## 1st property

The opposite sides of a parallelogram are congruent.*H*: ABCD is parallelogram.

*T*:

**Demonstration:**

*Affirmative*

1.

2.

*Justification*

1. Parallel to parallel segments.

2. Parallel to Parallel Segments.

## 2nd property

Each parallelogram diagonal divides it into two congruent triangles. |

H: ABCD is parallelogram.

T:

**Demonstration:**

*Affirmative*

1.

2.

3.

4.

*Justification*

1. Hypothesis.

2. Hypothesis.

3. Common side.

4. Case of L.L.L.

## 3rd property

The opposite angles of a parallelogram are congruent. |

H: ABCD is parallelogram

T:

**Demonstration:**

*Affirmative*

1.

2.

3.

4.

5.

*Justification*

1. is diagonal (2nd property)

2. Corresponding angles in congruent triangles.

3. Corresponding angles in congruent triangles.

4.

## 4th property

The diagonals of a parallelogram intersect each other in half. |

H: ABCD is parallelogram.

T:

**Demonstration**

*Affirmative*

1.

2.

3.

4.

5.

*Justification*

1. Internal alternate angles.

2. Opposite sides (1st property).

3. Internal alternate angles.

4. Case A.L.A.

5. Corresponding sides in congruent triangles.

**Summing up:**

In a parallelogram:

- opposite sides are congruent;
- each diagonal divides it into two congruent triangles;
- opposite angles are congruent;
- the diagonals intersect at their midpoint.

## Rectangle Characteristic Property

The diagonals of a rectangle are congruent. |

T: ABCD is rectangle.

H: .

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