Why is Pqrs a parallelogram?

Why is Pqrs a parallelogram?

Since the quadrilateral PQRS has two pairs of parallel sides, it is a parallelogram.

How do you prove PQRS is a parallelogram?

We will use the mid-point theorem here. It that states that the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and is half of it. Clearly, one pair of opposite sides of quadrilateral PQRS is parallel and equal. Hence, PQRS is a parallelogram.

What reason can be used to prove that ABCD is a parallelogram?

Then ABCD is a parallelogram because its diagonals bisect each other. The square on each diagonal is the sum of the squares on any two adjacent sides. Since opposite sides are equal in length, the squares on both diagonals are the same.

Can quadrilateral PQRS be a parallelogram?

Yes, it can parallelogram. As we know that opposite sides of parallelogram is equal and sum of its adjacent angles be 180 degrees.

In which of the following Pqrs can be a parallelogram?

Answer: Yes, it can parallelogram. As we know that opposite sides of parallelogram is equal and sum of its adjacent angles be 180 degrees. But we can not claim it to be a parallelogram because to be sure it’s a parallelogram it’s opposite sides must be parallel to each other.

Which type of quadrilateral is PQRS?

Rhombus, parallelogram and kite have their opposite angles equal (i.e. in the ratio 1:1). Therefore, the quadrilateral PQRS is a trapezium.

What is mid point theorem Class 9?

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

What is quadrilateral PQRS?

The word quadrilateral means the four sides, quad means four, and laterals mean sides, therefore, quadrilateral has four sides. The name of the four sides of the PQRS are: PQ, QR, RS, and SP are the four sides of the quadrilateral.

What are the 5 ways to prove a quadrilateral is a parallelogram?

There are five ways to prove that a quadrilateral is a parallelogram:

• Prove that both pairs of opposite sides are congruent.
• Prove that both pairs of opposite sides are parallel.
• Prove that one pair of opposite sides is both congruent and parallel.
• Prove that the diagonals of the quadrilateral bisect each other.

What do you need to prove a shape is a parallelogram?

Well, we must show one of the six basic properties of parallelograms to be true!

1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are congruent.
4. Diagonals bisect each other.
5. One angle is supplementary to both consecutive angles (same-side interior)

What kind of quadrilateral PQRS if PQ is parallel to RS and ∠ P ∠ R?

In the above figure (ii), ∠PSR is greater than 180°. Parallelogram: A quadrilateral whose opposite sides are parallel, is called a parallelogram. In the given figure PQRS is a parallelogram in which PQ ∥ SR and PS ∥ QR. Rectangle: A parallelogram is called a rectangle if one of its angle is a right angle.

How do you prove adjacent angles are supplementary?

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°. Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.

Which geometrical shape is generated by Pqrs *?

i.e. One pair of opposite sides in quadrilateral PARS is equal and parallel. ∴ PQRS is a parallelogram.

How do you prove PQRS is a rectangle?

Since ∠SPQ and ∠PQR are interior angles on the same side of the transversal PQ, they form a pair of supplementary angles. Clearly, PQRS is a parallelogram having one of its interior angles as 90°. Hence, PQRS is a rectangle.

What is the Cpct rule?

What is CPCT? CPCT stands for Corresponding parts of congruent triangles are congruent is a statement on congruent trigonometry. It states that if two or more triangles are congruent, then all of their corresponding angles and sides are as well congruent.

Which maths book is best for class 9?

Best reference books for class 9 Board Exams

Which geometrical shape is generated by PQRS?

What is the opposite angle of PQRS?

Pairs of opposite angles: ∠QPS,∠SRQ and ∠PSR,∠RQP.

What are the 4 properties of a parallelogram?

Properties of parallelograms

• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

How do you identify a parallelogram?

To identify a parallelogram, the shape has to meet one of the following criteria:

1. It has two pairs of parallel opposite sides.
2. It has two pairs of equal opposite angles.
3. It has two pairs of equal and parallel opposite sides.
4. Its diagonals bisect each other.

What are the properties of a parallelogram?

Convex polygonParallelogram / Properties

How do you know if the figure is a parallelogram or not?

There are six important properties of parallelograms to know:

• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

How many pairs of consecutive sides has quadrilateral PQRS?

The name of the four sides of the PQRS are: PQ, QR, RS, and SP are the four sides of the quadrilateral.

Can two adjacent angles be supplementary give reason?

Yes, adjacent angles can be supplementary if they sum up to 180°. Adjacent angles can be defined as two angles that have a common vertex and a common side. Any two adjacent angles can be complementary angles or supplementary angles according to the sum of the measurement of angles.

Is Pqrs a square justify your answer?

P, Q, R and S are the mid-points of AB, BC, CD, and DA respectively. It can be observed that all sides of the given quadrilateral are of the same measure. However, the diagonals are of different lengths. Therefore, PQRS is a rhombus.