**Parallelogram With Four Congruent Sides** – These words are used all the time by teachers, and we are used to hearing them, but what do they really mean and how can we tell the difference between these special quadrilaterals?

Together, we will put our knowledge to the test and discover amazing properties about these three particular parallelograms.

## Parallelogram With Four Congruent Sides

First, it is important to note that rectangles, squares, and rhombuses (plural of rhombus) are all quadrilaterals that have all the properties of parallelograms.

#### Properties Of Rhombuses, Rectangles, And Squares

The biggest distinguishing features have to do with their four sides and four corners. A rectangle is a parallelogram with four right angles. A rhombus, sometimes called a rhombus or rhombus, as Mathematics is Fun puts it, is a parallelogram with four congruent sides. And a square is a parallelogram with four right angles and four equal sides.

A: For a rhombus, we are assured that all sides are the same length, while a parallelogram only specifies that opposite sides are congruent.

A: A square and a rhombus both have four congruent sides, but a square also has four congruent right angles, while a rhombus only specifies that opposite angles are congruent and do not have to be at 90 degrees.

A: A square is a rectangle because it satisfies all the properties of a rectangle. Remember, for a parallelogram to be a rectangle, it must have four right angles, congruent opposite sides, parallel opposite sides, congruent opposite angles, intersecting diagonals, and congruent diagonals. A square meets all these requirements, so a square is still a rectangle.

### What Is A Square? (definition, Properties, & Video) // Tutors.com

A: A diamond can only be a rectangle if all four corners of the diamond are 90 degrees.

Together we will look at several examples where we will use our properties of rectangles, rhombuses and squares, as well as our knowledge of the relationships between pairs of angles, to determine missing angles and side lengths.

In addition, we will draw on our understanding of isosceles, equilateral and right triangles to find the given measurements as well as the perimeter of a given polygon.1. A rhombus is a parallelogram with four congruent sides. 2. A rectangle is a parallelogram with four right angles. 3. A square is a parallelogram with four congruent sides and four right angles.

4 Corollary of the rhombus A quadrilateral is a rhombus if and only if it has four congruent sides. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

### Quadrilaterals And Their Properties Diagram

If a quadrilateral is a rhombus, then it has four congruent sides. Given: quad. ABCD is a rhombus If a quadrilateral has four congruent sides, then it is a rhombus. Try: quad. ABCD is a rhombus

6 Corollary A quadrilateral rectangle is a rectangle if and only if four right angles. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

If a quadrilateral is a rectangle, then it has four right angles. Given: quad. ABCD is a rectangle If a quadrilateral has four right angles, then it is a rectangle. Try: quad. ABCD is a rectangle

8 Square Corollary A quadrilateral is a square if and only if it is a rhombus and a rectangle. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

#### Parallelogram Lines Of Symmetry Explained! — Mashup Math

If a quadrilateral is a square, then it is a rhombus and a rectangle. Given: quad. ABCD is a square Prove: quad. ABCD is a rhombus and a rectangle If a quadrilateral is a rhombus and a rectangle, then it is a square. Given: quad. ABCD is a rhombus and a rectangle Try: a quad. ABCD is a square

10 The Venn diagram on the next slide shows some important relationships between parallelograms, rhombuses, rectangles and squares. For example, you can see that a square is a rhombus because it is a parallelogram with four congruent sides. Because it has four right angles, a square is also a rectangle.

12 Example 1 For each rectangle ABCD, decide whether the statement is always true or sometimes true. Sketch and explain your reasoning. This is still true because a rectangle is also a parallelogram by definition. A B C D

14 Example 2 For any RSTV diamond, decide whether the statement is always true or sometimes true. Sketch and explain your reasoning.

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17 Example 3 Classify the special quadrilateral. Explain your reasoning. a. This is a rhombus. It is a parallelogram whose consecutive sides are equal. Which means all sides are congruent.

18b. It is a rhombus as it is a quadrilateral with 4 congruent sides but the four angles are not right angles.

20 A parallelogram is a rhombus if and only if its diagonals are perpendicular. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

If a parallelogram is a rhombus, then its diagonals are perpendicular. Let: the parallelogram ABCD is a rhombus If a parallelogram has perpendicular diagonals, then it is a rhombus. Prove that the parallelogram ABCD is a rhombus

#### A Rhombus Is A Parallelogram With Four Congruent Sides.

22 A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

23 If a parallelogram is a rhombus, then each diagonal bisects opposite angles. Let: the parallelogram ABCD is a rhombus If each diagonal of a parallelogram intersects opposite angles, then it is a rhombus. Prove that the parallelogram ABCD is a rhombus

24 A parallelogram is a rectangle if and only if its diagonals are congruent. Rewrite the biconditional as two conditionals, then write the given one and try using the given diagram.

If a parallelogram is a rectangle, then its diagonals are congruent. Let: the parallelogram ABCD is a rectangle If the diagonals of a parallelogram are congruent, then it is a rectangle. Prove that parallelogram ABCD is a rectangle

### Quadrilaterals Card Sort

1. All sides are congruent. 2. The two pairs of opposite sides are parallel. 3. The two pairs of opposite angles are equal. 4. The diagonals intersect each other. 5. The diagonals are perpendicular. 6. Each diagonal bisects opposite angles.

1. All angles are right angles. 2. The two pairs of opposite sides are parallel. 3. The two pairs of opposite sides are congruent. 4. The diagonals intersect each other. 5. The diagonals are congruent.

1. All angles are right angles. 2. All sides are congruent. 3. The two pairs of opposite sides are parallel. 4. The diagonals intersect each other. 5. The diagonals are congruent. 6. The diagonals are perpendicular. 7. Each diagonal bisects opposite angles.

To operate this website, we log user data and share it with contractors. To use this website, you must accept our privacy policy, including the cookie policy.PROPERTIES OF SPECIAL PARALLELOGRAMS A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. | | A square is a parallelogram with four congruent sides and four right angles.

### Lesson Video: Properties And Special Cases Of Parallelograms

The Venn diagram shows the relationships between parallelograms, rhombuses, rectangles and squares. Each shape has the properties of each group it belongs to. For example, a square is a rectangle, a rhombus and a parallelogram, so it has all the properties of each of these shapes.

Describe a special parallelogram Decide whether the statement is always true, sometimes or never. A rhombus is a rectangle. Help SOLUTION The statement is sometimes true. In the Venn diagram, the diamond and rectangle regions overlap. If the rhombus is a square, it is a rectangle.

Describe a special parallelogram Decide whether the statement is always true, sometimes or never. A parallelogram is a rectangle. Help SOLUTION The statement is sometimes true. Some parallelograms are rectangles. In the Venn diagram, you can see that some of the box shapes of the parallelogram are in the region of rectangles, but most are not.

Using special properties of parallelograms 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 by definition. The definition also says that rectangles are parallelograms, so ABCD has all the properties of a parallelogram: 1 Opposite sides are parallel and congruent. 2 Opposite angles are equal and consecutive angles are supplementary. 3 diagonals intersect in their middle.

#### Determine Whether The Quadrilateral Is A Parallelogram. Justify Your Answer. A) Yes; Opposite Angles

Using special properties of parallelograms ABCD is a rectangle. What else do you know about ABCD? A B D C A rectangle is defined as a parallelogram with four right angles. But every quadrilateral with four right angles is a rectangle because every quadrilateral with four right angles is a parallelogram.

SPECIAL QUADRILATERAL COLLARS LOZENGE COLLARS A quadrilateral is a rhombus if and only if it has four congruent sides. COROLLARY RECTANGLE A quadrilateral is a rectangle if and only if it has four right angles. SQUARE COLLARIUM A quadrilateral is a square if and only if it is a rhombus and a rectangle. You can use these corollaries to prove that a quadrilateral is a rhombus, rectangle, or square without first proving that the quadrilateral is a parallelogram.

In the diagram, PQRS is a diamond. What is the value of y? 2y + 3 5y – 6 P Q R S SOLUTION The four sides of a rhombus are congruent, so RS = PS. 5a – 6 = 2a +

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