# Three Sides and Two Diagonals

Construct a quadrilateral ABCD, given that = 5cm = 7cm = 4cm and diagonal = 9cm and diagonal = 6cm

Steps :

(a)** **

(b) With A and B as centres and 4cm and 6cm as radii respectively, draw arcs to cut each other at D.

(c) Join AD and BD. With A and B as centres and 9cm and 7cms as radii respectively, draw arcs to cut each other at C.

(d) Join AC and BC. Join also DC. ABCD is the required quadrilateral.

Construction

Constructing Î”BCD |

Constructing Î”ADC |

To construct a quadrilateral given three sides and two diagonals (SSSDD case)

Let the sides be AD = 4.2 cm, DC = 6.5 cm, CB = 5.8 cm, and the diagonals be CA = 6.9 cm, BD = 7.2 cm.

The two triangles we can construct to complete the quadrilateral are DBCD and DACD.

Constructing DBCD

1. Draw DC = 6.5 cm.

2. With D as centre and radius 7.2 cm, draw an arc.

3. With C as centre and radius 5.8 cm, draw another arc, to cut the previous arc at B.

4. Join CB and DB.

Constructing DACD

5. With C as centre and radius 6.9 cm, draw an arc on the same side of DC.

6. With D as centre and 4.2 cm radius, draw another arc to cut the previous arc at A.

7. Join CA and DA.

8. Join AB.

Then ABCD is the required quadrilateral, with diagonals AC and BD.