Skip to main content


Scientific Calculator

TI 30Xa Solar best pic

Click on icon to access FSA online calculator

Congruence, Similarity, Right Triangles & Trig - 46%


Circles, Geometric Measurement & Geometric Properties with Equations - 38%


Modeling with Geometry - 16%


In Your Text

Videos From



What You Need To Know...

MAFS.912.G-CO.3.11 - prove theorems about parallelograms; use theorems about parallelograms to solve problems.

1. The benchmark will be assessed using Drag and Drop response, Hot Text Response, Movable Text Response, Multi-select Response, Multiple Choice Response, Open Response, or Selectable Text.

2. Items may require students to sequence the steps of a construction, explain the steps of a construction or complete a viable geometric argument.

3. Theorems are restricted to opposite sides are congruent; opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals.

4. Items may ask students to classify a quadrilateral as a parallelogram based on given properties or measures or to prove a quadrilateral is a parallelogram.

5.  Items can include narrative proofs, flow-chart proofs, two-column proofs, or informal proofs.

Example One

CO3 11 Ex1

          Click For Solution

Example Two

CO3 11 Ex2

                                            Click For Solution

Example Three

Example Four


In the figure below, AB is parallel to DC .






Which of the following statements about the figure must be true?



1-3 Answers



Click For Solution


Example Five

Figure ABCD is a rhombus.  The length of AE is (x + 5) units, and the length of EC is (2x - 3) units.



Which statement best explains why the equation x + 5 = 2x - 3 can be used to solve for x?

  1. All four sides of a rhombus are congruent.
  2. Opposite sides of a rhombus are parallel.
  3. Diagonals of a rhombus are perpendicular.
  4. Diagonals of a rhombus bisect each other.

Click For Solution

Example Six

For his mathematics assignment, Armando must determine the conditions that will make quadrilateral ABCD, shown below, a parallelogram.


Given that the m∠ DAB = 40°, which of the following statements will guarantee that ABCD is a parallelogram?

  1. m∠ ADC + m∠ DCB + m∠ ABC + 40°  = 360°.  
  2. m∠ DCB  = 40°; m∠ ABC  = 140° 
  3. m∠ ABC + 40° = 180° 
  4. m∠ DCB  = 40° 

Click For Solution

Additional Examples

coming-soon gif

Properties of Parallelograms
Properties of Diagonals
Real-World Application

Reference Sheet


Select sample problems taken from FLDVIPN teacher materials

Violet Esopakis - Palm Beach Co.
Stephanie Fitzwater - Seminole Co.
Angela Kerins - Orange Co.
Lisa Lasseter - St. Johns Co.
Jeremy Lowery - Escambia Co.
Jodi Van Wagoner - Brevard Co.