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.
- Step 5: Construct a 60 degree angle with line AB at the point A.
- 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.
- Step 9: Join the points B and C using a ruler.
Thus, you obtained a triangle ABC of the required measurements.
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