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MA.912.G.3.4 Theorems Involving Quadrilaterals

What You Need To Know...

Theorems involving quadrilaterals.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may require the use of relationships among quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid, and kite).
  3. Items may include proofs.

Example One

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

3-4.jpg

 

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 HERE FOR SOLUTION

Example Two

Four students are choreographing their dance routine for the high school talent show.  The stage is rectangular and measures 15 yards by 10 yards.  The stage is represented by the coordinate grid below.  Three of the students - Riley (R), Krista (K), and Julian (J) - graphed their starting positions, as shown below.

3-4B.jpg

Let H represent Hannah's starting position on the stage.  What should be the x-coordinate of point H so that RKJH is a parallelogram?

Blank Grid.jpg

 

CLICK HERE FOR SOLUTION

Additional Examples

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Quadrilateral Overview

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Sides of Parallelograms

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Angles of Parallelograms

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Parallelogram Diagonals

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Diagonals of a Rhombus

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Trapezoids and Kites

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Reference Sheet

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