# Constructing Quadrilaterals

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Construction of quadrilaterals can be categorized by the length of its sides and the size of its angles.

The quadrilateral family includes

__squares, rectangles, rhombuses, parallelograms, trapezoid( trapezium), kites and other less regular shapes__.

Constructing quadrilaterals can be done through 4 ways.

**1) When 4 sides and one diagonal are given.**

Construct the quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.5 cm, AD= 5 cm and AC = 8 cm.

The given quadrilateral ABCD can be drawn as follows:

**Step 1:**Draw a line segment AC of 8 cm

**Step 2:**With 4 cm as radius from A draw an arc.

**Step 3:**With 6 cm as radius cut the arc drawn in step 2. Let that point of intersection be B. Join AB and CB.

**Step 4:**With 5 cm as radius from A draw an arc to the opposite side of AC.

**Step 5:**From C take 5.5 cm as radius and cut the arc drawn in step 4. Let the point of intersection be D. Join AD and CD.

ABCD is the required quadrilateral.

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**2) When 3 sides and two diagonals are given**

Construct the quadrilateral PQRS in which PQ = 4 cm, QR = 3 cm, PS = 2.5 cm, PR = 4.5 cm and QS = 4 cm.

**Step 1:**Draw a line segment PQ = 4 cm.

**Step 2:**With 4.5 cm from P draw an arc.

**Step 3:**From Q take radius 3 cm and cut the arc drawn in step 2. Let the point of intersection be R.

**Step 4:**Take 2.5 cm from P and draw an arc.

**Step 5:**Take 4 cm from Q and cut the arc drawn in step 4. Let the point of intersection of arcs be S.

**Step 6:**Join SR

PQRS is the required quadrilateral.

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**3) Constructing quadrilateral when its 4 sides and one angle are given.**

Construct a trapezoid ABCD in which AB || CD, AB = 8 cm, BC = 6.0 cm and CD = 4 cm and ∠B = 60°.

In a trapezoid, ABCD, AB || DC.

∴ ∠B + ∠C = 180°

or, 60° + ∠C = 180°

or, ∠C = 180° - 60° = 120°

**Steps of construction:**

**Step 1 :**Draw AB = 8cm.

**Step 2 :**At B, draw ∠ABX = 60°.

**Step 3 :**From ray BX, cut off BC = 6 cm.

**Step 4 :**At C, draw ∠BCY = 120°

**Step 5 :**From ray CY, cut off CD = 4 cm.

**Step 6 :**Join D to A.

**Step 7 :**ABCD is the required trapezoid.

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**4) When 3 sides and their included angles are given**

Construct the quadrilateral TRUE in which TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75° and ∠U =120°.

**Step 1:**Draw a line segment RU of 3 cm and an angle of 120º at point U. As vertex E is 4 cm away from vertex U, cut a line segment UE of 4 cm from this ray.

**Step 2:**Draw an angle of 75º at point R. As vertex T is 3.5 cm away from vertex R, cut a line segment RT of 3.5 cm from this ray.

**Step 3:**Join T to E.

TRUE is the required quadrilateral.

**Geometrical Constructions**

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

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