Question

PQRS is a quadrilateral where A,B,C and D are the midpoints of the sides PQ,RS,QR and SP. PR is the diagonal. Show that
i)DC||PR and DC=1/2 PR
ii)DC=AB
​

Answer 1

Answer:

The angles of quadrilateral are in the ratio 3 : 5 : 9 : quadrilateral.

Sol: Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.

∵ Sum of all the angles of quadrilateral = 360°

∴ 3x + 5x + 9x + 13x = 360°

⇒ 30x = 360°

∴ 3x = 3 × 12° = 36°

5x = 5 × 12°= 60°

9x = 9 × 12° = 108°

13x = 13 × 12° = 156°

⇒ The required angles of the quadrilateral are 36°, 60°, 108° and 156°.

Answer 2

Answer:

HOPE IT HELPS

The angles of quadrilateral are in the ratio 3 : 5 : 9 : quadrilateral.

Sol: Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.

∵ Sum of all the angles of quadrilateral = 360°

∴ 3x + 5x + 9x + 13x = 360°

⇒ 30x = 360°

∴ 3x = 3 × 12° = 36°

5x = 5 × 12°= 60°

9x = 9 × 12° = 108°

13x = 13 × 12° = 156°

⇒ The required angles of the quadrilateral are 36°, 60°, 108° and 156°.

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