Application of the Properties of Parallelograms

The video explores the properties of parallelograms and their special cases: rectangles, rhombuses, and squares. It provides proofs for each case, demonstrating how specific conditions on diagonals lead to these shapes. The video also covers applications of parallelogram properties and additional proofs involving triangles and parallelograms.

What happens when the diagonals of a parallelogram are equal?

• It remains a parallelogram.

• It becomes a rectangle.

• It becomes a rhombus.

• It becomes a square.

If the diagonals of a parallelogram bisect each other at right angles, what shape does it form?

• Rectangle

• Square

• Rhombus

• Trapezoid

In the proof that a parallelogram with equal diagonals is a rectangle, which property of triangles is used?

• ASA Congruence

• SSS Congruence

• SAS Congruence

• Pythagorean Theorem

Which theorem is applied in the proof that a parallelogram with diagonals bisecting at right angles is a rhombus?

• Parallel Postulate

• Pythagorean Theorem

• Triangle Sum Theorem

• Congruence Theorem

What is the result when the diagonals of a parallelogram are equal and bisect each other at right angles?

• It remains a parallelogram.

• It becomes a square.

• It becomes a rhombus.

• It becomes a rectangle.

In proving a square from a parallelogram, which congruence rule is used?

• SSS Congruence

• ASA Congruence

• AAS Congruence

• SAS Congruence

What is the significance of a diagonal bisecting an angle in a parallelogram?

• It proves the parallelogram is a trapezoid.

• It proves the parallelogram is a square.

• It proves the parallelogram is a rhombus.

• It proves the parallelogram is a rectangle.

What condition must be met for a quadrilateral to be a parallelogram?

• Opposite sides must be parallel and equal.

• Diagonals must be equal.

• All sides must be equal.

• All angles must be right angles.

According to Euclid, what happens when lines parallel to the sides of a parallelogram are drawn through a point on its diagonal?

• The parallelogram becomes a square.

• The segments of the diagonal are equal in area.

• The parallelogram becomes a rhombus.

• The segments of the diagonal are unequal in area.

What is the result when two points on a diagonal of a parallelogram are equidistant from the center?

• The quadrilateral formed is a parallelogram.

• The quadrilateral formed is a rhombus.

• The quadrilateral formed is a rectangle.

• The quadrilateral formed is a square.