Sage-Tips

How do you prove ABCD?

If — BC — AD and — BC ≅ — AD , then ABCD is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If — BD and — AC bisect each other, then ABCD is a parallelogram.

How do you prove that the opposite sides of a parallelogram are equal?

The opposite sides of a parallelogram are equal. ABCD is a parallelogram. To prove that AB = CD and AD = BC….A quadrilateral is a parallelogram if:

1. its opposite angles are equal, or.
2. its opposite sides are equal, or.
3. one pair of opposite sides are equal and parallel, or.
4. its diagonals bisect each other.

How can you prove that two quadrilaterals are congruent?

Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent. If a quadrilateral has opposite sides congruent then its diagonals divide the quadrilateral into congruent triangles.

How do you prove that 4 points make a rectangle?

If you already know that the shape is a parallelogram, you will only have to show that one of the angles is a right angle and then it would follow that all of the angles are right angles. Example: Prove that the following four points will form a rectangle when connected in order….Prove it is a Rectangle.

Statements	Reasons
AC ≅ BD	CPCTC

How do you describe any two opposite side in a parallelogram?

Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other.

Is ABCD in the figure a parallelogram Why?

between AC and DB which makes AC and DB parallel and equal lines. Hence, ABCD is a parallelogram.

How do you prove two rectangles are congruent?

Two rectangles are congruent if both of them have the opposite sides are equal. Two squares are congruent if both of them have the same edges. Thus, the method of comparing two figures is known as the method of superposition.

Are ABCD and Efgh congruent?

Parallelograms ABCD and EFGH have four congruent sides but they are not congruent since they have different angles (and also different area).

Is ABCD congruent?

Both pairs of opposite sides of a parallelogram are congruent. So for ABCD, AB ≅ CD and BC ≅ DA. Both pairs of opposite angles are congruent So for ABCD, ∠B ≅ ∠D and ∠A ≅ ∠C….Sample Problem.

Statements	Reasons
1. ABCD is a parallelogram	Given
2. AB || CD and BC || DA	Definition of a parallelogram (1)