Special Cases of Construction of Quadrilateral

IMPORTANT

Special Cases of Construction of Quadrilateral: Overview

This topic covers concepts such as Construction of a Quadrilateral when Four Sides and One Angle are Given, Necessary Conditions for Construction of Unique Quadrilateral, Necessary Conditions for Construction of Unique Rhombus, etc.

Important Questions on Special Cases of Construction of Quadrilateral

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A quadrilateral PQRS in which QS=6 cm and PR=8 cm are perpendicular to each other, is a _____. (Kite/Rhombus/Parallelogram)

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AB=6 cm, BC=4.5 cm, AD=5 cm, AC=6 cm and D=100° these five measurements are sufficient to construct a quadrilateral ABCD: _____ (yes/no)

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A _____ cannot be constructed with the data of the three angles alone, the measurements of the two included sides are also required.

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Are these five measurements sufficient to draw a unique quadrilateral ABCD in which AB=6 cm, BC=4.5 cm, AD=5 cm, AC=6 cm and D=100°? (Write answer as Yes or No)

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Steps of construction of a rhombus, whose one side is 4 cm and a diagonal is equal to 6 cm are given below.

Step 1: Mark the points of intersection of arcs above PR as S and below PR as Q.

Step 2: With R as a centre, draw arcs of 4 cm above and below of PR.

Step 3: Draw PR=6 cm.

Step 4: Join PQ, QR, RS and PS.

Step 5: With P as the centre, draw arcs of 4 cm above and below of PR.

Identify the correct order of construction of the Rhombus.

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It is possible to construct a quadrilateral with one side and three angles.

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A quadrilateral ABCD in which AC=6 cm and  BD=4cm are perpendicular to each other is a _____ . (Square/Rhombus/Parallelogram)

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It is possible to construct a square ABCD having AC=6.8 cm.

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If a quadrilateral ABCD has  AC=6.6 cm and the diagonals intersecting at 60° then it is a rectangle.

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Which type of quadrilateral is formed by using following measurements:

A quadrilateral with ABCD having AB=5 cm and AC=6cm.

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 A diagonal of a quadrilateral is a line segment that joins two _____ vertices of the quadrilateral. (Opposite/Adjacent)

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To construct a quadrilateral minimum number of elements required are _____.

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Which type of quadrilateral is obtained by measurements given below:

A quadrilateral CART with CR=6 cm, AT=4.8 cm

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Which type of quadrilateral is obtained by following measurements?

Quadrilateral ABCD in which ABCD, AB=8 cm, BC=6 cm, CD=4 cm and B=60o.

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Can you draw a parallelogram BATS where BA=5 cm, AT=6 cm and AS=6.5 cm? (Yes/No)

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Suppose the two diagonals of a Rhombus are equal in length. Which quadrilateral do you obtain? 

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Can you construct the below quadrilateral (rhombus) by taking BD as a base instead of AC ? (Yes/No)

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Can you construct the below quadrilateral ABCD by taking BC as base instead of AB? (Yes/No)

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Can you construct the quadrilateral PLAN if PL=6 cm, LA=9.5 cm, P=75° , L=15° and A=140° . (yes/no)

HARD
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Can you construct the above quadrilateral PQRS, if we have an angle of 100° at P instead of 75°. [Yes / No]

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