# SAS Triangle Construction

In SAS Triangle construction we need length of two sides and the angle. But the angle should lie between the two sides.**SAS Δ Construction**

**Construct a ΔABC, in which ∠B = 70**

^{0}, AB = 4.8 cm and BC = 5.2 cm.Before doing construction, draw a rough sketch, so that you will get an idea which side is taken as a base.Here after drawing a rough sketch, we are sure that the base is AB = 4.8 cm.

Step 1 : Draw AB = 4.8 cm.

Step 2 : Using protractor, draw ∠ABK = 70

^{0}.

Step 3 : On the line segment BK, cut off BC = 5.2 cm.

Step 4 : Join A and C.

ΔABC is the required triangle.

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**Construct an isosceles triangle PQR such that PQ = PR = 5cm and P = 110**

^{0}.Before doing construction, draw a rough sketch, so that you will get an idea which side is taken as a base.Here after drawing a rough sketch, we are sure that the base is AB = 4.8 cm.

Step 1 : Draw PR = 5 cm.

Step 2 : Using protractor, draw ∠QPM = 110

^{0}.

Step 3 : On the line segment PM, cut off PQ = 5 cm.

Step 4 : Join Q and R.

ΔPQR is the required triangle.

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**Practice Problems**

1) In a triangle ABC if AB = 3 cm , AC = 5 cm and ∠B = 30°. Can we draw this triangle uniquely ?

2) Can we Construct ΔABC such that AB = AC = 5cm and ∠A = 60°?

3) Construct a ABC, in which ∠B = 70, AB = 4.8 cm and BC = 5.2 cm.

4) Construct a PQR, in which ∠Q = 135, PQ = 5.2 cm and QR = 6 cm .

5) In a triangle ABC if AB = 3 cm , AC = 5 cm and ∠B = 30°. Can we draw this triangle uniquely ?

**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)