Construction of a quadrilateral when two diagonals and three sides are given — lesson. Mathematics State Board, Class 8.

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Depending on the sides and diagonal lengths, establish an $ACD$ triangle. Based on $SSS$ construction.

Make an arc at a specified distance of point $C$ (third side), on the front arc. Name the two points intersection as $B$ .

$A$ , $C$ and $D$ join $B$ . This completes both diagonals of the quadrilateral $PQRS$ .

Example:

Construct a

$GOLD$ with quadrilateral measures as follows.

$OL = 7.5 cm$ ,

$GL = 6 cm$ ,

$GD = 6 cm$ ,

$LD = 5 cm$ ,

$OD = 10 cm$ .

Step 1: Draw Side

$GD = 6 cm$ and cut the

$G$ (

$6 cm$ ) and

$D$ (

$5 cm$ ) arcs above it. Mark the intersection as

$L$ .

$GL$ and

$DL$ are joined.

Step 2: Draw and arc from

$L$ equal to

$7.5 cm$ and from

$D$ equal to

$10 cm$ , which is the length of

$OL$ and

$OD$ respectively.

Step 3:Mark the intersection with

$O$ and

$OG$ ,

$OL$ and

$OD$ join.

Thus, the

$GOLD$ is a required quadrilateral.

Did you find an error?

6. Construction of a quadrilateral when two diagonals and three sides are given