Question

what do we require to constract a quadrilateral if measures of three angles are given​

Answer 1

Five measurements can determine a quadrilateral uniquely. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given. A quadrilateral can be constructed uniquely if the lengths of its three sides and two diagonals are given

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Answer 2

Step-by-step explanation:

. Construction of quadrilaterals when three sides and two diagonals are given:

2. Construct a quadrilateral ABCD in which AB = 4 cm BC = 3.8 cm, AD = 3 cm, diagonal AC = 5 cm and diagonal BD = 4.6 cm.

Construction of Quadrilaterals

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Solution:

First we draw a rough sketch of quadrilateral ABCD and write down its dimensions, as shown.

We may divide it into two triangles, namely ∆ABC and ∆ABD. (Rough Sketch) →

Steps of Construction:

Steps of Construction of Quadrilaterals

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Step 1: Draw AB = 4 cm.

Step 2: With A as center and radius equal to 5 cm, draw an arc.

Step 3: With B as center and radius equal to 3.8 cm, draw another arc, cutting the previous arc at C.

Step 4: Join BC.

Step 5: With A as center and radius equal to 3 cm, draw an arc.

Step 6: With B as center and radius equal to 4.6 cm draw another arc, cutting the previous arc at D.

Step 7: Join AD and CD.

Then, ABCD is the required quadrilateral.

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