Constructing Triangles, SAS

To satisfy the condition for SAS, two sides and enclosed angle must be given (or known) to us. The construction is not possible when any other angle is provided.

Requirements: For the construction of triangle using SAS criteria we require a Ruler and a Compass.

Let us say, in a triangle ABC, the lengths of the sides are AB = 4 cm, AC = 7 cm and ∠CAB = 60 degrees. The steps for its construction are:

  • Step 1: Draw a straight line and mark its left endpoint as A.
  • Step 2: Set the compass to a width of 4 cm.
  • Step 3: Place the pointer head of the compass at A and cut an arc on the line.
  • Step 4: Mark the point as B where the arc crosses the line.

Constructing Triangles

  • Step 5: Construct a 60 degree angle with line AB at the point A.

Constructing Triangles

  • Step 6: Set the compass to a width of 7 cm.
  • Step 7: Place the pointer head of the compass at A and cut an arc on the 60 degree line.
  • Step 8: Mark the point as C where the arc crosses the line.

Constructing Triangles

  • Step 9: Join the points B and C using a ruler.

Constructing Triangles

Thus, you obtained a triangle ABC of the required measurements.

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Practise This Question

Goutham has been asked to draw a triangle with three lengths given to him. He hasn't checked the given lengths and promised that he will draw the triangle thinking that a triangle can always be constructed with any three lengths. Is it true that a triangle can always be constructed with any three lengths?