Question

Draw a quadrilateral PQRS in which PQ = 7 cm, QR = 4 cm, SR = 3 cm, PS = 6 cmand PR = 5 cm. What type of quadrilateral is it?​

Answer 1

Answer:

Step-by-step explanation:

PQ=4cm

QR=6cm

RS=5cm

PS=5.5cm

PR=7cm

Firstly, we will draw a rough sketch ,

PR is diagonal

Now Steps for Construction:

Step 1: Draw a line PR as diagonal (PR = 7cm)

Step 2: Draw an arc 4cm top of the PR and  P as center.

Step 3: Taking 6cm and mark arc top of the PR named Q.

Step 4: Draw an arc 5.5 cm bottom of the PR and  P as center.

Step 5: Taking 5cm and mark arc below of the PR named S.

∴ PQRS is required quadrilateral.

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Answer 2

Answer:

PQRS is a square.

Step-by-step explanation:

To draw the quadrilateral PQRS, we can observe these steps:

1. Draw a line phase PQ of size 7 cm.
2. Draw any other line section PR of size 5 cm that meets PQ at factor P and is no longer parallel to PQ.
3. From factor R, draw a line section QR of size four cm that meets PR at factor P and is now not parallel to PR.
4. From factor R, draw a line section SR of size three cm that meets PQ at factor S and is now not parallel to PQ.

To decide what kind of quadrilateral PQRS is, we can use the following houses of quadrilaterals:

1. A quadrilateral is a parallelogram if contrary aspects are parallel.
2. A quadrilateral is a trapezoid if precisely one pair of contrary facets is parallel.
3. A quadrilateral is a kite if two pairs of adjoining aspects are congruent.
4. A quadrilateral is a rhombus if all 4 aspects are congruent.
5. A quadrilateral is a rectangle if all 4 angles are proper angles.
6. A quadrilateral is a rectangular if it is each a rhombus and a rectangle.

In PQRS, we can see that contrary aspects PQ and SR are no longer parallel, so PQRS is now not a parallelogram. Similarly, contrary facets QR and PS are no longer parallel, so PQRS is no longer a parallelogram or a trapezoid.

Finally, considering all 4 facets of a rectangle are congruent, PQRS is additionally a square. Therefore, PQRS is a square.

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