Constructing Triangles, ASA

For the ASA criterion to be satisfied, the given side must necessarily be the one that is enclosed by the known angles. The criterion does not hold if any of the other sides’ measurements is provided.

Now coming back to constructing triangles with the ASA criterion, you will require a ruler and a protractor. Let us say, in a triangle ABC, the measures of the angles are ∠CAB = 45 degrees and ∠ABC = 60 degrees. The length of side AB = 3cm. The steps for its construction are as follows:

  • Step 1: Using the ruler, construct a line segment AB of length 3 cm.

Triangle Construction

  • Step 2: Using the protractor, draw a ray at point B making 60 degrees with the line BA.

Triangle Construction

  • Step 3: Similarly, draw a ray at point A making 45 degrees with the line AB using the protractor.

Triangle Construction

  • Step 4: Mark the point where the two rays meet as C.

Triangle Construction

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

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Practise This Question

Raman had to draw an isosceles triangle with base angles measuring 65 each and base length of 5cm. Raman said the given data is insufficient. Is he correct?