# MAFS.912.G-CO.3.11

## Scientific Calculator

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Congruence, Similarity, Right Triangles & Trig - 46%

## MAFS.912.G-

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

## MAFS.912.G-

Modeling with Geometry - 16%

## 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 Four

In the figure below,  is parallel to  .

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

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## Example Five

Figure ABCD is a rhombus.  The length of  is (x + 5) units, and the length of  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.

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## 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°

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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.
Jodi Van Wagoner - Brevard Co.