ()
  • Shared Side ()
A B C D
Draw lines to match

Build the Formal Proof

Connect each statement on the left to its logical reason on the right.

{{r.text}}
Tap to cycle

Coordinate Geometry Logic

Given quadrilateral ABCD with vertices , , , .
Complete the paragraph proof.

A B C D
The slope of diagonal AC is
{{ s4State.c1.opts[s4State.c1.idx] }}
and the slope of diagonal BD is
{{ s4State.c2.opts[s4State.c2.idx] }}
.

Because their product is
{{ s4State.c3.opts[s4State.c3.idx] }}
, the diagonals are
{{ s4State.c4.opts[s4State.c4.idx] }}
.

Therefore, the parallelogram is a
{{ s4State.c5.opts[s4State.c5.idx] }}
.

Proof Complete!

You've mastered identifying properties and building logical proofs for quadrilaterals.