﻿ We saw that 5 measurements of a quadrilateral can determine a quadrilateral uniquely. Do you think any five measurements of the quadrilateral can do this? from Mathematics Practical Geometry Class 8 Manipur Board

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A student attempted to draw a quadrilateral PLAY where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm and LY = 6 cm, hut could not draw it. What is the reason?

Let us draw the rough sketch of the quadrilateral PLAY and mark its measurements, No, this quadrilateral cannot be drawn.
∵ Point P cannot be located. In ∆ LPY, sum of the lengths of PL and PY is less than LY, i.e. (2 cm + 3 cm) < 6 cm.

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Can you draw a rhombus ZEAL where ZE = 3.5 cm, diagonal EL = 5 cm? Why?

Let us draw a rough sketch of the (rhombus) quadrilateral ZEAL and mark the given measurements on it. Yes, we can draw the required rhombus, because its all sides are equal to 3.5 cm and a diagonal EL is known.

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# We saw that 5 measurements of a quadrilateral can determine a quadrilateral uniquely. Do you think any five measurements of the quadrilateral can do this?

No, any 5 measurements (elements) cannot determine a quadrilateral. Actually to construct a quadrilateral, we need a specific combination of measurements such as:

(a) Four sides and one diagonal.
or
(b) Three sides and two diagonals.
or
(c) Two adjacent sides and three angles.
or
(d) Three sides and two included angles.
or
(e) Some special properties are given.

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Can you draw a parallelogram BATS where BA = 5 cm, AT = 6 cm and AS = 6.5 cm? Why?

Let us draw a rough sketch of BATS as given.
Here, we cannot locate the points T and B without knowing the measurements ST and SB respectively.
Thus, we cannot draw a parallelogram with the given measurements.

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Arshad has five measurements of a quadrilateral ABCD. These are AB = 5 cm, ∠A = 50°, AC = 4 cm, BD = 5 cm and AD = 6 cm. Can he construct a unique quadrilateral? Give reasons for your answer.

Solution not provided.

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