# Properties of parallelograms

## 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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