Which of the following two conditions are sufficient to ensure that a quadrilateral ABCD is a parallelogram?

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

What are the two conditions of a rectangles?

To qualify as a rectangle, the shape must have four sides with four right angles whose opposite sides are parallel and equal in length to each other with diagonals of equal length and intersecting at their midpoints.

How would you prove a quadrilateral is a rectangle using slope?

When you are trying to prove a quadrilateral is a rectangle which method should you use: 1) Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.

What is sufficient condition for a quadrilateral to be a parallelogram?

“If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram”. The converse statement stated above is a necessary condition for a quadrilateral to be a parallelogram. “If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram”.

Which of the following is a sufficient to guarantee that a quadrilateral is a parallelogram?

Criteria proving a quadrilateral is parallelogram 1) If a quadrilateral has one pair of sides that are both parallel and congruent. 2) If all opposite sides of the quadrilateral are congruent. 3) Both pairs of opposite sides are parallel. 4) Opposite angles are congruent.

What makes a rectangle a rectangle?

A rectangle is a 2D shape in geometry, having 4 sides and 4 corners. Its two sides meet at right angles. Thus, a rectangle has 4 angles, each measuring 90 ̊. The opposite sides of a rectangle have the same lengths and are parallel.

What are properties of rectangle?

Convex polygon
Isogonal figure
Rectangle/Properties

Which of these are sufficient conditions to construct a quadrilateral?

Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurements. To construct a unique quadrilateral we need to know 5 measurements (elements). Note: To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient.

What is the condition for making a quadrilateral?

All sides are equal and, opposite sides are parallel to each other. Diagonals bisect each other perpendicularly. Sum of any two adjacent angles is 180°

Which of the following is sufficient to guarantee that a quadrilateral?

How do you prove that a quadrilateral is a rectangle?

A quadrilateral can be a rectangle only if the opposite sides of the quadrilateral are equal, and all the angles are 90° First off, draw the diagonals and show that they are perpendicular to each other.

What are the properties of a quadrilateral in geometry?

Properties of Quadrilateral. A quadrilateral is a four-sided polygon. Properties of quadrilateral are: Every quadrilateral has 4 vertices and 4 sides enclosing 4 angles. The sum of its interior angles is 360 degrees. A quadrilateral which has all 4 equal sides and 4 angles as 90 degrees is a square.

What is the total of the interior angles of a quadrilateral?

The total of its interior angles = 360 degrees. A quadrilateral with four equal sides and four right angles is a square. A quadrilateral that has opposite sides equal and measure of every angle is 90 degrees is a rectangle. Parallelogram, trapezium, rhombus, and kite are other examples of quadrilaterals.

How many pairs of opposite angles does a quadrilateral have?

Only one pair of opposite angles are of the same measure. A quadrilateral is a trapezoid or a trapezium if 2 of its sides parallel to each other. A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other.