**Parallelogram With 4 Congruent Sides** – Properties of Special IAL Parallelograms A rhombus is a parallelogram with four sides. A rectangle is a parallelogram with four right angles. | | A square is a parallelogram with four congruent sides and four right angles.

A Venn diagram shows the relationship between parallelograms, rhombuses, rectangles, and squares. Each diagram has characteristics of each group it contains. For example, a square is a rectangle, a rhombus, and a parallelogram, so it has all the properties of each shape.

## Parallelogram With 4 Congruent Sides

Defining an Indefinite Parallel Determine whether the expression is always, sometimes, or never true. A rhombus is a rectangle. Help Solution The statement is sometimes true. In a Venn diagram, the rhombus and rectangle regions are overlapping. If a rhombus is a square, then it is a rectangle.

## Quadrilaterals Brett Solberg Ahs ’11 ‘ Ppt Download

Defining an Indefinite Parallel Determine whether the expression is always, sometimes, or never true. A parallelogram is a rectangle. Help Solution The statement is sometimes true. Some examples are rectangular. In the Venn diagram, you can see that some of the shapes in the parallelogram are in the area of the rectangle, but most are not.

Using the properties of irregular parallelogram ABCD is a rectangle. What else do you know about ABCD? A B D C Solution Since ABCD is a rectangle, it has four right angles. The definition also says that a rectangle is a parallelogram, so ABCD has all the properties of a parallelogram: 1 Opposite sides are congruent and congruent. 2 opposite angles are congruent and adjacent sides are supplementary. 3 diagonals bisect each other.

Using the properties of irregular parallelogram ABCD is a rectangle. What else do you know about ABCD? A B D C A A rectangle is defined as a parallelogram with four right angles. But all quadrilaterals with right angles are right angles because all quadrilaterals with right angles are parallelograms.

Corollaries on Quadrilaterals Special Rhombus Corollary A quadrilateral is a brand if and only if it has four congruent sides. A regular quadrilateral is a rectangle if and only if it has angles. Square Corollary A quadrilateral is a square if and only if it is a rhombus and a rectangle. You can use these definitions to prove that a quadrilateral is a quadrilateral, rectangle, or square without proving that the quadrilateral is a parallelogram.

### How To Teach About Quadrilaterals And Polygons

Fig. PQRS is a rhombus. What is the value of y? 2y + 3 5y – 6 P Q R S Solution 5y – 6 = 2y + 3 Compare the lengths of the corresponding sides. 5y = 2y + 9 Add 6 to the side. 3y = 9 Subtract 2y from the side. y = 3 Divide each side by 3.

Theorems Theorem 6.11 A parallelogram is an isosceles if and only if its diagonals are perpendicular. ABCD is a rhombus if and only if AC is BD

Chapter 6.12 B C D is a parallelogram if and only if each diagonal bisects two sides. ABCD is an isogram if and only if AC bisects DAB and BCD and BD bisects ADC and CBA

Theorem S Theorem 6.13 A parallelogram A B D C is a rectangle if and only if its diagonals are congruent. ABCD is a rectangle if and only if AC BD

#### Question Video: Checking The Congruence Between Two Given Polygons

Using the diagonals of irregular parallelograms you can write Theorem 6.11 as the desired definition and its converse. Required Statement: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Discussion: If a parallelogram is a quadrilateral, then its diagonals are perpendicular. To prove the theorem, you must prove both equations.

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