Construction of Quadrilateral when length of three sides and two diagonals are given
Construction of Quadrilateral when length of three sides and two diagonals are given
Construction of Quadrilateral when length of three sides and two diagonal are given: To construct a quadrilateral when three sides and two diagonals are given we will follow the following steps:
| Step 1: Draw aline segment equal to the length of one diagonal let us suppose AC |  |
| Step 2: With A as centre and radius equal to length given for AD draw an arc on one side of the AC. |  |
| Step 3: With C as centre and radius equal to length given for CD draw an arc intersecting an arc in step 2. Mark the point of intersection as D. |  |
| Step 4: With A as centre and radius equal to length given for AB draw an arc on the other side of the AC |  |
| Step 5: With D as centre and radius equal to length given for the other diagonal BD draw an arc intersecting an arc in step 4. Mark the point of intersection as B. |  |
| Step 6: Join AD, CD, AB and BC. ABCD is the required quadrilateral |  |
Illustration: Construct a quadrilateral ABCD in which AB = 5.5 cm, AD = 4.4 cm, CD = 6.5 cm, and BD = 7.1 cm.
Solution First we draw a rough sketch of quadrilateral ABCD.
Now, we follow the following steps to construct the required quadrilateral.
Steps of Construction:
Step 1: Draw AC = 6.5 cm.
Step 2: With A as centre and radius AD = 4.4 cm, draw an arc.
Step 3: With C as centre and radius CD = 6.5 cm, draw an arc to intersect the arc drawn in step 2 at and mark the point of intersection as D.
Step 4: With A as centre and radius AB = 5.5 cm, draw an arc on the side of AC opposite to that of D.
Step 5: With D as centre and radius BD = 7.1 cm, draw another arc to intersect the arc drawn in step 4 and mark the point of intersection as B.
Step 6: Join AD, CD, AB and CB to obtain the required quadrilateral.ABCD
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