Rectangle, rhombus, and square are special types of parallelograms. Rectangles have four right angles and congruent diagonals. Rhombuses have four equal sides and perpendicular diagonals that bisect opposite angles. Squares are both rectangles and rhombuses, with four congruent sides that are also right angles and diagonals that are perpendicular and congruent.

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SPECIAL PARALLELOGRAMS

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Rectangle, rhombus and square are quadrilaterals
that are parallelograms. They are known as
special parallelograms. They are special since all
the properties of a parallelogram are present in
square, rhombus and rectangle.

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Characteristics of Rectangle
1. Opposite sides are parallel and congruent.
2. Opposite angles are congruent and
supplementary.
3. All four angles are right angles.
4. Consecutive angles are supplementary.
5. Diagonals bisect each other and are
congruent.
6. Each diagonal separates the rectangle into
two congruent triangles.

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Theorems on Rectangle
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Theorem 1. If a parallelogram has right angle, then it has four
right angles and the parallelogram is a rectangle.
Given: □MATH is a parallelogram with∠ M is a right angle
Prove: ∠ A, ∠ T, and ∠H are right angles

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Given: □MATH is a rectangle with diagonals 𝑀𝑇 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
and 𝐻𝐴̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
Prove: 𝑀𝑇 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
≅ 𝐻𝐴̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
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Theorem 2. The diagonals of a rectangle are congruent.

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Examples:
□MATH is a rectangle. Find the value of x and the specified
sides
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Characteristics of Rhombus
1. All four sides are congruent.
2. Opposite sides are parallel.
3. Opposite angles are congruent.
4. Consecutive angles are supplementary.
5. Diagonals bisect each other and are
perpendicular.
6. Each diagonal bisects a pair of opposite angles.
7. Each diagonal separates the rhombus into two
congruent triangles
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Theorem 3. The diagonals of a rhombus are perpendicular.
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Given: □ FREN is a rhombus
Prove:

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Theorem 4. Each diagonal of a rhombus bisects
opposite angles.
Given: □ FREN is a rhombus
Prove: ∠1 ≅∠2 , ∠3 ≅∠4

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Characteristics of Square
1. All four sides are congruent.
2. All angles are right angles.
3. Opposite sides are parallel and congruent.
4. Opposite angles are congruent and supplementary.
5. Consecutive angles are supplementary and
congruent.
6. Diagonals bisect each other and are perpendicular
and congruent.
7. Each diagonal separates the square into two
congruent triangles.

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Theorem 5. The diagonals of a square are congruent
and perpendicular.
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Solution
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Thank You