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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