The quadrilateral obtained by joining the mid-points (in order) of the sides of quadrilateral ABCD is : 1. rectangle 2. rhombus 3. parallelogram 4. square

Let ABCD be the quadrilateral. P, Q, R and S are the mid-points of sides AB, BC, CD and DA. Join PQRS, AC and BD. By mid-point theorem, The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. In △ ABC, P and Q are mid-points of sides AB and BC respectively. ∴ PQ || AC and PQ = (By mid-point theorem) .......(1) In △ ADC, S and R are mid-points of sides AD and DC respectively. ∴ SR || AC and SR = (By mid-point theorem) ........(2) From equations (1) and (2), we get : ⇒ PQ = SR and PQ || SR. In △ ABD, P and S are mid-points of sides AB and AD respectively. ∴ SP || BD and SP = (By mid-point theorem) .......(3) In △ CBD, Q and R are mid-points of sides BC and DC respectively. ∴ QR || BD and QR = (By mid-point theorem) ........(4) From equations (3) and (4), we get : ⇒ SP = QR and SP || QR. Since, opposite sides are parallel and equal. ∴ PQRS is a parallelogram. Hence, Option 3 is the correct option.

In the given figure, ABCD is a rectangle. As per the given information, the length of PQ is :
12 cm
14 cm
20 cm
10 cm

View Answer Bookmark Now

If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, the perimeter of quadrilateral BCYX is :
31.8 cm
15.9 cm
29.8 cm
32.8 cm

View Answer Bookmark Now

In the given figure, AB = AC, P, Q and R are mid-points of sides BC, CA and AB respectively, then △ PQR is :
scalene
isosceles
equilateral
obtuse angled

View Answer Bookmark Now

P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively of rectangle ABCD, then quadrilateral PQRS is :
rectangle
rhombus
square
parallelogram

View Answer Bookmark Now

Mathematics

The quadrilateral obtained by joining the mid-points (in order) of the sides of quadrilateral ABCD is :
rectangle
rhombus
parallelogram
square

Mid-point Theorem

Related Questions

In the given figure, ABCD is a rectangle. As per the given information, the length of PQ is :
12 cm
14 cm
20 cm
10 cm

If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, the perimeter of quadrilateral BCYX is :
31.8 cm
15.9 cm
29.8 cm
32.8 cm

In the given figure, AB = AC, P, Q and R are mid-points of sides BC, CA and AB respectively, then △ PQR is :
scalene
isosceles
equilateral
obtuse angled

P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively of rectangle ABCD, then quadrilateral PQRS is :
rectangle
rhombus
square
parallelogram

Mathematics

The quadrilateral obtained by joining the mid-points (in order) of the sides of quadrilateral ABCD is :rectanglerhombusparallelogramsquare

Mid-point Theorem

Related Questions

In the given figure, ABCD is a rectangle. As per the given information, the length of PQ is :12 cm14 cm20 cm10 cm

If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, the perimeter of quadrilateral BCYX is :31.8 cm15.9 cm29.8 cm32.8 cm

In the given figure, AB = AC, P, Q and R are mid-points of sides BC, CA and AB respectively, then △ PQR is :scaleneisoscelesequilateralobtuse angled

P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively of rectangle ABCD, then quadrilateral PQRS is :rectanglerhombussquareparallelogram

The quadrilateral obtained by joining the mid-points (in order) of the sides of quadrilateral ABCD is :
rectangle
rhombus
parallelogram
square

In the given figure, ABCD is a rectangle. As per the given information, the length of PQ is :
12 cm
14 cm
20 cm
10 cm

If BC = 12 cm, AB = 14.8 cm, AC = 12.8 cm, the perimeter of quadrilateral BCYX is :
31.8 cm
15.9 cm
29.8 cm
32.8 cm

In the given figure, AB = AC, P, Q and R are mid-points of sides BC, CA and AB respectively, then △ PQR is :
scalene
isosceles
equilateral
obtuse angled

P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively of rectangle ABCD, then quadrilateral PQRS is :
rectangle
rhombus
square
parallelogram